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Instead of focusing solely on the input-output relationships like the transfer function +approach, the state-space approach represents systems as a set of first-order differential +equations. + +The state-space representation of a system can be written as: + + .. math:: + + \dot{x}(t) = A x(t) + B u(t) \\ + y(t) = C x(t) + D u(t) + + +Where :math:`x(t)` is the state vector, :math:`u(t)` is the input vector, :math:`y(t)` is the output vector, +:math:`A`, :math:`B`, :math:`C`, and :math:`D` are matrices that define the system dynamics. + +Below are some examples to demonstrate the use of StateSpace to solve Electrical problems. + +Example 1 +--------- + + .. image:: Electrical_Problems_Q1.svg + :align: center + +In a series RLC circuit, we have a resistor :math:`R`, an inductor :math:`L`, and a capacitor :math:`C` +connected in series with an input voltage :math:`v_{in}(t)`. The state variables are the current through +the inductor :math:`i(t)` and the voltage across the capacitor :math:`v_C(t)`. + +Applying **Kirchhoff's Voltage Law** (KVL) around the loop in the above diagram gives: + + .. math:: + + v_{in}(t) = R \cdot i(t) + L \frac{di(t)}{dt} + V_C(t) + +Where: :math:`v_{in}(t)` is the input voltage, :math:`i(t)` is the current through the inductor and +:math:`v_C(t)` is the voltage across the capacitor. + +This equation relates the input voltage to the elements of the RLC circuit. + +**Capacitor Voltage Equation** + +The voltage across the capacitor can be related to the current by: + + .. math:: + + V_C(t) = \frac{1}{C} \int i(t) \, dt + +Taking the time derivative of both sides, we obtain the rate of change of the capacitor voltage: + + .. math:: + + \dot{v}_C(t) = \frac{d v_C(t)}{dt} = \frac{i(t)}{C} + +This equation shows that the rate of change of the capacitor voltage is proportional to the current through the circuit. + +From the KVL equation, solving for the derivative of the current gives: + + .. math:: + + \frac{di(t)}{dt} = -\frac{R}{L} i(t) - \frac{1}{L} v_C(t) + \frac{1}{L} v_{in}(t) + +This is the first-order differential equation that describes the rate of change of the current in terms of the circuit's components and input voltage. + +The state-space representation expresses the system in terms of state variables, which are typically the variables that describe the energy stored in the circuit elements (such as current and voltage). + +We define the state vector `X(t)` as: + + .. math:: + + X(t) = \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix} = \begin{bmatrix} i(t) \\ v_C(t) \end{bmatrix} + +Here `x_1(t) = i(t)` is the current through the inductor and `x_2(t) = v_C(t)` is the voltage across the capacitor. + +The input vector `U(t)` is the input voltage: + + .. math:: + + U(t) = v_{in}(t) + +The system of differential equations in terms of the state variables becomes: + +1. The derivative of the current: + + .. math:: + + \dot{x}_1(t) = -\frac{R}{L} x_1(t) - \frac{1}{L} x_2(t) + \frac{1}{L} v_{in}(t) + +2. The derivative of the capacitor voltage: + + .. math:: + + \dot{x}_2(t) = \frac{x_1(t)}{C} + + +The matrices for the series RLC circuit are: + + .. math:: + + A = \begin{bmatrix} + -\frac{R}{L} & -\frac{1}{L} \\ + \frac{1}{C} & 0 + \end{bmatrix}, + B = \begin{bmatrix} + \frac{1}{L} \\ + 0 + \end{bmatrix}, + C = \begin{bmatrix} 0 & 1 \end{bmatrix}, + D = \begin{bmatrix} 0 \end{bmatrix} + + +Thus, the state-space representation of the series RLC circuit is: + + .. math:: + + \dot{X}(t) = \begin{bmatrix} + -\frac{R}{L} & -\frac{1}{L} \\ + \frac{1}{C} & 0 + \end{bmatrix} + \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix} + + \begin{bmatrix} + \frac{1}{L} \\ + 0 + \end{bmatrix} V_{in}(t) + + Y(t) = \begin{bmatrix} 0 & 1 \end{bmatrix} + \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix} + + \begin{bmatrix} 0 \end{bmatrix} V_{in}(t) + + +The state-space representation provides a compact way of modeling +the series RLC circuit by using matrices to describe the system's +dynamics. The matrices :math:`A`, :math:`B`, :math:`C`, and :math:`D` +capture the relationships between the circuit's state variables, +input, and output. This representation is particularly useful for +analyzing the system's behavior in the time domain and for designing +control systems. + +Solution + + >>> from sympy import Matrix, symbols, pprint + >>> from sympy.physics.control import * + >>> R, L, C = symbols('R L C') + >>> A = Matrix([[-R/L, -1/L], [1/C, 0]]) + >>> B = Matrix([[1/L], [0]]) + >>> C = Matrix([[0, 1]]) + >>> D = Matrix([[0]]) + >>> ss = StateSpace(A, B, C, D) + >>> ss + StateSpace(Matrix([ + [-R/L, -1/L], + [ 1/C, 0]]), Matrix([ + [1/L], + [ 0]]), Matrix([[0, 1]]), Matrix([[0]])) + + We can convert the StateSpace to TransferFunction by rewrite method. + + >>> tf = ss.rewrite(TransferFunction)[0][0] + >>> tf + TransferFunction(1, C*L*s**2 + C*R*s + 1, s) + + +Example 2 +--------- + + .. image:: Electrical_Problems_Q2.svg + :align: center + +Obtain the state model for a system represented by an electrical +system as shown in figure + +The system is modeled with two state variables, +`x_1(t)` and `x_2(t)`, which are related to the physical voltages at the nodes +`v_1(t)` and `v_2(t)` respectively. + +Let the two state variables be defined as: + + .. math:: + + v_1(t) = x_1(t) + + v_2(t) = x_2(t) + +The governing equations are derived by applying Kirchhoff's Current Law (KCL) at the nodes `v_1(t)` and `v_2(t)`. + +Applying KCL at node `v_1(t)`: + + .. math:: + + \frac{v_1(t) - u(t)}{R} + C \frac{d v_1(t)}{dt} + \frac{v_1(t) - v_2(t)}{R} = 0 + +Substituting the state variables: + + .. math:: + + \frac{x_1(t) - u(t)}{R} + C \frac{dx_1(t)}{dt} + \frac{x_1(t) - x_2(t)}{R} = 0 + +Simplifying: + + .. math:: + + C \dot{x_1}(t) = -\frac{2x_1(t)}{R} + \frac{x_2(t)}{R} + \frac{u(t)}{R} + +Thus, the state equation for `x_1(t)` becomes: + + .. math:: + + \dot{x_1}(t) = -\frac{2x_1(t)}{RC} + \frac{x_2(t)}{RC} + \frac{u(t)}{RC} + + +Applying KCL at node `v_2(t)`: + + .. math:: + + C \frac{d v_2(t)}{dt} + \frac{v_2(t) - v_1(t)}{R} = 0 + +Substituting the state variables: + + .. math:: + + C \frac{d x_2(t)}{dt} + \frac{x_2(t) - x_1(t)}{R} = 0 + +Simplifying: + + .. math:: + + C \dot{x_2}(t) = \frac{x_1(t)}{R} - \frac{x_2(t)}{R} + +Thus, the state equation for `x_2(t)` becomes: + + .. math:: + + \dot{x_2}(t) = \frac{x_1(t)}{RC} - \frac{x_2(t)}{RC} + +The state-space representation is given by the following matrix equation: + + .. math:: + + \begin{bmatrix} + \dot{x_1}(t) \\ + \dot{x_2}(t) + \end{bmatrix} + = + \begin{bmatrix} + -\frac{2}{RC} & \frac{1}{RC} \\ + \frac{1}{RC} & -\frac{1}{RC} + \end{bmatrix} + \begin{bmatrix} + x_1(t) \\ + x_2(t) + \end{bmatrix} + + + \begin{bmatrix} + \frac{1}{RC} \\ + 0 + \end{bmatrix} + u(t) + +The output of the circuit is defined as: + + .. math:: + + y(t) = v_2(t) = x_2(t) + +Thus, the output equation can be written as: + + .. math:: + + y(t) = \begin{bmatrix} 0 & 1 \end{bmatrix} + \begin{bmatrix} + x_1(t) \\ + x_2(t) + \end{bmatrix} + + +Solution + + >>> from sympy import symbols, Matrix + >>> from sympy.physics.control import * + >>> R, C = symbols('R C') + >>> A = Matrix([[-2/(R*C), 1/(R*C)], [1/(R*C), -1/(R*C)]]) + >>> B = Matrix([[1/(R*C)], [0]]) + >>> C = Matrix([[0, 1]]) + >>> ss = StateSpace(A, B, C) + >>> ss + StateSpace(Matrix([ + [-2/(C*R), 1/(C*R)], + [ 1/(C*R), -1/(C*R)]]), Matrix([ + [1/(C*R)], + [ 0]]), Matrix([[0, 1]]), Matrix([[0]])) + + +References +---------- +1. `bmsce.ac.in `_ diff --git a/dev/_sources/tutorials/physics/control/index.rst.txt b/dev/_sources/tutorials/physics/control/index.rst.txt new file mode 100644 index 00000000000..ea0cc82b906 --- /dev/null +++ b/dev/_sources/tutorials/physics/control/index.rst.txt @@ -0,0 +1,27 @@ +.. _control_tutorial: + +============================= +Control Tutorials +============================= + +The control module in SymPy provides essential tools for symbolic control system +analysis. The TransferFunction class allows for creating transfer functions and +analyzing their properties, such as stability is_stable(), poles, and zeros. +Series, Parallel, and Feedback classes enable constructing and simplifying +system interconnections. The TransferFunctionMatrix handles multi-input, multi-output +(MIMO) systems, while MIMOSeries, MIMOParallel, and MIMOFeedback extend these +functionalities for complex systems. + +Additionally, the module includes the StateSpace class, which allows for modeling +control systems using state variables, inputs, and outputs in matrix form. This +representation is particularly useful for time-domain analysis and handling complex +MIMO systems. + +This tutorial contains a breif guide on how to solve Control Problems using +`TransferFunction` and `StateSpace`. + +.. toctree:: + :maxdepth: 1 + + control_problems.rst + electrical_problems.rst diff --git a/dev/_sources/tutorials/physics/index.rst.txt b/dev/_sources/tutorials/physics/index.rst.txt index 91621828f13..d0c1ffe7b35 100644 --- a/dev/_sources/tutorials/physics/index.rst.txt +++ b/dev/_sources/tutorials/physics/index.rst.txt @@ -23,3 +23,4 @@ write to our `mailing list biomechanics/index.rst mechanics/index.rst + control/index.rst diff --git a/dev/citing.html b/dev/citing.html index 8fd905651f4..89b53e19eb6 100644 --- a/dev/citing.html +++ b/dev/citing.html @@ -329,18 +329,20 @@
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        • @@ -803,7 +805,7 @@
        Documentation Version

        A module which implements predicates and assumption context.

        -class sympy.assumptions.assume.AppliedPredicate(predicate, *args)[source]
        +class sympy.assumptions.assume.AppliedPredicate(predicate, *args)[source]

        The class of expressions resulting from applying Predicate to the arguments. AppliedPredicate merely wraps its argument and remain unevaluated. To evaluate it, use the ask() function.

        @@ -858,7 +860,7 @@
        Documentation Version
        -class sympy.assumptions.assume.AssumptionsContext[source]
        +class sympy.assumptions.assume.AssumptionsContext[source]

        Set containing default assumptions which are applied to the ask() function.

        Explanation

        @@ -903,7 +905,7 @@
        Documentation Version
        -add(*assumptions)[source]
        +add(*assumptions)[source]

        Add assumptions.

        @@ -911,7 +913,7 @@
        Documentation Version
        -class sympy.assumptions.assume.Predicate(*args, **kwargs)[source]
        +class sympy.assumptions.assume.Predicate(*args, **kwargs)[source]

        Base class for mathematical predicates. It also serves as a constructor for undefined predicate objects.

        Explanation

        @@ -983,7 +985,7 @@
        Documentation Version
        -eval(args, assumptions=True)[source]
        +eval(args, assumptions=True)[source]

        Evaluate self(*args) under the given assumptions.

        This uses only direct resolution methods, not logical inference.

        @@ -995,13 +997,13 @@
        Documentation Version
        -classmethod register(*types, **kwargs)[source]
        +classmethod register(*types, **kwargs)[source]

        Register the signature to the handler.

        -classmethod register_many(*types, **kwargs)[source]
        +classmethod register_many(*types, **kwargs)[source]

        Register multiple signatures to same handler.

        @@ -1009,7 +1011,7 @@
        Documentation Version
        -class sympy.assumptions.assume.UndefinedPredicate(name, handlers=None)[source]
        +class sympy.assumptions.assume.UndefinedPredicate(name, handlers=None)[source]

        Predicate without handler.

        Explanation

        This predicate is generated by using Predicate directly for @@ -1028,7 +1030,7 @@

        Documentation Version
        -sympy.assumptions.assume.assuming(*assumptions)[source]
        +sympy.assumptions.assume.assuming(*assumptions)[source]

        Context manager for assumptions.

        Examples

        >>> from sympy import assuming, Q, ask
diff --git a/dev/modules/assumptions/index.html b/dev/modules/assumptions/index.html
index c5bd15290bc..a6de8cca1aa 100644
--- a/dev/modules/assumptions/index.html
+++ b/dev/modules/assumptions/index.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
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        • @@ -802,7 +804,7 @@
        Documentation Version

        Refine

        -sympy.assumptions.refine.refine(expr, assumptions=True)[source]
        +sympy.assumptions.refine.refine(expr, assumptions=True)[source]

        Simplify an expression using assumptions.

        Explanation

        Unlike simplify() which performs structural simplification @@ -840,7 +842,7 @@

        Documentation Version
        -sympy.assumptions.refine.refine_Pow(expr, assumptions)[source]
        +sympy.assumptions.refine.refine_Pow(expr, assumptions)[source]

        Handler for instances of Pow.

        Examples

        >>> from sympy import Q
@@ -868,7 +870,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.assumptions.refine.refine_abs(expr, assumptions)[source]
        
+sympy.assumptions.refine.refine_abs(expr, assumptions)[source]
 
        Handler for the absolute value.
        
 
        Examples
        
 
        >>> from sympy import Q, Abs
@@ -885,7 +887,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.assumptions.refine.refine_arg(expr, assumptions)[source]
        
+sympy.assumptions.refine.refine_arg(expr, assumptions)[source]
 
        Handler for complex argument
        
 
        Explanation
        
 
        >>> from sympy.assumptions.refine import refine_arg
@@ -901,7 +903,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.assumptions.refine.refine_atan2(expr, assumptions)[source]
        
+sympy.assumptions.refine.refine_atan2(expr, assumptions)[source]
 
        Handler for the atan2 function.
        
 
        Examples
        
 
        >>> from sympy import Q, atan2
@@ -927,7 +929,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.assumptions.refine.refine_im(expr, assumptions)[source]
        
+sympy.assumptions.refine.refine_im(expr, assumptions)[source]
 
        Handler for imaginary part.
        
 
        Explanation
        
 
        >>> from sympy.assumptions.refine import refine_im
@@ -943,7 +945,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.assumptions.refine.refine_matrixelement(expr, assumptions)[source]
        
+sympy.assumptions.refine.refine_matrixelement(expr, assumptions)[source]
 
        Handler for symmetric part.
        
 
        Examples
        
 
        >>> from sympy.assumptions.refine import refine_matrixelement
@@ -959,7 +961,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.assumptions.refine.refine_re(expr, assumptions)[source]
        
+sympy.assumptions.refine.refine_re(expr, assumptions)[source]
 
        Handler for real part.
        
 
        Examples
        
 
        >>> from sympy.assumptions.refine import refine_re
@@ -975,7 +977,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.assumptions.refine.refine_sign(expr, assumptions)[source]
        
+sympy.assumptions.refine.refine_sign(expr, assumptions)[source]
 
        Handler for sign.
        
 
        Examples
        
 
        >>> from sympy.assumptions.refine import refine_sign
diff --git a/dev/modules/calculus/index.html b/dev/modules/calculus/index.html
index 858db33572b..de76646de0c 100644
--- a/dev/modules/calculus/index.html
+++ b/dev/modules/calculus/index.html
@@ -329,18 +329,20 @@
 
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        • @@ -805,7 +807,7 @@
        Documentation Version
        Euler-Lagrange Equations for given Lagrangian.

        -sympy.calculus.euler.euler_equations(L, funcs=(), vars=())[source]
        +sympy.calculus.euler.euler_equations(L, funcs=(), vars=())[source]

        Find the Euler-Lagrange equations [R31] for a given Lagrangian.

        Parameters:
        @@ -891,7 +893,7 @@
        Documentation Version
        symbol=None,
        -)[source] +)[source]

        Return whether the function is decreasing in the given interval.

        Parameters:
        @@ -949,7 +951,7 @@
        Documentation Version
        symbol=None,
        -)[source] +)[source]

        Return whether the function is increasing in the given interval.

        Parameters:
        @@ -1003,7 +1005,7 @@
        Documentation Version
        symbol=None,
        -)[source] +)[source]

        Return whether the function is monotonic in the given interval.

        Parameters:
        @@ -1065,7 +1067,7 @@
        Documentation Version
        symbol=None,
        -)[source] +)[source]

        Return whether the function is strictly decreasing in the given interval.

        Parameters:
        @@ -1119,7 +1121,7 @@
        Documentation Version
        symbol=None,
        -)[source] +)[source]

        Return whether the function is strictly increasing in the given interval.

        Parameters:
        @@ -1174,7 +1176,7 @@
        Documentation Version
        symbol=None,
        -)[source] +)[source]

        Helper function for functions checking function monotonicity.

        Parameters:
        @@ -1213,7 +1215,7 @@
        Documentation Version
        -sympy.calculus.singularities.singularities(expression, symbol, domain=None)[source]
        +sympy.calculus.singularities.singularities(expression, symbol, domain=None)[source]

        Find singularities of a given function.

        Parameters:
        @@ -1300,7 +1302,7 @@
        Documentation Version
        -sympy.calculus.finite_diff.apply_finite_diff(order, x_list, y_list, x0=0)[source]
        +sympy.calculus.finite_diff.apply_finite_diff(order, x_list, y_list, x0=0)[source]

        Calculates the finite difference approximation of the derivative of requested order at x0 from points provided in x_list and y_list.

        @@ -1380,7 +1382,7 @@
        Documentation Version
        evaluate=False,
        -)[source] +)[source]

        Differentiate expr and replace Derivatives with finite differences.

        Parameters:
        @@ -1432,7 +1434,7 @@
        Documentation Version
        -sympy.calculus.finite_diff.finite_diff_weights(order, x_list, x0=1)[source]
        +sympy.calculus.finite_diff.finite_diff_weights(order, x_list, x0=1)[source]

        Calculates the finite difference weights for an arbitrarily spaced one-dimensional grid (x_list) for derivatives at x0 of order 0, 1, …, up to order using a recursive formula. Order of accuracy @@ -1570,7 +1572,7 @@

        Documentation Version
        -sympy.calculus.util.continuous_domain(f, symbol, domain)[source]
        +sympy.calculus.util.continuous_domain(f, symbol, domain)[source]

        Returns the domain on which the function expression f is continuous.

        This function is limited by the ability to determine the various singularities and discontinuities of the given function. @@ -1623,7 +1625,7 @@

        Documentation Version
        -sympy.calculus.util.function_range(f, symbol, domain)[source]
        +sympy.calculus.util.function_range(f, symbol, domain)[source]

        Finds the range of a function in a given domain. This method is limited by the ability to determine the singularities and determine limits.

        @@ -1680,7 +1682,7 @@
        Documentation Version
        -sympy.calculus.util.is_convex(f, *syms, domain=Reals)[source]
        +sympy.calculus.util.is_convex(f, *syms, domain=Reals)[source]

        Determines the convexity of the function passed in the argument.

        Parameters:
        @@ -1757,7 +1759,7 @@
        Documentation Version
        -sympy.calculus.util.lcim(numbers)[source]
        +sympy.calculus.util.lcim(numbers)[source]

        Returns the least common integral multiple of a list of numbers.

        The numbers can be rational or irrational or a mixture of both. \(None\) is returned for incommensurable numbers.

        @@ -1789,7 +1791,7 @@
        Documentation Version
        -sympy.calculus.util.maximum(f, symbol, domain=Reals)[source]
        +sympy.calculus.util.maximum(f, symbol, domain=Reals)[source]

        Returns the maximum value of a function in the given domain.

        Parameters:
        @@ -1836,7 +1838,7 @@
        Documentation Version
        -sympy.calculus.util.minimum(f, symbol, domain=Reals)[source]
        +sympy.calculus.util.minimum(f, symbol, domain=Reals)[source]

        Returns the minimum value of a function in the given domain.

        Parameters:
        @@ -1883,7 +1885,7 @@
        Documentation Version
        -sympy.calculus.util.not_empty_in(finset_intersection, *syms)[source]
        +sympy.calculus.util.not_empty_in(finset_intersection, *syms)[source]

        Finds the domain of the functions in finset_intersection in which the finite_set is not-empty.

        @@ -1930,7 +1932,7 @@
        Documentation Version
        -sympy.calculus.util.periodicity(f, symbol, check=False)[source]
        +sympy.calculus.util.periodicity(f, symbol, check=False)[source]

        Tests the given function for periodicity in the given symbol.

        Parameters:
        @@ -1990,7 +1992,7 @@
        Documentation Version
        -sympy.calculus.util.stationary_points(f, symbol, domain=Reals)[source]
        +sympy.calculus.util.stationary_points(f, symbol, domain=Reals)[source]

        Returns the stationary points of a function (where derivative of the function is 0) in the given domain.

        diff --git a/dev/modules/categories.html b/dev/modules/categories.html index 2798dc36400..81a22d6c515 100644 --- a/dev/modules/categories.html +++ b/dev/modules/categories.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
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  • How-to Guides
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      +
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      +
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      +
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  • How-to Guides
    • Assumptions
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    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Gray Code

        -class sympy.combinatorics.graycode.GrayCode(n, *args, **kw_args)[source]
        +class sympy.combinatorics.graycode.GrayCode(n, *args, **kw_args)[source]

        A Gray code is essentially a Hamiltonian walk on a n-dimensional cube with edge length of one. The vertices of the cube are represented by vectors @@ -856,7 +858,7 @@

        Documentation Version
        -generate_gray(**hints)[source]
        +generate_gray(**hints)[source]

        Generates the sequence of bit vectors of a Gray Code.

        Examples

        >>> from sympy.combinatorics import GrayCode
@@ -898,7 +900,7 @@ 
        Documentation Version
        
 
 
        
 
        
-next(delta=1)[source]
        
+next(delta=1)[source]
 
        Returns the Gray code a distance delta (default = 1) from the
 current value in canonical order.
        
 
        Examples
        
@@ -961,7 +963,7 @@ 
        Documentation Version
        
 
 
        
 
        
-skip()[source]
        
+skip()[source]
 
        Skips the bit generation.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import GrayCode
@@ -988,7 +990,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod unrank(n, rank)[source]
        
+classmethod unrank(n, rank)[source]
 
        Unranks an n-bit sized Gray code of rank k. This method exists
 so that a derivative GrayCode class can define its own code of
 a given rank.
        
@@ -1012,7 +1014,7 @@ 
        Documentation Version
        
 
 
        
 
        
-graycode.random_bitstring()[source]
        
+graycode.random_bitstring()[source]
 
        Generates a random bitlist of length n.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.graycode import random_bitstring
@@ -1024,7 +1026,7 @@ 
        Documentation Version
        
 
 
        
 
        
-graycode.gray_to_bin()[source]
        
+graycode.gray_to_bin()[source]
 
        Convert from Gray coding to binary coding.
        
 
        We assume big endian encoding.
        
 
        Examples
        
@@ -1041,7 +1043,7 @@ 
        Documentation Version
        
 
 
        
 
        
-graycode.bin_to_gray()[source]
        
+graycode.bin_to_gray()[source]
 
        Convert from binary coding to gray coding.
        
 
        We assume big endian encoding.
        
 
        Examples
        
@@ -1058,7 +1060,7 @@ 
        Documentation Version
        
 
 
        
 
        
-graycode.get_subset_from_bitstring(bitstring)[source]
        
+graycode.get_subset_from_bitstring(bitstring)[source]
 
        Gets the subset defined by the bitstring.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.graycode import get_subset_from_bitstring
@@ -1076,7 +1078,7 @@ 
        Documentation Version
        
 
 
        
 
        
-graycode.graycode_subsets()[source]
        
+graycode.graycode_subsets()[source]
 
        Generates the subsets as enumerated by a Gray code.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.graycode import graycode_subsets
diff --git a/dev/modules/combinatorics/group_constructs.html b/dev/modules/combinatorics/group_constructs.html
index 951e7e2e5fd..3e4c55976d5 100644
--- a/dev/modules/combinatorics/group_constructs.html
+++ b/dev/modules/combinatorics/group_constructs.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
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      +
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  • How-to Guides
    • Assumptions
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      • -
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      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Number of groups

        -sympy.combinatorics.group_numbers.is_nilpotent_number(n) → bool[source]
        +sympy.combinatorics.group_numbers.is_nilpotent_number(n) → bool[source]

        Check whether \(n\) is a nilpotent number. A number \(n\) is said to be nilpotent if and only if every finite group of order \(n\) is nilpotent. For more information see [R48].

        @@ -832,7 +834,7 @@
        Documentation Version
        -sympy.combinatorics.group_numbers.is_abelian_number(n) → bool[source]
        +sympy.combinatorics.group_numbers.is_abelian_number(n) → bool[source]

        Check whether \(n\) is an abelian number. A number \(n\) is said to be abelian if and only if every finite group of order \(n\) is abelian. For more information see [R50].

        @@ -864,7 +866,7 @@
        Documentation Version
        -sympy.combinatorics.group_numbers.is_cyclic_number(n) → bool[source]
        +sympy.combinatorics.group_numbers.is_cyclic_number(n) → bool[source]

        Check whether \(n\) is a cyclic number. A number \(n\) is said to be cyclic if and only if every finite group of order \(n\) is cyclic. For more information see [R52].

        @@ -896,7 +898,7 @@
        Documentation Version
        -sympy.combinatorics.group_numbers.groups_count(n)[source]
        +sympy.combinatorics.group_numbers.groups_count(n)[source]

        Number of groups of order \(n\). In [R54], gnu(n) is given, so we follow this notation here as well.

        diff --git a/dev/modules/combinatorics/index.html b/dev/modules/combinatorics/index.html index 3705a8c75ea..a32bd609ea6 100644 --- a/dev/modules/combinatorics/index.html +++ b/dev/modules/combinatorics/index.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Named Groups

        -sympy.combinatorics.named_groups.SymmetricGroup(n)[source]
        +sympy.combinatorics.named_groups.SymmetricGroup(n)[source]

        Generates the symmetric group on n elements as a permutation group.

        Explanation

        The generators taken are the n-cycle @@ -839,7 +841,7 @@

        Documentation Version
        -sympy.combinatorics.named_groups.CyclicGroup(n)[source]
        +sympy.combinatorics.named_groups.CyclicGroup(n)[source]

        Generates the cyclic group of order n as a permutation group.

        Explanation

        The generator taken is the n-cycle (0 1 2 ... n-1) @@ -865,7 +867,7 @@

        Documentation Version
        -sympy.combinatorics.named_groups.DihedralGroup(n)[source]
        +sympy.combinatorics.named_groups.DihedralGroup(n)[source]

        Generates the dihedral group \(D_n\) as a permutation group.

        Explanation

        The dihedral group \(D_n\) is the group of symmetries of the regular @@ -903,7 +905,7 @@

        Documentation Version
        -sympy.combinatorics.named_groups.AlternatingGroup(n)[source]
        +sympy.combinatorics.named_groups.AlternatingGroup(n)[source]

        Generates the alternating group on n elements as a permutation group.

        Explanation

        For n > 2, the generators taken are (0 1 2), (0 1 2 ... n-1) for @@ -938,7 +940,7 @@

        Documentation Version
        -sympy.combinatorics.named_groups.AbelianGroup(*cyclic_orders)[source]
        +sympy.combinatorics.named_groups.AbelianGroup(*cyclic_orders)[source]

        Returns the direct product of cyclic groups with the given orders.

        Explanation

        According to the structure theorem for finite abelian groups ([1]), diff --git a/dev/modules/combinatorics/partitions.html b/dev/modules/combinatorics/partitions.html index c9f3285dd91..f5cecf93aee 100644 --- a/dev/modules/combinatorics/partitions.html +++ b/dev/modules/combinatorics/partitions.html @@ -329,18 +329,20 @@

      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Partitions

        -class sympy.combinatorics.partitions.Partition(*partition)[source]
        +class sympy.combinatorics.partitions.Partition(*partition)[source]

        This class represents an abstract partition.

        A partition is a set of disjoint sets whose union equals a given set.

        @@ -835,7 +837,7 @@
        Documentation Version
        -classmethod from_rgs(rgs, elements)[source]
        +classmethod from_rgs(rgs, elements)[source]

        Creates a set partition from a restricted growth string.

        Explanation

        The indices given in rgs are assumed to be the index @@ -883,7 +885,7 @@

        Documentation Version
        -sort_key(order=None)[source]
        +sort_key(order=None)[source]

        Return a canonical key that can be used for sorting.

        Ordering is based on the size and sorted elements of the partition and ties are broken with the rank.

        @@ -906,7 +908,7 @@
        Documentation Version
        -class sympy.combinatorics.partitions.IntegerPartition(partition, integer=None)[source]
        +class sympy.combinatorics.partitions.IntegerPartition(partition, integer=None)[source]

        This class represents an integer partition.

        Explanation

        In number theory and combinatorics, a partition of a positive integer, @@ -930,7 +932,7 @@

        Documentation Version
        -as_dict()[source]
        +as_dict()[source]

        Return the partition as a dictionary whose keys are the partition integers and the values are the multiplicity of that integer.

        @@ -944,7 +946,7 @@
        Documentation Version
        -as_ferrers(char='#')[source]
        +as_ferrers(char='#')[source]

        Prints the ferrer diagram of a partition.

        Examples

        >>> from sympy.combinatorics.partitions import IntegerPartition
@@ -971,7 +973,7 @@ 
        Documentation Version
        
 
 
        
 
        
-next_lex()[source]
        
+next_lex()[source]
 
        Return the next partition of the integer, n, in lexical order,
 wrapping around to [n] if the partition is [1, …, 1].
        
 
        Examples
        
@@ -987,7 +989,7 @@ 
        Documentation Version
        
 
 
        
 
        
-prev_lex()[source]
        
+prev_lex()[source]
 
        Return the previous partition of the integer, n, in lexical order,
 wrapping around to [1, …, 1] if the partition is [n].
        
 
        Examples
        
@@ -1005,7 +1007,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.combinatorics.partitions.random_integer_partition(n, seed=None)[source]
        
+sympy.combinatorics.partitions.random_integer_partition(n, seed=None)[source]
 
        Generates a random integer partition summing to n as a list
 of reverse-sorted integers.
        
 
        Examples
        
@@ -1026,7 +1028,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.combinatorics.partitions.RGS_generalized(m)[source]
        
+sympy.combinatorics.partitions.RGS_generalized(m)[source]
 
        Computes the m + 1 generalized unrestricted growth strings
 and returns them as rows in matrix.
        
 
        Examples
        
@@ -1046,7 +1048,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.combinatorics.partitions.RGS_enum(m)[source]
        
+sympy.combinatorics.partitions.RGS_enum(m)[source]
 
        RGS_enum computes the total number of restricted growth strings
 possible for a superset of size m.
        
 
        Examples
        
@@ -1075,7 +1077,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.combinatorics.partitions.RGS_unrank(rank, m)[source]
        
+sympy.combinatorics.partitions.RGS_unrank(rank, m)[source]
 
        Gives the unranked restricted growth string for a given
 superset size.
        
 
        Examples
        
@@ -1090,7 +1092,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.combinatorics.partitions.RGS_rank(rgs)[source]
        
+sympy.combinatorics.partitions.RGS_rank(rgs)[source]
 
        Computes the rank of a restricted growth string.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.partitions import RGS_rank, RGS_unrank
diff --git a/dev/modules/combinatorics/pc_groups.html b/dev/modules/combinatorics/pc_groups.html
index 9f9f9577e10..47f770ab2a1 100644
--- a/dev/modules/combinatorics/pc_groups.html
+++ b/dev/modules/combinatorics/pc_groups.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
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  • How-to Guides
      +
    +
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  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
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      • -
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      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Permutation Groups

        -class sympy.combinatorics.perm_groups.PermutationGroup(*args, dups=True, **kwargs)[source]
        +class sympy.combinatorics.perm_groups.PermutationGroup(*args, dups=True, **kwargs)[source]

        The class defining a Permutation group.

        Explanation

        PermutationGroup([p1, p2, ..., pn]) returns the permutation group @@ -922,7 +924,7 @@

        Documentation Version
        -__contains__(i)[source]
        +__contains__(i)[source]

        Return True if i is contained in PermutationGroup.

        Examples

        >>> from sympy.combinatorics import Permutation, PermutationGroup
@@ -935,7 +937,7 @@ 
        Documentation Version
        
 
 
        
 
        
-__mul__(other)[source]
        
+__mul__(other)[source]
 
        Return the direct product of two permutation groups as a permutation
 group.
        
 
        Explanation
        
@@ -968,7 +970,7 @@ 
        Documentation Version
        
 
        **kwargs,
        
 
        
 
-)[source]
+)[source]
 
        The default constructor. Accepts Cycle and Permutation forms.
 Removes duplicates unless dups keyword is False.
        @@ -981,14 +983,14 @@
        Documentation Version
        -_coset_representative(g, H)[source]
        +_coset_representative(g, H)[source]

        Return the representative of Hg from the transversal that would be computed by self.coset_transversal(H).

        -classmethod _distinct_primes_lemma(primes)[source]
        +classmethod _distinct_primes_lemma(primes)[source]

        Subroutine to test if there is only one cyclic group for the order.

        @@ -1002,7 +1004,7 @@
        Documentation Version
        perms=None,
        -)[source] +)[source]

        A test using monte-carlo algorithm.

        Parameters:
        @@ -1034,13 +1036,13 @@
        Documentation Version
        only_alt=False,
        -)[source] +)[source]

        A naive test using the group order.

        -_p_elements_group(p)[source]
        +_p_elements_group(p)[source]

        For an abelian p-group, return the subgroup consisting of all elements of order p (and the identity)

        @@ -1055,7 +1057,7 @@
        Documentation Version
        _random_prec_n=None,
        -)[source] +)[source]

        Initialize random generators for the product replacement algorithm.

        Explanation

        The implementation uses a modification of the original product @@ -1090,7 +1092,7 @@

        Documentation Version
        -_sylow_alt_sym(p)[source]
        +_sylow_alt_sym(p)[source]

        Return a p-Sylow subgroup of a symmetric or an alternating group.

        Explanation

        @@ -1137,7 +1139,7 @@
        Documentation Version
        not_rep,
        -)[source] +)[source]

        Merges two classes in a union-find data structure.

        Explanation

        Used in the implementation of Atkinson’s algorithm as suggested in [1], @@ -1168,7 +1170,7 @@

        Documentation Version
        -_union_find_rep(num, parents)[source]
        +_union_find_rep(num, parents)[source]

        Find representative of a class in a union-find data structure.

        Explanation

        Used in the implementation of Atkinson’s algorithm as suggested in [1], @@ -1198,7 +1200,7 @@

        Documentation Version
        -_verify(K, phi, z, alpha)[source]
        +_verify(K, phi, z, alpha)[source]

        Return a list of relators rels in generators gens`_h` that are mapped to ``H.generators by phi so that given a finite presentation <gens_k | rels_k> of K on a subset of gens_h @@ -1239,7 +1241,7 @@

        Documentation Version
        -abelian_invariants()[source]
        +abelian_invariants()[source]

        Returns the abelian invariants for the given group. Let G be a nontrivial finite abelian group. Then G is isomorphic to the direct product of finitely many nontrivial cyclic groups of @@ -1312,7 +1314,7 @@

        Documentation Version
        strong_gens_distr=None,
        -)[source] +)[source]

        Swap two consecutive base points in base and strong generating set.

        Parameters:
        @@ -1471,7 +1473,7 @@
        Documentation Version
        -center()[source]
        +center()[source]

        Return the center of a permutation group.

        Explanation

        The center for a group \(G\) is defined as @@ -1498,7 +1500,7 @@

        Documentation Version
        -centralizer(other)[source]
        +centralizer(other)[source]

        Return the centralizer of a group/set/element.

        Parameters:
        @@ -1543,7 +1545,7 @@
        Documentation Version
        -commutator(G, H)[source]
        +commutator(G, H)[source]

        Return the commutator of two subgroups.

        Explanation

        For a permutation group K and subgroups G, H, the @@ -1572,7 +1574,7 @@

        Documentation Version
        -composition_series()[source]
        +composition_series()[source]

        Return the composition series for a group as a list of permutation groups.

        Explanation

        @@ -1619,7 +1621,7 @@
        Documentation Version
        -conjugacy_class(x)[source]
        +conjugacy_class(x)[source]

        Return the conjugacy class of an element in the group.

        Explanation

        The conjugacy class of an element g in a group G is the set of @@ -1656,7 +1658,7 @@

        Documentation Version
        -conjugacy_classes()[source]
        +conjugacy_classes()[source]

        Return the conjugacy classes of the group.

        Explanation

        As described in the documentation for the .conjugacy_class() function, @@ -1673,7 +1675,7 @@

        Documentation Version
        -contains(g, strict=True)[source]
        +contains(g, strict=True)[source]

        Test if permutation g belong to self, G.

        Explanation

        If g is an element of G it can be written as a product @@ -1729,7 +1731,7 @@

        Documentation Version
        factor_index=False,
        -)[source] +)[source]

        Return G’s (self’s) coset factorization of g

        Explanation

        If g is an element of G then it can be written as the product @@ -1784,7 +1786,7 @@

        Documentation Version
        -coset_rank(g)[source]
        +coset_rank(g)[source]

        rank using Schreier-Sims representation.

        Explanation

        The coset rank of g is the ordering number in which @@ -1812,21 +1814,21 @@

        Documentation Version
        -coset_table(H)[source]
        +coset_table(H)[source]

        Return the standardised (right) coset table of self in H as a list of lists.

        -coset_transversal(H)[source]
        +coset_transversal(H)[source]

        Return a transversal of the right cosets of self by its subgroup H using the second method described in [1], Subsection 4.6.7

        -coset_unrank(rank, af=False)[source]
        +coset_unrank(rank, af=False)[source]

        unrank using Schreier-Sims representation

        coset_unrank is the inverse operation of coset_rank if 0 <= rank < order; otherwise it returns None.

        @@ -1862,7 +1864,7 @@
        Documentation Version
        -derived_series()[source]
        +derived_series()[source]

        Return the derived series for the group.

        Returns:
        @@ -1899,7 +1901,7 @@
        Documentation Version
        -derived_subgroup()[source]
        +derived_subgroup()[source]

        Compute the derived subgroup.

        Explanation

        The derived subgroup, or commutator subgroup is the subgroup generated @@ -1937,7 +1939,7 @@

        Documentation Version
        -equals(other)[source]
        +equals(other)[source]

        Return True if PermutationGroup generated by elements in the group are same i.e they represent the same PermutationGroup.

        Examples

        @@ -1962,7 +1964,7 @@
        Documentation Version
        af=False,
        -)[source] +)[source]

        Return iterator to generate the elements of the group.

        Explanation

        Iteration is done with one of these methods:

        @@ -2007,7 +2009,7 @@
        Documentation Version
        -generate_dimino(af=False)[source]
        +generate_dimino(af=False)[source]

        Yield group elements using Dimino’s algorithm.

        If af == True it yields the array form of the permutations.

        Examples

        @@ -2032,7 +2034,7 @@
        Documentation Version
        -generate_schreier_sims(af=False)[source]
        +generate_schreier_sims(af=False)[source]

        Yield group elements using the Schreier-Sims representation in coset_rank order

        If af = True it yields the array form of the permutations

        @@ -2057,7 +2059,7 @@
        Documentation Version
        original=False,
        -)[source] +)[source]

        Return a list of strong generators \([s1, \dots, sn]\) s.t \(g = sn \times \dots \times s1\). If original=True, make the list contain only the original group generators

        @@ -2086,7 +2088,7 @@
        Documentation Version
        -index(H)[source]
        +index(H)[source]

        Returns the index of a permutation group.

        Examples

        >>> from sympy.combinatorics import Permutation, PermutationGroup
@@ -2128,7 +2130,7 @@ 
        Documentation Version
        
 
        _random_prec=None,
        -)[source] +)[source]

        Monte Carlo test for the symmetric/alternating group for degrees >= 8.

        Explanation

        @@ -2281,7 +2283,7 @@
        Documentation Version
        -is_elementary(p)[source]
        +is_elementary(p)[source]

        Return True if the group is elementary abelian. An elementary abelian group is a finite abelian group, where every nontrivial element has order \(p\), where \(p\) is a prime.

        @@ -2330,7 +2332,7 @@
        Documentation Version
        -is_normal(gr, strict=True)[source]
        +is_normal(gr, strict=True)[source]

        Test if G=self is a normal subgroup of gr.

        Explanation

        G is normal in gr if @@ -2384,7 +2386,7 @@

        Documentation Version
        -is_primitive(randomized=True)[source]
        +is_primitive(randomized=True)[source]

        Test if a group is primitive.

        Explanation

        A permutation group G acting on a set S is called primitive if @@ -2436,7 +2438,7 @@

        Documentation Version
        -is_subgroup(G, strict=True)[source]
        +is_subgroup(G, strict=True)[source]

        Return True if all elements of self belong to G.

        If strict is False then if self’s degree is smaller than G’s, the elements will be resized to have the same degree.

        @@ -2512,7 +2514,7 @@
        Documentation Version
        -is_transitive(strict=True)[source]
        +is_transitive(strict=True)[source]

        Test if the group is transitive.

        Explanation

        A group is transitive if it has a single orbit.

        @@ -2556,7 +2558,7 @@
        Documentation Version
        -lower_central_series()[source]
        +lower_central_series()[source]

        Return the lower central series for the group.

        The lower central series for a group \(G\) is the series \(G = G_0 > G_1 > G_2 > \ldots\) where @@ -2585,7 +2587,7 @@

        Documentation Version
        -make_perm(n, seed=None)[source]
        +make_perm(n, seed=None)[source]

        Multiply n randomly selected permutations from pgroup together, starting with the identity permutation. If n is a list of integers, those @@ -2639,7 +2641,7 @@

        Documentation Version
        -minimal_block(points)[source]
        +minimal_block(points)[source]

        For a transitive group, finds the block system generated by points.

        Explanation

        @@ -2681,7 +2683,7 @@
        Documentation Version
        -minimal_blocks(randomized=True)[source]
        +minimal_blocks(randomized=True)[source]

        For a transitive group, return the list of all minimal block systems. If a group is intransitive, return \(False\).

        Examples

        @@ -2702,7 +2704,7 @@
        Documentation Version
        -normal_closure(other, k=10)[source]
        +normal_closure(other, k=10)[source]

        Return the normal closure of a subgroup/set of permutations.

        Parameters:
        @@ -2749,7 +2751,7 @@
        Documentation Version
        -orbit(alpha, action='tuples')[source]
        +orbit(alpha, action='tuples')[source]

        Compute the orbit of alpha \(\{g(\alpha) | g \in G\}\) as a set.

        Explanation

        The time complexity of the algorithm used here is \(O(|Orb|*r)\) where @@ -2788,7 +2790,7 @@

        Documentation Version
        schreier_vector=None,
        -)[source] +)[source]

        Return a group element which sends alpha to beta.

        Explanation

        If beta is not in the orbit of alpha, the function returns @@ -2816,7 +2818,7 @@

        Documentation Version
        pairs=False,
        -)[source] +)[source]

        Computes a transversal for the orbit of alpha as a set.

        Explanation

        For a permutation group \(G\), a transversal for the orbit @@ -2840,7 +2842,7 @@

        Documentation Version
        -orbits(rep=False)[source]
        +orbits(rep=False)[source]

        Return the orbits of self, ordered according to lowest element in each orbit.

        Examples

        @@ -2856,7 +2858,7 @@
        Documentation Version
        -order()[source]
        +order()[source]

        Return the order of the group: the number of permutations that can be generated from elements of the group.

        The number of permutations comprising the group is given by @@ -2900,7 +2902,7 @@

        Documentation Version
        incremental=True,
        -)[source] +)[source]

        Return the pointwise stabilizer for a set of points.

        Explanation

        For a permutation group \(G\) and a set of points @@ -2930,7 +2932,7 @@

        Documentation Version
        -polycyclic_group()[source]
        +polycyclic_group()[source]

        Return the PolycyclicGroup instance with below parameters:

        Explanation

          @@ -2947,14 +2949,14 @@
          Documentation Version
          -presentation(eliminate_gens=True)[source]
          +presentation(eliminate_gens=True)[source]

          Return an \(FpGroup\) presentation of the group.

          The algorithm is described in [1], Chapter 6.1.

          -random(af=False)[source]
          +random(af=False)[source]

          Return a random group element

          @@ -2968,7 +2970,7 @@
          Documentation Version
          _random_prec=None,
        -)[source] +)[source]

        Return a random group element using product replacement.

        Explanation

        For the details of the product replacement algorithm, see @@ -2991,7 +2993,7 @@

        Documentation Version
        _random_prec=None,
        -)[source] +)[source]

        Random element from the stabilizer of alpha.

        The schreier vector for alpha is an optional argument used for speeding up repeated calls. The algorithm is described in [1], p.81

        @@ -3003,7 +3005,7 @@
        Documentation Version
        -schreier_sims()[source]
        +schreier_sims()[source]

        Schreier-Sims algorithm.

        Explanation

        It computes the generators of the chain of stabilizers @@ -3036,7 +3038,7 @@

        Documentation Version
        slp_dict=False,
        -)[source] +)[source]

        Extend a sequence of points and generating set to a base and strong generating set.

        @@ -3107,7 +3109,7 @@
        Documentation Version
        _random_prec=None,
        -)[source] +)[source]

        Randomized Schreier-Sims algorithm.

        Parameters:
        @@ -3177,7 +3179,7 @@
        Documentation Version
        -schreier_vector(alpha)[source]
        +schreier_vector(alpha)[source]

        Computes the schreier vector for alpha.

        Explanation

        The Schreier vector efficiently stores information @@ -3206,7 +3208,7 @@

        Documentation Version
        -stabilizer(alpha)[source]
        +stabilizer(alpha)[source]

        Return the stabilizer subgroup of alpha.

        Explanation

        The stabilizer of \(\alpha\) is the group \(G_\alpha = @@ -3256,7 +3258,7 @@

        Documentation Version
        -strong_presentation()[source]
        +strong_presentation()[source]

        Return a strong finite presentation of group. The generators of the returned group are in the same order as the strong generators of group.

        @@ -3278,7 +3280,7 @@
        Documentation Version
        -subgroup(gens)[source]
        +subgroup(gens)[source]

        Return the subgroup generated by \(gens\) which is a list of elements of the group

        @@ -3295,7 +3297,7 @@
        Documentation Version
        init_subgroup=None,
        -)[source] +)[source]

        Find the subgroup of all elements satisfying the property prop.

        Parameters:
        @@ -3374,7 +3376,7 @@
        Documentation Version
        -sylow_subgroup(p)[source]
        +sylow_subgroup(p)[source]

        Return a p-Sylow subgroup of the group.

        The algorithm is described in [1], Chapter 4, Section 7

        Examples

        diff --git a/dev/modules/combinatorics/permutations.html b/dev/modules/combinatorics/permutations.html index 3f9bb59021a..04f1995075a 100644 --- a/dev/modules/combinatorics/permutations.html +++ b/dev/modules/combinatorics/permutations.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Permutations

        -class sympy.combinatorics.permutations.Permutation(*args, size=None, **kwargs)[source]
        +class sympy.combinatorics.permutations.Permutation(*args, size=None, **kwargs)[source]

        A permutation, alternatively known as an ‘arrangement number’ or ‘ordering’ is an arrangement of the elements of an ordered list into a one-to-one mapping with itself. The permutation of a given arrangement is given by @@ -1206,7 +1208,7 @@

        Documentation Version
        -apply(i)[source]
        +apply(i)[source]

        Apply the permutation to an expression.

        Parameters:
        @@ -1260,7 +1262,7 @@
        Documentation Version
        -ascents()[source]
        +ascents()[source]

        Returns the positions of ascents in a permutation, ie, the location where p[i] < p[i+1]

        Examples

        @@ -1278,7 +1280,7 @@
        Documentation Version
        -atoms()[source]
        +atoms()[source]

        Returns all the elements of a permutation

        Examples

        >>> from sympy.combinatorics import Permutation
@@ -1309,7 +1311,7 @@ 
        Documentation Version
        
 
 
        
 
        
-commutator(x)[source]
        
+commutator(x)[source]
 
        Return the commutator of self and x: ~x*~self*x*self
        
 
        If f and g are part of a group, G, then the commutator of f and g
 is the group identity iff f and g commute, i.e. fg == gf.
        
@@ -1348,7 +1350,7 @@ 
        Documentation Version
        
 
 
        
 
        
-commutes_with(other)[source]
        
+commutes_with(other)[source]
 
        Checks if the elements are commuting.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -1421,7 +1423,7 @@ 
        Documentation Version
        
 
 
        
 
        
-descents()[source]
        
+descents()[source]
 
        Returns the positions of descents in a permutation, ie, the location
 where p[i] > p[i+1]
        
 
        Examples
        
@@ -1439,7 +1441,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod from_inversion_vector(inversion)[source]
        
+classmethod from_inversion_vector(inversion)[source]
 
        Calculates the permutation from the inversion vector.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -1453,7 +1455,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod from_sequence(i, key=None)[source]
        
+classmethod from_sequence(i, key=None)[source]
 
        Return the permutation needed to obtain i from the sorted
 elements of i. If custom sorting is desired, a key can be given.
        
 
        Examples
        
@@ -1484,7 +1486,7 @@ 
        Documentation Version
        
 
 
        
 
        
-get_adjacency_distance(other)[source]
        
+get_adjacency_distance(other)[source]
 
        Computes the adjacency distance between two permutations.
        
 
        Explanation
        
 
        This metric counts the number of times a pair i,j of jobs is
@@ -1511,7 +1513,7 @@ 
        Documentation Version
        
 
 
        
 
        
-get_adjacency_matrix()[source]
        
+get_adjacency_matrix()[source]
 
        Computes the adjacency matrix of a permutation.
        
 
        Explanation
        
 
        If job i is adjacent to job j in a permutation p
@@ -1545,7 +1547,7 @@ 
        Documentation Version
        
 
 
        
 
        
-get_positional_distance(other)[source]
        
+get_positional_distance(other)[source]
 
        Computes the positional distance between two permutations.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -1566,7 +1568,7 @@ 
        Documentation Version
        
 
 
        
 
        
-get_precedence_distance(other)[source]
        
+get_precedence_distance(other)[source]
 
        Computes the precedence distance between two permutations.
        
 
        Explanation
        
 
        Suppose p and p’ represent n jobs. The precedence metric
@@ -1590,7 +1592,7 @@ 
        Documentation Version
        
 
 
        
 
        
-get_precedence_matrix()[source]
        
+get_precedence_matrix()[source]
 
        Gets the precedence matrix. This is used for computing the
 distance between two permutations.
        
 
        Examples
        
@@ -1618,7 +1620,7 @@ 
        Documentation Version
        
 
 
        
 
        
-index()[source]
        
+index()[source]
 
        Returns the index of a permutation.
        
 
        The index of a permutation is the sum of all subscripts j such
 that p[j] is greater than p[j+1].
        
@@ -1633,7 +1635,7 @@ 
        Documentation Version
        
 
 
        
 
        
-inversion_vector()[source]
        
+inversion_vector()[source]
 
        Return the inversion vector of the permutation.
        
 
        The inversion vector consists of elements whose value
 indicates the number of elements in the permutation
@@ -1672,7 +1674,7 @@ 
        Documentation Version
        
 
 
        
 
        
-inversions()[source]
        
+inversions()[source]
 
        Computes the number of inversions of a permutation.
        
 
        Explanation
        
 
        An inversion is where i > j but p[i] < p[j].
        
@@ -1807,7 +1809,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod josephus(m, n, s=1)[source]
        
+classmethod josephus(m, n, s=1)[source]
 
        Return as a permutation the shuffling of range(n) using the Josephus
 scheme in which every m-th item is selected until all have been chosen.
 The returned permutation has elements listed by the order in which they
@@ -1852,7 +1854,7 @@ 
        Documentation Version
        
 
 
        
 
        
-length()[source]
        
+length()[source]
 
        Returns the number of integers moved by a permutation.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -1870,7 +1872,7 @@ 
        Documentation Version
        
 
 
        
 
        
-list(size=None)[source]
        
+list(size=None)[source]
 
        Return the permutation as an explicit list, possibly
 trimming unmoved elements if size is less than the maximum
 element in the permutation; if this is desired, setting
@@ -1896,7 +1898,7 @@ 
        Documentation Version
        
 
 
        
 
        
-max() → int[source]
        
+max() → int[source]
 
        The maximum element moved by the permutation.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -1913,7 +1915,7 @@ 
        Documentation Version
        
 
 
        
 
        
-min() → int[source]
        
+min() → int[source]
 
        The minimum element moved by the permutation.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -1930,13 +1932,13 @@ 
        Documentation Version
        
 
 
        
 
        
-mul_inv(other)[source]
        
+mul_inv(other)[source]
 
        other*~self, self and other have _array_form
        
 
        
 
 
        
 
        
-next_lex()[source]
        
+next_lex()[source]
 
        Returns the next permutation in lexicographical order.
 If self is the last permutation in lexicographical order
 it returns None.
@@ -1958,7 +1960,7 @@ 
        Documentation Version
        
 
 
        
 
        
-next_nonlex()[source]
        
+next_nonlex()[source]
 
        Returns the next permutation in nonlex order [3].
 If self is the last permutation in this order it returns None.
        
 
        Examples
        
@@ -1981,7 +1983,7 @@ 
        Documentation Version
        
 
 
        
 
        
-next_trotterjohnson()[source]
        
+next_trotterjohnson()[source]
 
        Returns the next permutation in Trotter-Johnson order.
 If self is the last permutation it returns None.
 See [4] section 2.4. If it is desired to generate all such
@@ -2008,7 +2010,7 @@ 
        Documentation Version
        
 
 
        
 
        
-order()[source]
        
+order()[source]
 
        Computes the order of a permutation.
        
 
        When the permutation is raised to the power of its
 order it equals the identity permutation.
        
@@ -2031,7 +2033,7 @@ 
        Documentation Version
        
 
 
        
 
        
-parity()[source]
        
+parity()[source]
 
        Computes the parity of a permutation.
        
 
        Explanation
        
 
        The parity of a permutation reflects the parity of the
@@ -2055,7 +2057,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod random(n)[source]
        
+classmethod random(n)[source]
 
        Generates a random permutation of length n.
        
 
        Uses the underlying Python pseudo-random number generator.
        
 
        Examples
        
@@ -2068,7 +2070,7 @@ 
        Documentation Version
        
 
 
        
 
        
-rank()[source]
        
+rank()[source]
 
        Returns the lexicographic rank of the permutation.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -2088,7 +2090,7 @@ 
        Documentation Version
        
 
 
        
 
        
-rank_nonlex(inv_perm=None)[source]
        
+rank_nonlex(inv_perm=None)[source]
 
        This is a linear time ranking algorithm that does not
 enforce lexicographic order [3].
        
 
        Examples
        
@@ -2106,7 +2108,7 @@ 
        Documentation Version
        
 
 
        
 
        
-rank_trotterjohnson()[source]
        
+rank_trotterjohnson()[source]
 
        Returns the Trotter Johnson rank, which we get from the minimal
 change algorithm. See [4] section 2.4.
        
 
        Examples
        
@@ -2127,7 +2129,7 @@ 
        Documentation Version
        
 
 
        
 
        
-resize(n)[source]
        
+resize(n)[source]
 
        Resize the permutation to the new size n.
        
 
        
 
        Parameters:
        
@@ -2174,7 +2176,7 @@ 
        Documentation Version
        
 
 
        
 
        
-static rmul(*args)[source]
        
+static rmul(*args)[source]
 
        Return product of Permutations [a, b, c, …] as the Permutation whose
 ith value is a(b(c(i))).
        
 
        a, b, c, … can be Permutation objects or tuples.
        
@@ -2210,14 +2212,14 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod rmul_with_af(*args)[source]
        
+classmethod rmul_with_af(*args)[source]
 
        same as rmul, but the elements of args are Permutation objects
 which have _array_form
        
 
        
 
 
        
 
        
-runs()[source]
        
+runs()[source]
 
        Returns the runs of a permutation.
        
 
        An ascending sequence in a permutation is called a run [5].
        
 
        Examples
        
@@ -2234,7 +2236,7 @@ 
        Documentation Version
        
 
 
        
 
        
-signature()[source]
        
+signature()[source]
 
        Gives the signature of the permutation needed to place the
 elements of the permutation in canonical order.
        
 
        The signature is calculated as (-1)^<number of inversions>
        
@@ -2276,7 +2278,7 @@ 
        Documentation Version
        
 
 
        
 
        
-support()[source]
        
+support()[source]
 
        Return the elements in permutation, P, for which P[i] != i.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -2291,7 +2293,7 @@ 
        Documentation Version
        
 
 
        
 
        
-transpositions()[source]
        
+transpositions()[source]
 
        Return the permutation decomposed into a list of transpositions.
        
 
        Explanation
        
 
        It is always possible to express a permutation as the product of
@@ -2319,7 +2321,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod unrank_lex(size, rank)[source]
        
+classmethod unrank_lex(size, rank)[source]
 
        Lexicographic permutation unranking.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -2340,7 +2342,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod unrank_nonlex(n, r)[source]
        
+classmethod unrank_nonlex(n, r)[source]
 
        This is a linear time unranking algorithm that does not
 respect lexicographic order [3].
        
 
        Examples
        
@@ -2361,7 +2363,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod unrank_trotterjohnson(size, rank)[source]
        
+classmethod unrank_trotterjohnson(size, rank)[source]
 
        Trotter Johnson permutation unranking. See [4] section 2.4.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Permutation
@@ -2381,7 +2383,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.combinatorics.permutations.Cycle(*args)[source]
        
+class sympy.combinatorics.permutations.Cycle(*args)[source]
 
        Wrapper around dict which provides the functionality of a disjoint cycle.
        
 
        Explanation
        
 
        A cycle shows the rule to use to move subsets of elements to obtain
@@ -2452,7 +2454,7 @@ 
        Documentation Version
        
 
        
 
        
 
        
-list(size=None)[source]
        
+list(size=None)[source]
 
        Return the cycles as an explicit list starting from 0 up
 to the greater of the largest value in the cycles and size.
        
 
        Truncation of trailing unmoved items will occur when size
@@ -2479,7 +2481,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.combinatorics.permutations._af_parity(pi)[source]
        
+sympy.combinatorics.permutations._af_parity(pi)[source]
 
        Computes the parity of a permutation in array form.
        
 
        Explanation
        
 
        The parity of a permutation reflects the parity of the
@@ -2503,7 +2505,7 @@ 
        Documentation Version
        
 
        Generators
        
 
        
 
        
-generators.symmetric()[source]
        
+generators.symmetric()[source]
 
        Generates the symmetric group of order n, Sn.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.generators import symmetric
@@ -2515,7 +2517,7 @@ 
        Documentation Version
        
 
 
        
 
        
-generators.cyclic()[source]
        
+generators.cyclic()[source]
 
        Generates the cyclic group of order n, Cn.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.generators import cyclic
@@ -2532,7 +2534,7 @@ 
        Documentation Version
        
 
 
        
 
        
-generators.alternating()[source]
        
+generators.alternating()[source]
 
        Generates the alternating group of order n, An.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.generators import alternating
@@ -2544,7 +2546,7 @@ 
        Documentation Version
        
 
 
        
 
        
-generators.dihedral()[source]
        
+generators.dihedral()[source]
 
        Generates the dihedral group of order 2n, Dn.
        
 
        The result is given as a subgroup of Sn, except for the special cases n=1
 (the group S2) and n=2 (the Klein 4-group) where that’s not possible
diff --git a/dev/modules/combinatorics/polyhedron.html b/dev/modules/combinatorics/polyhedron.html
index 70408840e41..4333101ca75 100644
--- a/dev/modules/combinatorics/polyhedron.html
+++ b/dev/modules/combinatorics/polyhedron.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Prufer Sequences

        -class sympy.combinatorics.prufer.Prufer(*args, **kw_args)[source]
        +class sympy.combinatorics.prufer.Prufer(*args, **kw_args)[source]

        The Prufer correspondence is an algorithm that describes the bijection between labeled trees and the Prufer code. A Prufer code of a labeled tree is unique up to isomorphism and has @@ -818,7 +820,7 @@

        Documentation Version
        -static edges(*runs)[source]
        +static edges(*runs)[source]

        Return a list of edges and the number of nodes from the given runs that connect nodes in an integer-labelled tree.

        All node numbers will be shifted so that the minimum node is 0. It is @@ -841,7 +843,7 @@

        Documentation Version
        -next(delta=1)[source]
        +next(delta=1)[source]

        Generates the Prufer sequence that is delta beyond the current one.

        Examples

        >>> from sympy.combinatorics.prufer import Prufer
@@ -875,7 +877,7 @@ 
        Documentation Version
        
 
 
        
 
        
-prev(delta=1)[source]
        
+prev(delta=1)[source]
 
        Generates the Prufer sequence that is -delta before the current one.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.prufer import Prufer
@@ -897,7 +899,7 @@ 
        Documentation Version
        
 
 
        
 
        
-prufer_rank()[source]
        
+prufer_rank()[source]
 
        Computes the rank of a Prufer sequence.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.prufer import Prufer
@@ -972,7 +974,7 @@ 
        Documentation Version
        
 
 
        
 
        
-static to_prufer(tree, n)[source]
        
+static to_prufer(tree, n)[source]
 
        Return the Prufer sequence for a tree given as a list of edges where
 n is the number of nodes in the tree.
        
 
        Examples
        
@@ -995,7 +997,7 @@ 
        Documentation Version
        
 
 
        
 
        
-static to_tree(prufer)[source]
        
+static to_tree(prufer)[source]
 
        Return the tree (as a list of edges) of the given Prufer sequence.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.prufer import Prufer
@@ -1042,7 +1044,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod unrank(rank, n)[source]
        
+classmethod unrank(rank, n)[source]
 
        Finds the unranked Prufer sequence.
        
 
        Examples
        
 
        >>> from sympy.combinatorics.prufer import Prufer
diff --git a/dev/modules/combinatorics/subsets.html b/dev/modules/combinatorics/subsets.html
index 18c3b931903..d39c83658d1 100644
--- a/dev/modules/combinatorics/subsets.html
+++ b/dev/modules/combinatorics/subsets.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Subsets

        -class sympy.combinatorics.subsets.Subset(subset, superset)[source]
        +class sympy.combinatorics.subsets.Subset(subset, superset)[source]

        Represents a basic subset object.

        Explanation

        We generate subsets using essentially two techniques, @@ -821,7 +823,7 @@

        Documentation Version
        -classmethod bitlist_from_subset(subset, superset)[source]
        +classmethod bitlist_from_subset(subset, superset)[source]

        Gets the bitlist corresponding to a subset.

        Examples

        >>> from sympy.combinatorics import Subset
@@ -854,7 +856,7 @@ 
        Documentation Version
        
 
 
        
 
        
-iterate_binary(k)[source]
        
+iterate_binary(k)[source]
 
        This is a helper function. It iterates over the
 binary subsets by k steps. This variable can be
 both positive or negative.
        
@@ -876,7 +878,7 @@ 
        Documentation Version
        
 
 
        
 
        
-iterate_graycode(k)[source]
        
+iterate_graycode(k)[source]
 
        Helper function used for prev_gray and next_gray.
 It performs k step overs to get the respective Gray codes.
        
 
        Examples
        
@@ -896,7 +898,7 @@ 
        Documentation Version
        
 
 
        
 
        
-next_binary()[source]
        
+next_binary()[source]
 
        Generates the next binary ordered subset.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -916,7 +918,7 @@ 
        Documentation Version
        
 
 
        
 
        
-next_gray()[source]
        
+next_gray()[source]
 
        Generates the next Gray code ordered subset.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -933,7 +935,7 @@ 
        Documentation Version
        
 
 
        
 
        
-next_lexicographic()[source]
        
+next_lexicographic()[source]
 
        Generates the next lexicographically ordered subset.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -953,7 +955,7 @@ 
        Documentation Version
        
 
 
        
 
        
-prev_binary()[source]
        
+prev_binary()[source]
 
        Generates the previous binary ordered subset.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -973,7 +975,7 @@ 
        Documentation Version
        
 
 
        
 
        
-prev_gray()[source]
        
+prev_gray()[source]
 
        Generates the previous Gray code ordered subset.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -990,7 +992,7 @@ 
        Documentation Version
        
 
 
        
 
        
-prev_lexicographic()[source]
        
+prev_lexicographic()[source]
 
        Generates the previous lexicographically ordered subset.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -1100,7 +1102,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod subset_from_bitlist(super_set, bitlist)[source]
        
+classmethod subset_from_bitlist(super_set, bitlist)[source]
 
        Gets the subset defined by the bitlist.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -1116,7 +1118,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod subset_indices(subset, superset)[source]
        
+classmethod subset_indices(subset, superset)[source]
 
        Return indices of subset in superset in a list; the list is empty
 if all elements of subset are not in superset.
        
 
        Examples
        
@@ -1168,7 +1170,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod unrank_binary(rank, superset)[source]
        
+classmethod unrank_binary(rank, superset)[source]
 
        Gets the binary ordered subset of the specified rank.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -1184,7 +1186,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod unrank_gray(rank, superset)[source]
        
+classmethod unrank_gray(rank, superset)[source]
 
        Gets the Gray code ordered subset of the specified rank.
        
 
        Examples
        
 
        >>> from sympy.combinatorics import Subset
@@ -1204,7 +1206,7 @@ 
        Documentation Version
        
 
 
        
 
        
-subsets.ksubsets(k)[source]
        
+subsets.ksubsets(k)[source]
 
        Finds the subsets of size k in lexicographic order.
        
 
        This uses the itertools generator.
        
 
        Examples
        
diff --git a/dev/modules/combinatorics/tensor_can.html b/dev/modules/combinatorics/tensor_can.html
index 0772385dedd..a199361baf4 100644
--- a/dev/modules/combinatorics/tensor_can.html
+++ b/dev/modules/combinatorics/tensor_can.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Test Utilities

        -sympy.combinatorics.testutil._cmp_perm_lists(first, second)[source]
        +sympy.combinatorics.testutil._cmp_perm_lists(first, second)[source]

        Compare two lists of permutations as sets.

        Explanation

        This is used for testing purposes. Since the array form of a @@ -824,12 +826,12 @@

        Documentation Version
        -sympy.combinatorics.testutil._naive_list_centralizer(self, other, af=False)[source]
        +sympy.combinatorics.testutil._naive_list_centralizer(self, other, af=False)[source]
        -sympy.combinatorics.testutil._verify_bsgs(group, base, gens)[source]
        +sympy.combinatorics.testutil._verify_bsgs(group, base, gens)[source]

        Verify the correctness of a base and strong generating set.

        Explanation

        This is a naive implementation using the definition of a base and a strong @@ -853,7 +855,7 @@

        Documentation Version
        -sympy.combinatorics.testutil._verify_centralizer(group, arg, centr=None)[source]
        +sympy.combinatorics.testutil._verify_centralizer(group, arg, centr=None)[source]

        Verify the centralizer of a group/set/element inside another group.

        This is used for testing .centralizer() from sympy.combinatorics.perm_groups

        @@ -878,7 +880,7 @@
        Documentation Version
        -sympy.combinatorics.testutil._verify_normal_closure(group, arg, closure=None)[source]
        +sympy.combinatorics.testutil._verify_normal_closure(group, arg, closure=None)[source]
        diff --git a/dev/modules/combinatorics/util.html b/dev/modules/combinatorics/util.html index a3bf69eac17..8a6e7cc0948 100644 --- a/dev/modules/combinatorics/util.html +++ b/dev/modules/combinatorics/util.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Utilities

        -sympy.combinatorics.util._base_ordering(base, degree)[source]
        +sympy.combinatorics.util._base_ordering(base, degree)[source]

        Order \(\{0, 1, \dots, n-1\}\) so that base points come first and in order.

        Parameters:
        @@ -843,7 +845,7 @@
        Documentation Version
        -sympy.combinatorics.util._check_cycles_alt_sym(perm)[source]
        +sympy.combinatorics.util._check_cycles_alt_sym(perm)[source]

        Checks for cycles of prime length p with n/2 < p < n-2.

        Explanation

        Here \(n\) is the degree of the permutation. This is a helper function for @@ -867,7 +869,7 @@

        Documentation Version
        -sympy.combinatorics.util._distribute_gens_by_base(base, gens)[source]
        +sympy.combinatorics.util._distribute_gens_by_base(base, gens)[source]

        Distribute the group elements gens by membership in basic stabilizers.

        Parameters:
        @@ -921,7 +923,7 @@
        Documentation Version
        strong_gens_distr=None,
        -)[source] +)[source]

        Calculate BSGS-related structures from those present.

        Parameters:
        @@ -971,7 +973,7 @@
        Documentation Version
        slp=False,
        -)[source] +)[source]

        Compute basic orbits and transversals from a base and strong generating set.

        Parameters:
        @@ -1022,7 +1024,7 @@
        Documentation Version
        strong_gens_distr=None,
        -)[source] +)[source]

        Remove redundant generators from a strong generating set.

        Parameters:
        @@ -1063,7 +1065,7 @@
        Documentation Version
        -sympy.combinatorics.util._strip(g, base, orbits, transversals)[source]
        +sympy.combinatorics.util._strip(g, base, orbits, transversals)[source]

        Attempt to decompose a permutation using a (possibly partial) BSGS structure.

        @@ -1123,7 +1125,7 @@
        Documentation Version
        -sympy.combinatorics.util._strong_gens_from_distr(strong_gens_distr)[source]
        +sympy.combinatorics.util._strong_gens_from_distr(strong_gens_distr)[source]

        Retrieve strong generating set from generators of basic stabilizers.

        This is just the union of the generators of the first and second basic stabilizers.

        diff --git a/dev/modules/concrete.html b/dev/modules/concrete.html index 63f5ef175f3..47163d4db53 100644 --- a/dev/modules/concrete.html +++ b/dev/modules/concrete.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -821,7 +823,7 @@

        Discrete

        Fast Fourier Transform

        -sympy.discrete.transforms.fft(seq, dps=None)[source]
        +sympy.discrete.transforms.fft(seq, dps=None)[source]

        Performs the Discrete Fourier Transform (DFT) in the complex domain.

        The sequence is automatically padded to the right with zeros, as the radix-2 FFT requires the number of sample points to be a power of 2.

        @@ -876,7 +878,7 @@

        Fast Fourier Transform
        -sympy.discrete.transforms.ifft(seq, dps=None)[source]
        +sympy.discrete.transforms.ifft(seq, dps=None)[source]

        Performs the Discrete Fourier Transform (DFT) in the complex domain.

        The sequence is automatically padded to the right with zeros, as the radix-2 FFT requires the number of sample points to be a power of 2.

        @@ -934,7 +936,7 @@

        Fast Fourier TransformNumber Theoretic Transform

        -sympy.discrete.transforms.ntt(seq, prime)[source]
        +sympy.discrete.transforms.ntt(seq, prime)[source]

        Performs the Number Theoretic Transform (NTT), which specializes the Discrete Fourier Transform (DFT) over quotient ring \(Z/pZ\) for prime \(p\) instead of complex numbers \(C\).

        @@ -984,7 +986,7 @@

        Number Theoretic Transform
        -sympy.discrete.transforms.intt(seq, prime)[source]
        +sympy.discrete.transforms.intt(seq, prime)[source]

        Performs the Number Theoretic Transform (NTT), which specializes the Discrete Fourier Transform (DFT) over quotient ring \(Z/pZ\) for prime \(p\) instead of complex numbers \(C\).

        @@ -1037,7 +1039,7 @@

        Number Theoretic Transform

        -sympy.discrete.transforms.fwht(seq)[source]
        +sympy.discrete.transforms.fwht(seq)[source]

        Performs the Walsh Hadamard Transform (WHT), and uses Hadamard ordering for the sequence.

        The sequence is automatically padded to the right with zeros, as the @@ -1079,7 +1081,7 @@

        Fast Walsh Hadamard Transform
        -sympy.discrete.transforms.ifwht(seq)[source]
        +sympy.discrete.transforms.ifwht(seq)[source]

        Performs the Walsh Hadamard Transform (WHT), and uses Hadamard ordering for the sequence.

        The sequence is automatically padded to the right with zeros, as the @@ -1124,7 +1126,7 @@

        Fast Walsh Hadamard Transform

        -sympy.discrete.transforms.mobius_transform(seq, subset=True)[source]
        +sympy.discrete.transforms.mobius_transform(seq, subset=True)[source]

        Performs the Mobius Transform for subset lattice with indices of sequence as bitmasks.

        The indices of each argument, considered as bit strings, correspond @@ -1192,7 +1194,7 @@

        Möbius Transform
        -sympy.discrete.transforms.inverse_mobius_transform(seq, subset=True)[source]
        +sympy.discrete.transforms.inverse_mobius_transform(seq, subset=True)[source]

        Performs the Mobius Transform for subset lattice with indices of sequence as bitmasks.

        The indices of each argument, considered as bit strings, correspond @@ -1283,7 +1285,7 @@

        Convolutionsubset=None,

        -)[source] +)[source]

        Performs convolution by determining the type of desired convolution using hints.

        Exactly one of dps, prime, dyadic, subset arguments @@ -1357,7 +1359,7 @@

        Convolution

        -sympy.discrete.convolutions.convolution_fft(a, b, dps=None)[source]
        +sympy.discrete.convolutions.convolution_fft(a, b, dps=None)[source]

        Performs linear convolution using Fast Fourier Transform.

        Parameters:
        @@ -1402,7 +1404,7 @@

        Convolution using Fast Fourier Transform

        -sympy.discrete.convolutions.convolution_ntt(a, b, prime)[source]
        +sympy.discrete.convolutions.convolution_ntt(a, b, prime)[source]

        Performs linear convolution using Number Theoretic Transform.

        Parameters:
        @@ -1445,7 +1447,7 @@

        Convolution using Number Theoretic Transform

        -sympy.discrete.convolutions.convolution_fwht(a, b)[source]
        +sympy.discrete.convolutions.convolution_fwht(a, b)[source]

        Performs dyadic (bitwise-XOR) convolution using Fast Walsh Hadamard Transform.

        The convolution is automatically padded to the right with zeros, as the @@ -1496,7 +1498,7 @@

        Convolution using Fast Walsh Hadamard Transform

        -sympy.discrete.convolutions.convolution_subset(a, b)[source]
        +sympy.discrete.convolutions.convolution_subset(a, b)[source]

        Performs Subset Convolution of given sequences.

        The indices of each argument, considered as bit strings, correspond to subsets of a finite set.

        @@ -1543,7 +1545,7 @@

        Subset Convolution

        -sympy.discrete.convolutions.covering_product(a, b)[source]
        +sympy.discrete.convolutions.covering_product(a, b)[source]

        Returns the covering product of given sequences.

        The indices of each argument, considered as bit strings, correspond to subsets of a finite set.

        @@ -1592,7 +1594,7 @@

        Covering Product

        -sympy.discrete.convolutions.intersecting_product(a, b)[source]
        +sympy.discrete.convolutions.intersecting_product(a, b)[source]

        Returns the intersecting product of given sequences.

        The indices of each argument, considered as bit strings, correspond to subsets of a finite set.

        diff --git a/dev/modules/evalf.html b/dev/modules/evalf.html index c032de66436..7d428bb7ae8 100644 --- a/dev/modules/evalf.html +++ b/dev/modules/evalf.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model

      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -803,7 +805,7 @@
        Documentation Version

        This module implements various combinatorial functions.

        -class sympy.functions.combinatorial.numbers.bell(n, k_sym=None, symbols=None)[source]
        +class sympy.functions.combinatorial.numbers.bell(n, k_sym=None, symbols=None)[source]

        Bell numbers / Bell polynomials

        The Bell numbers satisfy \(B_0 = 1\) and

        @@ -877,7 +879,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.bernoulli(n, x=None)[source]
        +class sympy.functions.combinatorial.numbers.bernoulli(n, x=None)[source]

        Bernoulli numbers / Bernoulli polynomials / Bernoulli function

        The Bernoulli numbers are a sequence of rational numbers defined by \(B_0 = 1\) and the recursive relation (\(n > 0\)):

        @@ -995,7 +997,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.factorials.binomial(n, k)[source]
        +class sympy.functions.combinatorial.factorials.binomial(n, k)[source]

        Implementation of the binomial coefficient. It can be defined in two ways depending on its desired interpretation:

        @@ -1104,7 +1106,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.catalan(n)[source]
        +class sympy.functions.combinatorial.numbers.catalan(n)[source]

        Catalan numbers

        The \(n^{th}\) catalan number is given by:

        @@ -1199,7 +1201,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.euler(n, x=None)[source]
        +class sympy.functions.combinatorial.numbers.euler(n, x=None)[source]

        Euler numbers / Euler polynomials / Euler function

        The Euler numbers are given by:

        @@ -1296,7 +1298,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.factorials.factorial(n)[source]
        +class sympy.functions.combinatorial.factorials.factorial(n)[source]

        Implementation of factorial function over nonnegative integers. By convention (consistent with the gamma function and the binomial coefficients), factorial of a negative integer is complex infinity.

        @@ -1348,7 +1350,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.factorials.subfactorial(arg)[source]
        +class sympy.functions.combinatorial.factorials.subfactorial(arg)[source]

        The subfactorial counts the derangements of \(n\) items and is defined for non-negative integers as:

        @@ -1396,7 +1398,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.factorials.factorial2(arg)[source]
        +class sympy.functions.combinatorial.factorials.factorial2(arg)[source]

        The double factorial \(n!!\), not to be confused with \((n!)!\)

        The double factorial is defined for nonnegative integers and for odd negative integers as:

        @@ -1437,7 +1439,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.factorials.FallingFactorial(x, k)[source]
        +class sympy.functions.combinatorial.factorials.FallingFactorial(x, k)[source]

        Falling factorial (related to rising factorial) is a double valued function arising in concrete mathematics, hypergeometric functions and series expansions. It is defined by

        @@ -1507,7 +1509,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.fibonacci(n, sym=None)[source]
        +class sympy.functions.combinatorial.numbers.fibonacci(n, sym=None)[source]

        Fibonacci numbers / Fibonacci polynomials

        The Fibonacci numbers are the integer sequence defined by the initial terms \(F_0 = 0\), \(F_1 = 1\) and the two-term recurrence @@ -1554,7 +1556,7 @@

        Documentation Version
        -class sympy.functions.combinatorial.numbers.tribonacci(n, sym=None)[source]
        +class sympy.functions.combinatorial.numbers.tribonacci(n, sym=None)[source]

        Tribonacci numbers / Tribonacci polynomials

        The Tribonacci numbers are the integer sequence defined by the initial terms \(T_0 = 0\), \(T_1 = 1\), \(T_2 = 1\) and the three-term @@ -1599,7 +1601,7 @@

        Documentation Version
        -class sympy.functions.combinatorial.numbers.harmonic(n, m=None)[source]
        +class sympy.functions.combinatorial.numbers.harmonic(n, m=None)[source]

        Harmonic numbers

        The nth harmonic number is given by \(\operatorname{H}_{n} = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}\).

        @@ -1750,7 +1752,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.lucas(n)[source]
        +class sympy.functions.combinatorial.numbers.lucas(n)[source]

        Lucas numbers

        Lucas numbers satisfy a recurrence relation similar to that of the Fibonacci sequence, in which each term is the sum of the @@ -1786,7 +1788,7 @@

        Documentation Version
        -class sympy.functions.combinatorial.numbers.genocchi(n, x=None)[source]
        +class sympy.functions.combinatorial.numbers.genocchi(n, x=None)[source]

        Genocchi numbers / Genocchi polynomials / Genocchi function

        The Genocchi numbers are a sequence of integers \(G_n\) that satisfy the relation:

        @@ -1845,7 +1847,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.andre(n)[source]
        +class sympy.functions.combinatorial.numbers.andre(n)[source]

        Andre numbers / Andre function

        The Andre number \(\mathcal{A}_n\) is Luschny’s name for half the number of alternating permutations on \(n\) elements, where a permutation is alternating @@ -1914,7 +1916,7 @@

        Documentation Version
        -class sympy.functions.combinatorial.numbers.partition(n)[source]
        +class sympy.functions.combinatorial.numbers.partition(n)[source]

        Partition numbers

        The Partition numbers are a sequence of integers \(p_n\) that represent the number of distinct ways of representing \(n\) as a sum of natural numbers @@ -1951,7 +1953,7 @@

        Documentation Version
        -class sympy.functions.combinatorial.numbers.divisor_sigma(n, k=1)[source]
        +class sympy.functions.combinatorial.numbers.divisor_sigma(n, k=1)[source]

        Calculate the divisor function \(\sigma_k(n)\) for positive integer n

        divisor_sigma(n, k) is equal to sum([x**k for x in divisors(n)])

        If n’s prime factorization is:

        @@ -1992,7 +1994,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.udivisor_sigma(n, k=1)[source]
        +class sympy.functions.combinatorial.numbers.udivisor_sigma(n, k=1)[source]

        Calculate the unitary divisor function \(\sigma_k^*(n)\) for positive integer n

        udivisor_sigma(n, k) is equal to sum([x**k for x in udivisors(n)])

        If n’s prime factorization is:

        @@ -2043,7 +2045,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.legendre_symbol(a, p)[source]
        +class sympy.functions.combinatorial.numbers.legendre_symbol(a, p)[source]

        Returns the Legendre symbol \((a / p)\).

        For an integer a and an odd prime p, the Legendre symbol is defined as

        @@ -2071,7 +2073,7 @@
        Documentation Version
        -class sympy.functions.combinatorial.numbers.jacobi_symbol(m, n)[source]
        +class sympy.functions.combinatorial.numbers.jacobi_symbol(m, n)[source]

        Returns the Jacobi symbol \((m / n)\).

        For any integer m and any positive odd integer n the Jacobi symbol is defined as the product of the Legendre symbols corresponding to the @@ -2120,7 +2122,7 @@

        Documentation Version
        -class sympy.functions.combinatorial.numbers.kronecker_symbol(a, n)[source]
        +class sympy.functions.combinatorial.numbers.kronecker_symbol(a, n)[source]

        Returns the Kronecker symbol \((a / n)\).

        Examples

        >>> from sympy.functions.combinatorial.numbers import kronecker_symbol
@@ -2145,7 +2147,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.functions.combinatorial.numbers.mobius(n)[source]
        
+class sympy.functions.combinatorial.numbers.mobius(n)[source]
 
        Mobius function maps natural number to {-1, 0, 1}
        
 
        
 
        It is defined as follows:
          
@@ -2200,7 +2202,7 @@ 
          Documentation Version
          
 
 
          
 
          
-class sympy.functions.combinatorial.numbers.primenu(n)[source]
          
+class sympy.functions.combinatorial.numbers.primenu(n)[source]
 
          Calculate the number of distinct prime factors for a positive integer n.
          
 
          If n’s prime factorization is:
          
 
          
@@ -2239,7 +2241,7 @@ 
          Documentation Version
          
 
 
          
 
          
-class sympy.functions.combinatorial.numbers.primeomega(n)[source]
          
+class sympy.functions.combinatorial.numbers.primeomega(n)[source]
 
          Calculate the number of prime factors counting multiplicities for a
 positive integer n.
          
 
          If n’s prime factorization is:
          
@@ -2279,7 +2281,7 @@ 
          Documentation Version
          
 
 
          
 
          
-class sympy.functions.combinatorial.numbers.totient(n)[source]
          
+class sympy.functions.combinatorial.numbers.totient(n)[source]
 
          Calculate the Euler totient function phi(n)
          
 
          totient(n) or \(\phi(n)\) is the number of positive integers \(\leq\) n
 that are relatively prime to n.
          
@@ -2316,7 +2318,7 @@ 
          Documentation Version
          
 
 
          
 
          
-class sympy.functions.combinatorial.numbers.reduced_totient(n)[source]
          
+class sympy.functions.combinatorial.numbers.reduced_totient(n)[source]
 
          Calculate the Carmichael reduced totient function lambda(n)
          
 
          reduced_totient(n) or \(\lambda(n)\) is the smallest m > 0 such that
 \(k^m \equiv 1 \mod n\) for all k relatively prime to n.
          
@@ -2353,7 +2355,7 @@ 
          Documentation Version
          
 
 
          
 
          
-class sympy.functions.combinatorial.numbers.primepi(n)[source]
          
+class sympy.functions.combinatorial.numbers.primepi(n)[source]
 
          Represents the prime counting function pi(n) = the number
 of prime numbers less than or equal to n.
          
 
          Examples
          
@@ -2396,12 +2398,12 @@ 
          Documentation Version
          
 
 
          
 
          
-class sympy.functions.combinatorial.factorials.MultiFactorial(*args)[source]
          
+class sympy.functions.combinatorial.factorials.MultiFactorial(*args)[source]
 
          
 
 
          
 
          
-class sympy.functions.combinatorial.factorials.RisingFactorial(x, k)[source]
          
+class sympy.functions.combinatorial.factorials.RisingFactorial(x, k)[source]
 
          Rising factorial (also called Pochhammer symbol [R268]) is a double valued
 function arising in concrete mathematics, hypergeometric functions
 and series expansions. It is defined by:
          
@@ -2468,7 +2470,7 @@ 
          Documentation Version
          
 
 
          
 
          
-sympy.functions.combinatorial.numbers.stirling(n, k, d=None, kind=2, signed=False)[source]
          
+sympy.functions.combinatorial.numbers.stirling(n, k, d=None, kind=2, signed=False)[source]
 
          Return Stirling number \(S(n, k)\) of the first or second (default) kind.
          
 
          The sum of all Stirling numbers of the second kind for \(k = 1\)
 through \(n\) is bell(n). The recurrence relationship for these numbers
@@ -2576,7 +2578,7 @@ 
          Enumeration
 
          
-sympy.functions.combinatorial.numbers.nC(n, k=None, replacement=False)[source]
          
+sympy.functions.combinatorial.numbers.nC(n, k=None, replacement=False)[source]
 
          Return the number of combinations of n items taken k at a time.
          
 
          Possible values for n:
          
 
          
@@ -2642,7 +2644,7 @@ 
          Enumeration
 
          
-sympy.functions.combinatorial.numbers.nP(n, k=None, replacement=False)[source]
          
+sympy.functions.combinatorial.numbers.nP(n, k=None, replacement=False)[source]
 
          Return the number of permutations of n items taken k at a time.
          
 
          Possible values for n:
          
 
          
@@ -2700,7 +2702,7 @@ 
          Enumeration
 
          
-sympy.functions.combinatorial.numbers.nT(n, k=None)[source]
          
+sympy.functions.combinatorial.numbers.nT(n, k=None)[source]
 
          Return the number of k-sized partitions of n items.
          
 
          Possible values for n:
          
 
          
diff --git a/dev/modules/functions/elementary.html b/dev/modules/functions/elementary.html
index b54ed7fd246..d03b823c7de 100644
--- a/dev/modules/functions/elementary.html
+++ b/dev/modules/functions/elementary.html
@@ -329,18 +329,20 @@
 
        1. Linearized Carvallo-Whipple Bicycle Model
          2.
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -812,7 +814,7 @@
        Documentation Version
        **kwargs,
        -)[source] +)[source]

        An elliptical GeometryEntity.

        Parameters:
        @@ -928,7 +930,7 @@
        Documentation Version
        -arbitrary_point(parameter='t')[source]
        +arbitrary_point(parameter='t')[source]

        A parameterized point on the ellipse.

        Parameters:
        @@ -981,7 +983,7 @@
        Documentation Version
        -auxiliary_circle()[source]
        +auxiliary_circle()[source]

        Returns a Circle whose diameter is the major axis of the ellipse.

        Examples

        >>> from sympy import Ellipse, Point, symbols
@@ -1041,7 +1043,7 @@ 
        Documentation Version
        
 
 
        
 
        
-director_circle()[source]
        
+director_circle()[source]
 
        Returns a Circle consisting of all points where two perpendicular
 tangent lines to the ellipse cross each other.
        
 
        
@@ -1092,7 +1094,7 @@ 
        Documentation Version
        
 
 
        
 
        
-encloses_point(p)[source]
        
+encloses_point(p)[source]
 
        Return True if p is enclosed by (is inside of) self.
        
 
        
 
        Parameters:
        
@@ -1124,7 +1126,7 @@ 
        Documentation Version
        
 
 
        
 
        
-equation(x='x', y='y', _slope=None)[source]
        
+equation(x='x', y='y', _slope=None)[source]
 
        Returns the equation of an ellipse aligned with the x and y axes;
 when slope is given, the equation returned corresponds to an ellipse
 with a major axis having that slope.
        
@@ -1191,7 +1193,7 @@ 
        Documentation Version
        
 
 
        
 
        
-evolute(x='x', y='y')[source]
        
+evolute(x='x', y='y')[source]
 
        The equation of evolute of the ellipse.
        
 
        
 
        Parameters:
        
@@ -1298,7 +1300,7 @@ 
        Documentation Version
        
 
 
        
 
        
-intersection(o)[source]
        
+intersection(o)[source]
 
        The intersection of this ellipse and another geometrical entity
 \(o\).
        
 
        
@@ -1346,7 +1348,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_tangent(o)[source]
        
+is_tangent(o)[source]
 
        Is \(o\) tangent to the ellipse?
        
 
        
 
        Parameters:
        
@@ -1459,7 +1461,7 @@ 
        Documentation Version
        
 
 
        
 
        
-normal_lines(p, prec=None)[source]
        
+normal_lines(p, prec=None)[source]
 
        Normal lines between \(p\) and the ellipse.
        
 
        
 
        Parameters:
        
@@ -1521,7 +1523,7 @@ 
        Documentation Version
        
 
 
        
 
        
-plot_interval(parameter='t')[source]
        
+plot_interval(parameter='t')[source]
 
        The plot interval for the default geometric plot of the Ellipse.
        
 
        
 
        Parameters:
        
@@ -1548,7 +1550,7 @@ 
        Documentation Version
        
 
 
        
 
        
-polar_second_moment_of_area()[source]
        
+polar_second_moment_of_area()[source]
 
        Returns the polar second moment of area of an Ellipse
        
 
        It is a constituent of the second moment of area, linked through
 the perpendicular axis theorem. While the planar second moment of
@@ -1580,7 +1582,7 @@ 
        Documentation Version
        
 
 
        
 
        
-random_point(seed=None)[source]
        
+random_point(seed=None)[source]
 
        A random point on the ellipse.
        
 
        
 
        Returns:
        
@@ -1625,7 +1627,7 @@ 
        Documentation Version
        
 
 
        
 
        
-reflect(line)[source]
        
+reflect(line)[source]
 
        Override GeometryEntity.reflect since the radius
 is not a GeometryEntity.
        
 
        Examples
        
@@ -1650,7 +1652,7 @@ 
        Documentation Version
        
 
 
        
 
        
-rotate(angle=0, pt=None)[source]
        
+rotate(angle=0, pt=None)[source]
 
        Rotate angle radians counterclockwise about Point pt.
        
 
        Note: since the general ellipse is not supported, only rotations that
 are integer multiples of pi/2 are allowed.
        
@@ -1666,7 +1668,7 @@ 
        Documentation Version
        
 
 
        
 
        
-scale(x=1, y=1, pt=None)[source]
        
+scale(x=1, y=1, pt=None)[source]
 
        Override GeometryEntity.scale since it is the major and minor
 axes which must be scaled and they are not GeometryEntities.
        
 
        Examples
        
@@ -1681,7 +1683,7 @@ 
        Documentation Version
        
 
 
        
 
        
-second_moment_of_area(point=None)[source]
        
+second_moment_of_area(point=None)[source]
 
        Returns the second moment and product moment area of an ellipse.
        
 
        
 
        Parameters:
        
@@ -1719,7 +1721,7 @@ 
        Documentation Version
        
 
 
        
 
        
-section_modulus(point=None)[source]
        
+section_modulus(point=None)[source]
 
        Returns a tuple with the section modulus of an ellipse
        
 
        Section modulus is a geometric property of an ellipse defined as the
 ratio of second moment of area to the distance of the extreme end of
@@ -1808,7 +1810,7 @@ 
        Documentation Version
        
 
 
        
 
        
-tangent_lines(p)[source]
        
+tangent_lines(p)[source]
 
        Tangent lines between \(p\) and the ellipse.
        
 
        If \(p\) is on the ellipse, returns the tangent line through point \(p\).
 Otherwise, returns the tangent line(s) from \(p\) to the ellipse, or
@@ -1867,7 +1869,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.ellipse.Circle(*args, **kwargs)[source]
        
+class sympy.geometry.ellipse.Circle(*args, **kwargs)[source]
 
        A circle in space.
        
 
        Constructed simply from a center and a radius, from three
 non-collinear points, or the equation of a circle.
        
@@ -1955,7 +1957,7 @@ 
        Documentation Version
        
 
 
        
 
        
-equation(x='x', y='y')[source]
        
+equation(x='x', y='y')[source]
 
        The equation of the circle.
        
 
        
 
        Parameters:
        
@@ -1983,7 +1985,7 @@ 
        Documentation Version
        
 
 
        
 
        
-intersection(o)[source]
        
+intersection(o)[source]
 
        The intersection of this circle with another geometrical entity.
        
 
        
 
        Parameters:
        
@@ -2034,7 +2036,7 @@ 
        Documentation Version
        
 
 
        
 
        
-reflect(line)[source]
        
+reflect(line)[source]
 
        Override GeometryEntity.reflect since the radius
 is not a GeometryEntity.
        
 
        Examples
        
@@ -2047,7 +2049,7 @@ 
        Documentation Version
        
 
 
        
 
        
-scale(x=1, y=1, pt=None)[source]
        
+scale(x=1, y=1, pt=None)[source]
 
        Override GeometryEntity.scale since the radius
 is not a GeometryEntity.
        
 
        Examples
        
diff --git a/dev/modules/geometry/entities.html b/dev/modules/geometry/entities.html
index 3a73b5ffa50..578488c4fac 100644
--- a/dev/modules/geometry/entities.html
+++ b/dev/modules/geometry/entities.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Entities

        -class sympy.geometry.entity.GeometryEntity(*args, **kwargs)[source]
        +class sympy.geometry.entity.GeometryEntity(*args, **kwargs)[source]

        The base class for all geometrical entities.

        This class does not represent any particular geometric entity, it only provides the implementation of some methods common to all subclasses.

        @@ -821,7 +823,7 @@
        Documentation Version
        -encloses(o)[source]
        +encloses(o)[source]

        Return True if o is inside (not on or outside) the boundaries of self.

        The object will be decomposed into Points and individual Entities need only define an encloses_point method for their class.

        @@ -843,7 +845,7 @@
        Documentation Version
        -intersection(o)[source]
        +intersection(o)[source]

        Returns a list of all of the intersections of self with o.

        Notes

        An entity is not required to implement this method.

        @@ -858,7 +860,7 @@
        Documentation Version
        -is_similar(other)[source]
        +is_similar(other)[source]

        Is this geometrical entity similar to another geometrical entity?

        Two entities are similar if a uniform scaling (enlarging or shrinking) of one of the entities will allow one to obtain the other.

        @@ -876,7 +878,7 @@
        Documentation Version
        -parameter_value(other, t)[source]
        +parameter_value(other, t)[source]

        Return the parameter corresponding to the given point. Evaluating an arbitrary point of the entity at this parameter value will return the given point.

        @@ -895,7 +897,7 @@
        Documentation Version
        -reflect(line)[source]
        +reflect(line)[source]

        Reflects an object across a line.

        Parameters:
        @@ -923,7 +925,7 @@
        Documentation Version
        -rotate(angle, pt=None)[source]
        +rotate(angle, pt=None)[source]

        Rotate angle radians counterclockwise about Point pt.

        The default pt is the origin, Point(0, 0)

        Examples

        @@ -943,7 +945,7 @@
        Documentation Version
        -scale(x=1, y=1, pt=None)[source]
        +scale(x=1, y=1, pt=None)[source]

        Scale the object by multiplying the x,y-coordinates by x and y.

        If pt is given, the scaling is done relative to that point; the object is shifted by -pt, scaled, and shifted by pt.

        @@ -966,7 +968,7 @@
        Documentation Version
        -translate(x=0, y=0)[source]
        +translate(x=0, y=0)[source]

        Shift the object by adding to the x,y-coordinates the values x and y.

        Examples

        >>> from sympy import RegularPolygon, Point, Polygon
diff --git a/dev/modules/geometry/index.html b/dev/modules/geometry/index.html
index 9919d81f7af..dc4dfbd5d10 100644
--- a/dev/modules/geometry/index.html
+++ b/dev/modules/geometry/index.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Lines

        -class sympy.geometry.line.LinearEntity(p1, p2=None, **kwargs)[source]
        +class sympy.geometry.line.LinearEntity(p1, p2=None, **kwargs)[source]

        A base class for all linear entities (Line, Ray and Segment) in n-dimensional Euclidean space.

        Notes

        @@ -868,7 +870,7 @@
        Documentation Version
        -angle_between(l2)[source]
        +angle_between(l2)[source]

        Return the non-reflex angle formed by rays emanating from the origin with directions the same as the direction vectors of the linear entities.

        @@ -923,7 +925,7 @@
        Documentation Version
        -arbitrary_point(parameter='t')[source]
        +arbitrary_point(parameter='t')[source]

        A parameterized point on the Line.

        Parameters:
        @@ -966,7 +968,7 @@
        Documentation Version
        -static are_concurrent(*lines)[source]
        +static are_concurrent(*lines)[source]

        Is a sequence of linear entities concurrent?

        Two or more linear entities are concurrent if they all intersect at a single point.

        @@ -1011,7 +1013,7 @@
        Documentation Version
        -bisectors(other)[source]
        +bisectors(other)[source]

        Returns the perpendicular lines which pass through the intersections of self and other that are in the same plane.

        @@ -1034,7 +1036,7 @@
        Documentation Version
        -contains(other)[source]
        +contains(other)[source]

        Subclasses should implement this method and should return True if other is on the boundaries of self; False if not on the boundaries of self; @@ -1075,7 +1077,7 @@

        Documentation Version
        -intersection(other)[source]
        +intersection(other)[source]

        The intersection with another geometrical entity.

        Parameters:
        @@ -1122,7 +1124,7 @@
        Documentation Version
        -is_parallel(l2)[source]
        +is_parallel(l2)[source]

        Are two linear entities parallel?

        Parameters:
        @@ -1165,7 +1167,7 @@
        Documentation Version
        -is_perpendicular(l2)[source]
        +is_perpendicular(l2)[source]

        Are two linear entities perpendicular?

        Parameters:
        @@ -1206,7 +1208,7 @@
        Documentation Version
        -is_similar(other)[source]
        +is_similar(other)[source]

        Return True if self and other are contained in the same line.

        Examples

        >>> from sympy import Point, Line
@@ -1271,7 +1273,7 @@ 
        Documentation Version
        
 
 
        
 
        
-parallel_line(p)[source]
        
+parallel_line(p)[source]
 
        Create a new Line parallel to this linear entity which passes
 through the point \(p\).
        
 
        
@@ -1309,7 +1311,7 @@ 
        Documentation Version
        
 
 
        
 
        
-perpendicular_line(p)[source]
        
+perpendicular_line(p)[source]
 
        Create a new Line perpendicular to this linear entity which passes
 through the point \(p\).
        
 
        
@@ -1345,7 +1347,7 @@ 
        Documentation Version
        
 
 
        
 
        
-perpendicular_segment(p)[source]
        
+perpendicular_segment(p)[source]
 
        Create a perpendicular line segment from \(p\) to this line.
        
 
        The endpoints of the segment are p and the closest point in
 the line containing self. (If self is not a line, the point might
@@ -1414,7 +1416,7 @@ 
        Documentation Version
        
 
 
        
 
        
-projection(other)[source]
        
+projection(other)[source]
 
        Project a point, line, ray, or segment onto this linear entity.
        
 
        
 
        Parameters:
        
@@ -1469,7 +1471,7 @@ 
        Documentation Version
        
 
 
        
 
        
-random_point(seed=None)[source]
        
+random_point(seed=None)[source]
 
        A random point on a LinearEntity.
        
 
        
 
        Returns:
        
@@ -1499,7 +1501,7 @@ 
        Documentation Version
        
 
 
        
 
        
-smallest_angle_between(l2)[source]
        
+smallest_angle_between(l2)[source]
 
        Return the smallest angle formed at the intersection of the
 lines containing the linear entities.
        
 
        
@@ -1529,7 +1531,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.line.Line(*args, **kwargs)[source]
        
+class sympy.geometry.line.Line(*args, **kwargs)[source]
 
        An infinite line in space.
        
 
        A 2D line is declared with two distinct points, point and slope, or
 an equation. A 3D line may be defined with a point and a direction ratio.
        
@@ -1594,7 +1596,7 @@ 
        Documentation Version
        -contains(other)[source]
        +contains(other)[source]

        Return True if \(other\) is on this Line, or False otherwise.

        Examples

        >>> from sympy import Line,Point
@@ -1621,7 +1623,7 @@ 
        Documentation Version
        
 
 
        
 
        
-distance(other)[source]
        
+distance(other)[source]
 
        Finds the shortest distance between a line and a point.
        
 
        
 
        Raises:
        
@@ -1648,13 +1650,13 @@ 
        Documentation Version
        
 
 
        
 
        
-equals(other)[source]
        
+equals(other)[source]
 
        Returns True if self and other are the same mathematical entities
        
 
        
 
 
        
 
        
-plot_interval(parameter='t')[source]
        
+plot_interval(parameter='t')[source]
 
        The plot interval for the default geometric plot of line. Gives
 values that will produce a line that is +/- 5 units long (where a
 unit is the distance between the two points that define the line).
        
@@ -1686,7 +1688,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.line.Ray(p1, p2=None, **kwargs)[source]
        
+class sympy.geometry.line.Ray(p1, p2=None, **kwargs)[source]
 
        A Ray is a semi-line in the space with a source point and a direction.
        
 
        
 
        Parameters:
        
@@ -1740,7 +1742,7 @@ 
        Documentation Version
        -contains(other)[source]
        +contains(other)[source]

        Is other GeometryEntity contained in this Ray?

        Examples

        >>> from sympy import Ray,Point,Segment
@@ -1770,7 +1772,7 @@ 
        Documentation Version
        
 
 
        
 
        
-distance(other)[source]
        
+distance(other)[source]
 
        Finds the shortest distance between the ray and a point.
        
 
        
 
        Raises:
        
@@ -1799,13 +1801,13 @@ 
        Documentation Version
        
 
 
        
 
        
-equals(other)[source]
        
+equals(other)[source]
 
        Returns True if self and other are the same mathematical entities
        
 
        
 
 
        
 
        
-plot_interval(parameter='t')[source]
        
+plot_interval(parameter='t')[source]
 
        The plot interval for the default geometric plot of the Ray. Gives
 values that will produce a ray that is 10 units long (where a unit is
 the distance between the two points that define the ray).
        
@@ -1858,7 +1860,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.line.Segment(p1, p2, **kwargs)[source]
        
+class sympy.geometry.line.Segment(p1, p2, **kwargs)[source]
 
        A line segment in space.
        
 
        
 
        Parameters:
        
@@ -1913,7 +1915,7 @@ 
        Documentation Version
        -contains(other)[source]
        +contains(other)[source]

        Is the other GeometryEntity contained within this Segment?

        Examples

        >>> from sympy import Point, Segment
@@ -1936,7 +1938,7 @@ 
        Documentation Version
        
 
 
        
 
        
-distance(other)[source]
        
+distance(other)[source]
 
        Finds the shortest distance between a line segment and a point.
        
 
        
 
        Raises:
        
@@ -1964,7 +1966,7 @@ 
        Documentation Version
        
 
 
        
 
        
-equals(other)[source]
        
+equals(other)[source]
 
        Returns True if self and other are the same mathematical entities
        
 
        
 
@@ -2016,7 +2018,7 @@ 
        Documentation Version
        
 
 
        
 
        
-perpendicular_bisector(p=None)[source]
        
+perpendicular_bisector(p=None)[source]
 
        The perpendicular bisector of this segment.
        
 
        If no point is specified or the point specified is not on the
 bisector then the bisector is returned as a Line. Otherwise a
@@ -2050,7 +2052,7 @@ 
        Documentation Version
        
 
 
        
 
        
-plot_interval(parameter='t')[source]
        
+plot_interval(parameter='t')[source]
 
        The plot interval for the default geometric plot of the Segment gives
 values that will produce the full segment in a plot.
        
 
        
@@ -2081,7 +2083,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.line.LinearEntity2D(p1, p2=None, **kwargs)[source]
        
+class sympy.geometry.line.LinearEntity2D(p1, p2=None, **kwargs)[source]
 
        A base class for all linear entities (line, ray and segment)
 in a 2-dimensional Euclidean space.
        
 
        Notes
        
@@ -2121,7 +2123,7 @@ 
        Documentation Version
        
 
 
        
 
        
-perpendicular_line(p)[source]
        
+perpendicular_line(p)[source]
 
        Create a new Line perpendicular to this linear entity which passes
 through the point \(p\).
        
 
        
@@ -2190,7 +2192,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.line.Line2D(p1, pt=None, slope=None, **kwargs)[source]
        
+class sympy.geometry.line.Line2D(p1, pt=None, slope=None, **kwargs)[source]
 
        An infinite line in space 2D.
        
 
        A line is declared with two distinct points or a point and slope
 as defined using keyword \(slope\).
        
@@ -2256,7 +2258,7 @@ 
        Documentation Version
        
 
 
        
 
        
-equation(x='x', y='y')[source]
        
+equation(x='x', y='y')[source]
 
        The equation of the line: ax + by + c.
        
 
        
 
        Parameters:
        
@@ -2291,7 +2293,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.line.Ray2D(p1, pt=None, angle=None, **kwargs)[source]
        
+class sympy.geometry.line.Ray2D(p1, pt=None, angle=None, **kwargs)[source]
 
        A Ray is a semi-line in the space with a source point and a direction.
        
 
        
 
        Parameters:
        
@@ -2348,7 +2350,7 @@ 
        Documentation Version
        -closing_angle(r2)[source]
        +closing_angle(r2)[source]

        Return the angle by which r2 must be rotated so it faces the same direction as r1.

        @@ -2428,7 +2430,7 @@
        Documentation Version
        -class sympy.geometry.line.Segment2D(p1, p2, **kwargs)[source]
        +class sympy.geometry.line.Segment2D(p1, p2, **kwargs)[source]

        A line segment in 2D space.

        Parameters:
        @@ -2473,7 +2475,7 @@
        Documentation Version
        -class sympy.geometry.line.LinearEntity3D(p1, p2, **kwargs)[source]
        +class sympy.geometry.line.LinearEntity3D(p1, p2, **kwargs)[source]

        An base class for all linear entities (line, ray and segment) in a 3-dimensional Euclidean space.

        Notes

        @@ -2542,7 +2544,7 @@
        Documentation Version
        -class sympy.geometry.line.Line3D(p1, pt=None, direction_ratio=(), **kwargs)[source]
        +class sympy.geometry.line.Line3D(p1, pt=None, direction_ratio=(), **kwargs)[source]

        An infinite 3D line in space.

        A line is declared with two distinct points or a point and direction_ratio as defined using keyword \(direction_ratio\).

        @@ -2568,7 +2570,7 @@
        Documentation Version
        -distance(other)[source]
        +distance(other)[source]

        Finds the shortest distance between a line and another object.

        Parameters:
        @@ -2604,7 +2606,7 @@
        Documentation Version
        -equation(x='x', y='y', z='z')[source]
        +equation(x='x', y='y', z='z')[source]

        Return the equations that define the line in 3D.

        Parameters:
        @@ -2642,7 +2644,7 @@
        Documentation Version
        -class sympy.geometry.line.Ray3D(p1, pt=None, direction_ratio=(), **kwargs)[source]
        +class sympy.geometry.line.Ray3D(p1, pt=None, direction_ratio=(), **kwargs)[source]

        A Ray is a semi-line in the space with a source point and a direction.

        Parameters:
        @@ -2769,7 +2771,7 @@
        Documentation Version
        -class sympy.geometry.line.Segment3D(p1, p2, **kwargs)[source]
        +class sympy.geometry.line.Segment3D(p1, p2, **kwargs)[source]

        A line segment in a 3D space.

        Parameters:
        diff --git a/dev/modules/geometry/plane.html b/dev/modules/geometry/plane.html index 1a061a9a585..06bc3fd100f 100644 --- a/dev/modules/geometry/plane.html +++ b/dev/modules/geometry/plane.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Plane

        -class sympy.geometry.plane.Plane(p1, a=None, b=None, **kwargs)[source]
        +class sympy.geometry.plane.Plane(p1, a=None, b=None, **kwargs)[source]

        A plane is a flat, two-dimensional surface. A plane is the two-dimensional analogue of a point (zero-dimensions), a line (one-dimension) and a solid (three-dimensions). A plane can generally be constructed by two types of @@ -834,7 +836,7 @@

        Documentation Version
        -angle_between(o)[source]
        +angle_between(o)[source]

        Angle between the plane and other geometric entity.

        Parameters:
        @@ -861,7 +863,7 @@
        Documentation Version
        -arbitrary_point(u=None, v=None)[source]
        +arbitrary_point(u=None, v=None)[source]

        Returns an arbitrary point on the Plane. If given two parameters, the point ranges over the entire plane. If given 1 or no parameters, returns a point with one parameter which, @@ -894,7 +896,7 @@

        Documentation Version
        -static are_concurrent(*planes)[source]
        +static are_concurrent(*planes)[source]

        Is a sequence of Planes concurrent?

        Two or more Planes are concurrent if their intersections are a common line.

        @@ -921,7 +923,7 @@
        Documentation Version
        -distance(o)[source]
        +distance(o)[source]

        Distance between the plane and another geometric entity.

        Parameters:
        @@ -951,7 +953,7 @@
        Documentation Version
        -equals(o)[source]
        +equals(o)[source]

        Returns True if self and o are the same mathematical entities.

        Examples

        >>> from sympy import Plane, Point3D
@@ -970,7 +972,7 @@ 
        Documentation Version
        
 
 
        
 
        
-equation(x=None, y=None, z=None)[source]
        
+equation(x=None, y=None, z=None)[source]
 
        The equation of the Plane.
        
 
        Examples
        
 
        >>> from sympy import Point3D, Plane
@@ -986,7 +988,7 @@ 
        Documentation Version
        
 
 
        
 
        
-intersection(o)[source]
        
+intersection(o)[source]
 
        The intersection with other geometrical entity.
        
 
        
 
        Parameters:
        
@@ -1015,7 +1017,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_coplanar(o)[source]
        
+is_coplanar(o)[source]
 
        Returns True if \(o\) is coplanar with self, else False.
        
 
        Examples
        
 
        >>> from sympy import Plane
@@ -1032,7 +1034,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_parallel(l)[source]
        
+is_parallel(l)[source]
 
        Is the given geometric entity parallel to the plane?
        
 
        
 
        Parameters:
        
@@ -1054,7 +1056,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_perpendicular(l)[source]
        
+is_perpendicular(l)[source]
 
        Is the given geometric entity perpendicualar to the given plane?
        
 
        
 
        Parameters:
        
@@ -1110,7 +1112,7 @@ 
        Documentation Version
        
 
 
        
 
        
-parallel_plane(pt)[source]
        
+parallel_plane(pt)[source]
 
        Plane parallel to the given plane and passing through the point pt.
        
 
        
 
        Parameters:
        
@@ -1131,7 +1133,7 @@ 
        Documentation Version
        
 
 
        
 
        
-parameter_value(other, u, v=None)[source]
        
+parameter_value(other, u, v=None)[source]
 
        Return the parameter(s) corresponding to the given point.
        
 
        Examples
        
 
        >>> from sympy import pi, Plane
@@ -1171,7 +1173,7 @@ 
        Documentation Version
        
 
 
        
 
        
-perpendicular_line(pt)[source]
        
+perpendicular_line(pt)[source]
 
        A line perpendicular to the given plane.
        
 
        
 
        Parameters:
        
@@ -1192,7 +1194,7 @@ 
        Documentation Version
        
 
 
        
 
        
-perpendicular_plane(*pts)[source]
        
+perpendicular_plane(*pts)[source]
 
        Return a perpendicular passing through the given points. If the
 direction ratio between the points is the same as the Plane’s normal
 vector then, to select from the infinite number of possible planes,
@@ -1224,7 +1226,7 @@ 
        Documentation Version
        
 
 
        
 
        
-projection(pt)[source]
        
+projection(pt)[source]
 
        Project the given point onto the plane along the plane normal.
        
 
        
 
        Parameters:
        
@@ -1258,7 +1260,7 @@ 
        Documentation Version
        
 
 
        
 
        
-projection_line(line)[source]
        
+projection_line(line)[source]
 
        Project the given line onto the plane through the normal plane
 containing the line.
        
 
        
@@ -1290,7 +1292,7 @@ 
        Documentation Version
        
 
 
        
 
        
-random_point(seed=None)[source]
        
+random_point(seed=None)[source]
 
        Returns a random point on the Plane.
        
 
        
 
        Returns:
        
diff --git a/dev/modules/geometry/points.html b/dev/modules/geometry/points.html
index 7888418200d..29709ad3c9c 100644
--- a/dev/modules/geometry/points.html
+++ b/dev/modules/geometry/points.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Points

        -class sympy.geometry.point.Point(*args, **kwargs)[source]
        +class sympy.geometry.point.Point(*args, **kwargs)[source]

        A point in a n-dimensional Euclidean space.

        Parameters:
        @@ -880,7 +882,7 @@
        Documentation Version
        -static affine_rank(*args)[source]
        +static affine_rank(*args)[source]

        The affine rank of a set of points is the dimension of the smallest affine space containing all the points. For example, if the points lie on a line (and are not all @@ -897,7 +899,7 @@

        Documentation Version
        -classmethod are_coplanar(*points)[source]
        +classmethod are_coplanar(*points)[source]

        Return True if there exists a plane in which all the points lie. A trivial True value is returned if \(len(points) < 3\) or all Points are 2-dimensional.

        @@ -929,7 +931,7 @@
        Documentation Version
        -canberra_distance(p)[source]
        +canberra_distance(p)[source]

        The Canberra Distance from self to point p.

        Returns the weighted sum of horizontal and vertical distances to point p.

        @@ -964,7 +966,7 @@
        Documentation Version
        -distance(other)[source]
        +distance(other)[source]

        The Euclidean distance between self and another GeometricEntity.

        Returns:
        @@ -1002,19 +1004,19 @@
        Documentation Version
        -dot(p)[source]
        +dot(p)[source]

        Return dot product of self with another Point.

        -equals(other)[source]
        +equals(other)[source]

        Returns whether the coordinates of self and other agree.

        -intersection(other)[source]
        +intersection(other)[source]

        The intersection between this point and another GeometryEntity.

        Parameters:
        @@ -1040,7 +1042,7 @@
        Documentation Version
        -is_collinear(*args)[source]
        +is_collinear(*args)[source]

        Returns \(True\) if there exists a line that contains \(self\) and \(points\). Returns \(False\) otherwise. A trivially True value is returned if no points are given.

        @@ -1071,7 +1073,7 @@
        Documentation Version
        -is_concyclic(*args)[source]
        +is_concyclic(*args)[source]

        Do \(self\) and the given sequence of points lie in a circle?

        Returns True if the set of points are concyclic and False otherwise. A trivial value of True is returned @@ -1115,7 +1117,7 @@

        Documentation Version
        -is_scalar_multiple(p)[source]
        +is_scalar_multiple(p)[source]

        Returns whether each coordinate of \(self\) is a scalar multiple of the corresponding coordinate in point p.

        @@ -1142,7 +1144,7 @@
        Documentation Version
        -midpoint(p)[source]
        +midpoint(p)[source]

        The midpoint between self and point p.

        Parameters:
        @@ -1191,7 +1193,7 @@
        Documentation Version
        -static project(a, b)[source]
        +static project(a, b)[source]

        Project the point \(a\) onto the line between the origin and point \(b\) along the normal direction.

        @@ -1223,7 +1225,7 @@
        Documentation Version
        -taxicab_distance(p)[source]
        +taxicab_distance(p)[source]

        The Taxicab Distance from self to point p.

        Returns the sum of the horizontal and vertical distances to point p.

        @@ -1259,7 +1261,7 @@
        Documentation Version
        -class sympy.geometry.point.Point2D(*args, _nocheck=False, **kwargs)[source]
        +class sympy.geometry.point.Point2D(*args, _nocheck=False, **kwargs)[source]

        A point in a 2-dimensional Euclidean space.

        Parameters:
        @@ -1341,7 +1343,7 @@
        Documentation Version
        -rotate(angle, pt=None)[source]
        +rotate(angle, pt=None)[source]

        Rotate angle radians counterclockwise about Point pt.

        Examples

        >>> from sympy import Point2D, pi
@@ -1360,7 +1362,7 @@ 
        Documentation Version
        
 
 
        
 
        
-scale(x=1, y=1, pt=None)[source]
        
+scale(x=1, y=1, pt=None)[source]
 
        Scale the coordinates of the Point by multiplying by
 x and y after subtracting pt – default is (0, 0) –
 and then adding pt back again (i.e. pt is the point of
@@ -1382,7 +1384,7 @@ 
        Documentation Version
        
 
 
        
 
        
-transform(matrix)[source]
        
+transform(matrix)[source]
 
        Return the point after applying the transformation described
 by the 3x3 Matrix, matrix.
        
 
        
@@ -1393,7 +1395,7 @@ 
        Documentation Version
        
 
 
        
 
        
-translate(x=0, y=0)[source]
        
+translate(x=0, y=0)[source]
 
        Shift the Point by adding x and y to the coordinates of the Point.
        
 
        Examples
        
 
        >>> from sympy import Point2D
@@ -1442,7 +1444,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.point.Point3D(*args, _nocheck=False, **kwargs)[source]
        
+class sympy.geometry.point.Point3D(*args, _nocheck=False, **kwargs)[source]
 
        A point in a 3-dimensional Euclidean space.
        
 
        
 
        Parameters:
        
@@ -1499,7 +1501,7 @@ 
        Documentation Version
        
 
        
 
        
 
        
-static are_collinear(*points)[source]
        
+static are_collinear(*points)[source]
 
        Is a sequence of points collinear?
        
 
        Test whether or not a set of points are collinear. Returns True if
 the set of points are collinear, or False otherwise.
        
@@ -1543,7 +1545,7 @@ 
        Documentation Version
        
 
 
        
 
        
-direction_cosine(point)[source]
        
+direction_cosine(point)[source]
 
        Gives the direction cosine between 2 points
        
 
        
 
        Parameters:
        
@@ -1564,7 +1566,7 @@ 
        Documentation Version
        
 
 
        
 
        
-direction_ratio(point)[source]
        
+direction_ratio(point)[source]
 
        Gives the direction ratio between 2 points
        
 
        
 
        Parameters:
        
@@ -1585,7 +1587,7 @@ 
        Documentation Version
        
 
 
        
 
        
-intersection(other)[source]
        
+intersection(other)[source]
 
        The intersection between this point and another GeometryEntity.
        
 
        
 
        Parameters:
        
@@ -1611,7 +1613,7 @@ 
        Documentation Version
        
 
 
        
 
        
-scale(x=1, y=1, z=1, pt=None)[source]
        
+scale(x=1, y=1, z=1, pt=None)[source]
 
        Scale the coordinates of the Point by multiplying by
 x and y after subtracting pt – default is (0, 0) –
 and then adding pt back again (i.e. pt is the point of
@@ -1633,7 +1635,7 @@ 
        Documentation Version
        
 
 
        
 
        
-transform(matrix)[source]
        
+transform(matrix)[source]
 
        Return the point after applying the transformation described
 by the 4x4 Matrix, matrix.
        
 
        
@@ -1644,7 +1646,7 @@ 
        Documentation Version
        
 
 
        
 
        
-translate(x=0, y=0, z=0)[source]
        
+translate(x=0, y=0, z=0)[source]
 
        Shift the Point by adding x and y to the coordinates of the Point.
        
 
        Examples
        
 
        >>> from sympy import Point3D
diff --git a/dev/modules/geometry/polygons.html b/dev/modules/geometry/polygons.html
index 2ac35372cf9..388255ad1f2 100644
--- a/dev/modules/geometry/polygons.html
+++ b/dev/modules/geometry/polygons.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Polygons

        -class sympy.geometry.polygon.Polygon(*args, n=0, **kwargs)[source]
        +class sympy.geometry.polygon.Polygon(*args, n=0, **kwargs)[source]

        A two-dimensional polygon.

        A simple polygon in space. Can be constructed from a sequence of points or from a center, radius, number of sides and rotation angle.

        @@ -933,7 +935,7 @@
        Documentation Version
        -arbitrary_point(parameter='t')[source]
        +arbitrary_point(parameter='t')[source]

        A parameterized point on the polygon.

        The parameter, varying from 0 to 1, assigns points to the position on the perimeter that is that fraction of the total perimeter. So the @@ -1011,7 +1013,7 @@

        Documentation Version
        -bisectors(prec=None)[source]
        +bisectors(prec=None)[source]

        Returns angle bisectors of a polygon. If prec is given then approximate the point defining the ray to that precision.

        The distance between the points defining the bisector ray is 1.

        @@ -1059,7 +1061,7 @@
        Documentation Version
        -cut_section(line)[source]
        +cut_section(line)[source]

        Returns a tuple of two polygon segments that lie above and below the intersecting line respectively.

        @@ -1112,7 +1114,7 @@
        Documentation Version
        -distance(o)[source]
        +distance(o)[source]

        Returns the shortest distance between self and o.

        If o is a point, then self does not need to be convex. If o is another polygon self and o must be convex.

        @@ -1128,7 +1130,7 @@
        Documentation Version
        -encloses_point(p)[source]
        +encloses_point(p)[source]

        Return True if p is enclosed by (is inside of) self.

        Parameters:
        @@ -1166,7 +1168,7 @@
        Documentation Version
        -first_moment_of_area(point=None)[source]
        +first_moment_of_area(point=None)[source]

        Returns the first moment of area of a two-dimensional polygon with respect to a certain point of interest.

        First moment of area is a measure of the distribution of the area @@ -1221,7 +1223,7 @@

        Documentation Version
        -intersection(o)[source]
        +intersection(o)[source]

        The intersection of polygon and geometry entity.

        The intersection may be empty and can contain individual Points and complete Line Segments.

        @@ -1258,7 +1260,7 @@
        Documentation Version
        -is_convex()[source]
        +is_convex()[source]

        Is the polygon convex?

        A polygon is convex if all its interior angles are less than 180 degrees and there are no intersections between sides.

        @@ -1309,7 +1311,7 @@
        Documentation Version
        -plot_interval(parameter='t')[source]
        +plot_interval(parameter='t')[source]

        The plot interval for the default geometric plot of the polygon.

        Parameters:
        @@ -1336,7 +1338,7 @@
        Documentation Version
        -polar_second_moment_of_area()[source]
        +polar_second_moment_of_area()[source]

        Returns the polar modulus of a two-dimensional polygon

        It is a constituent of the second moment of area, linked through the perpendicular axis theorem. While the planar second moment of @@ -1365,7 +1367,7 @@

        Documentation Version
        -second_moment_of_area(point=None)[source]
        +second_moment_of_area(point=None)[source]

        Returns the second moment and product moment of area of a two dimensional polygon.

        Parameters:
        @@ -1406,7 +1408,7 @@
        Documentation Version
        -section_modulus(point=None)[source]
        +section_modulus(point=None)[source]

        Returns a tuple with the section modulus of a two-dimensional polygon.

        Section modulus is a geometric property of a polygon defined as the @@ -1512,7 +1514,7 @@

        Documentation Version
        -class sympy.geometry.polygon.RegularPolygon(c, r, n, rot=0, **kwargs)[source]
        +class sympy.geometry.polygon.RegularPolygon(c, r, n, rot=0, **kwargs)[source]

        A regular polygon.

        Such a polygon has all internal angles equal and all sides the same length.

        @@ -1758,7 +1760,7 @@
        Documentation Version
        -encloses_point(p)[source]
        +encloses_point(p)[source]

        Return True if p is enclosed by (is inside of) self.

        Parameters:
        @@ -1923,7 +1925,7 @@
        Documentation Version
        -reflect(line)[source]
        +reflect(line)[source]

        Override GeometryEntity.reflect since this is not made of only points.

        Examples

        @@ -1938,7 +1940,7 @@
        Documentation Version
        -rotate(angle, pt=None)[source]
        +rotate(angle, pt=None)[source]

        Override GeometryEntity.rotate to first rotate the RegularPolygon about its center.

        >>> from sympy import Point, RegularPolygon, pi
@@ -1987,7 +1989,7 @@ 
        Documentation Version
        
 
 
        
 
        
-scale(x=1, y=1, pt=None)[source]
        
+scale(x=1, y=1, pt=None)[source]
 
        Override GeometryEntity.scale since it is the radius that must be
 scaled (if x == y) or else a new Polygon must be returned.
        
 
        >>> from sympy import RegularPolygon
@@ -2007,7 +2009,7 @@ 
        Documentation Version
        
 
 
        
 
        
-spin(angle)[source]
        
+spin(angle)[source]
 
        Increment in place the virtual Polygon’s rotation by ccw angle.
        
 
        See also: rotate method which moves the center.
        
 
        >>> from sympy import Polygon, Point, pi
@@ -2058,7 +2060,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.geometry.polygon.Triangle(*args, **kwargs)[source]
        
+class sympy.geometry.polygon.Triangle(*args, **kwargs)[source]
 
        A polygon with three vertices and three sides.
        
 
        
 
        Parameters:
        
@@ -2169,7 +2171,7 @@ 
        Documentation Version
        
 
 
        
 
        
-bisectors()[source]
        
+bisectors()[source]
 
        The angle bisectors of the triangle.
        
 
        An angle bisector of a triangle is a straight line through a vertex
 which cuts the corresponding angle in half.
        
@@ -2441,7 +2443,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_equilateral()[source]
        
+is_equilateral()[source]
 
        Are all the sides the same length?
        
 
        
 
        Returns:
        
@@ -2469,7 +2471,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_isosceles()[source]
        
+is_isosceles()[source]
 
        Are two or more of the sides the same length?
        
 
        
 
        Returns:
        
@@ -2491,7 +2493,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_right()[source]
        
+is_right()[source]
 
        Is the triangle right-angled.
        
 
        
 
        Returns:
        
@@ -2513,7 +2515,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_scalene()[source]
        
+is_scalene()[source]
 
        Are all the sides of the triangle of different lengths?
        
 
        
 
        Returns:
        
@@ -2535,7 +2537,7 @@ 
        Documentation Version
        
 
 
        
 
        
-is_similar(t2)[source]
        
+is_similar(t2)[source]
 
        Is another triangle similar to this one.
        
 
        Two triangles are similar if one can be uniformly scaled to the other.
        
 
        
diff --git a/dev/modules/geometry/utils.html b/dev/modules/geometry/utils.html
index 7af8a07d34f..5a557911e44 100644
--- a/dev/modules/geometry/utils.html
+++ b/dev/modules/geometry/utils.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Utils

        -sympy.geometry.util.intersection(*entities, pairwise=False, **kwargs)[source]
        +sympy.geometry.util.intersection(*entities, pairwise=False, **kwargs)[source]

        The intersection of a collection of GeometryEntity instances.

        Parameters:
        @@ -859,7 +861,7 @@
        Documentation Version
        -sympy.geometry.util.convex_hull(*args, polygon=True)[source]
        +sympy.geometry.util.convex_hull(*args, polygon=True)[source]

        The convex hull surrounding the Points contained in the list of entities.

        Parameters:
        @@ -912,7 +914,7 @@
        Documentation Version
        -sympy.geometry.util.are_similar(e1, e2)[source]
        +sympy.geometry.util.are_similar(e1, e2)[source]

        Are two geometrical entities similar.

        Can one geometrical entity be uniformly scaled to the other?

        @@ -952,7 +954,7 @@
        Documentation Version
        -sympy.geometry.util.centroid(*args)[source]
        +sympy.geometry.util.centroid(*args)[source]

        Find the centroid (center of mass) of the collection containing only Points, Segments or Polygons. The centroid is the weighted average of the individual centroid where the weights are the lengths (of segments) or areas (of polygons). @@ -998,7 +1000,7 @@

        Documentation Version
        -sympy.geometry.util.idiff(eq, y, x, n=1)[source]
        +sympy.geometry.util.idiff(eq, y, x, n=1)[source]

        Return dy/dx assuming that eq == 0.

        Parameters:
        diff --git a/dev/modules/holonomic/about.html b/dev/modules/holonomic/about.html index e06f0acbee8..b461d0d7e9e 100644 --- a/dev/modules/holonomic/about.html +++ b/dev/modules/holonomic/about.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -841,7 +843,7 @@

        Integration and Differentiationinitcond=False, -)[source] +)[source]

        Integrates the given holonomic function.

        Examples

        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
@@ -859,7 +861,7 @@ 
        Integration and Differentiation
 
        
-HolonomicFunction.diff(*args, **kwargs)[source]
        
+HolonomicFunction.diff(*args, **kwargs)[source]
 
        Differentiation of the given Holonomic function.
        
 
        Examples
        
 
        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
@@ -892,7 +894,7 @@ 
        Composition with polynomials**kwargs,
        
 
 
-)[source]
+)[source]
 
        Returns function after composition of a holonomic
 function with an algebraic function. The method cannot compute
 initial conditions for the result by itself, so they can be also be
@@ -920,7 +922,7 @@ 
        Composition with polynomials
        
 
        
 
        
-HolonomicFunction.to_sequence(lb=True)[source]
        
+HolonomicFunction.to_sequence(lb=True)[source]
 
        Finds recurrence relation for the coefficients in the series expansion
 of the function about \(x_0\), where \(x_0\) is the point at
 which the initial condition is stored.
        
@@ -982,7 +984,7 @@ 
        Series expansion_recur=None,
        
 
        
 
-)[source]
+)[source]
 
        Finds the power series expansion of given holonomic function about \(x_0\).
        
 
        Explanation
        
 
        A list of series might be returned if \(x_0\) is a regular point with
@@ -1019,7 +1021,7 @@ 
        Numerical evaluationderivatives=False,
        
 
 
-)[source]
+)[source]
 
        Finds numerical value of a holonomic function using numerical methods.
 (RK4 by default). A set of points (real or complex) must be provided
 which will be the path for the numerical integration.
        
@@ -1070,7 +1072,7 @@ 
        Convert to a linear combination of hypergeometric functions_recur=None,
        
 
 
-)[source]
+)[source]
 
        Returns a hypergeometric function (or linear combination of them)
 representing the given holonomic function.
        
 
        Explanation
        
@@ -1103,7 +1105,7 @@ 
        Convert to a linear combination of hypergeometric functions
        
 
        
 
        
-HolonomicFunction.to_meijerg()[source]
        
+HolonomicFunction.to_meijerg()[source]
 
        Returns a linear combination of Meijer G-functions.
        
 
        Examples
        
 
        >>> from sympy.holonomic import expr_to_holonomic
@@ -1126,7 +1128,7 @@ 
        Convert to a linear combination of Meijer G-functionsConvert to expressions
        
 
        
 
        
-HolonomicFunction.to_expr()[source]
        
+HolonomicFunction.to_expr()[source]
 
        Converts a Holonomic Function back to elementary functions.
        
 
        Examples
        
 
        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
diff --git a/dev/modules/holonomic/represent.html b/dev/modules/holonomic/represent.html
index 16d546223f6..44febe38fba 100644
--- a/dev/modules/holonomic/represent.html
+++ b/dev/modules/holonomic/represent.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •

      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
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  • How-to Guides
    • -
  • How-to Guides
      +
    +
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  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -802,7 +804,7 @@
        Documentation Version

        Lie Algebra

        -class sympy.liealgebras.root_system.RootSystem(cartantype)[source]
        +class sympy.liealgebras.root_system.RootSystem(cartantype)[source]

        Represent the root system of a simple Lie algebra

        Every simple Lie algebra has a unique root system. To find the root system, we first consider the Cartan subalgebra of g, which is the maximal @@ -837,7 +839,7 @@

        Documentation Version
        -add_as_roots(root1, root2)[source]
        +add_as_roots(root1, root2)[source]

        Add two roots together if and only if their sum is also a root

        It takes as input two vectors which should be roots. It then computes their sum and checks if it is in the list of all possible roots. If it @@ -856,7 +858,7 @@

        Documentation Version
        -add_simple_roots(root1, root2)[source]
        +add_simple_roots(root1, root2)[source]

        Add two simple roots together

        The function takes as input two integers, root1 and root2. It then uses these integers as keys in the dictionary of simple roots, and gets @@ -873,7 +875,7 @@

        Documentation Version
        -all_roots()[source]
        +all_roots()[source]

        Generate all the roots of a given root system

        The result is a dictionary where the keys are integer numbers. It generates the roots by getting the dictionary of all positive roots @@ -884,7 +886,7 @@

        Documentation Version
        -cartan_matrix()[source]
        +cartan_matrix()[source]

        Cartan matrix of Lie algebra associated with this root system

        Examples

        >>> from sympy.liealgebras.root_system import RootSystem
@@ -900,7 +902,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dynkin_diagram()[source]
        
+dynkin_diagram()[source]
 
        Dynkin diagram of the Lie algebra associated with this root system
        
 
        Examples
        
 
        >>> from sympy.liealgebras.root_system import RootSystem
@@ -914,7 +916,7 @@ 
        Documentation Version
        
 
 
        
 
        
-root_space()[source]
        
+root_space()[source]
 
        Return the span of the simple roots
        
 
        The root space is the vector space spanned by the simple roots, i.e. it
 is a vector space with a distinguished basis, the simple roots.  This
@@ -931,7 +933,7 @@ 
        Documentation Version
        
 
 
        
 
        
-simple_roots()[source]
        
+simple_roots()[source]
 
        Generate the simple roots of the Lie algebra
        
 
        The rank of the Lie algebra determines the number of simple roots that
 it has.  This method obtains the rank of the Lie algebra, and then uses
@@ -951,13 +953,13 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.type_a.TypeA(n)[source]
        
+class sympy.liealgebras.type_a.TypeA(n)[source]
 
        This class contains the information about
 the A series of simple Lie algebras.
 ====
        
 
        
 
        
-basic_root(i, j)[source]
        
+basic_root(i, j)[source]
 
        This is a method just to generate roots
 with a 1 iin the ith position and a -1
 in the jth position.
        
@@ -965,13 +967,13 @@ 
        Documentation Version
        
 
 
        
 
        
-basis()[source]
        
+basis()[source]
 
        Returns the number of independent generators of A_n
        
 
        
 
 
        
 
        
-cartan_matrix()[source]
        
+cartan_matrix()[source]
 
        Returns the Cartan matrix for A_n.
 The Cartan matrix matrix for a Lie algebra is
 generated by assigning an ordering to the simple
@@ -992,7 +994,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dimension()[source]
        
+dimension()[source]
 
        Dimension of the vector space V underlying the Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_type import CartanType
@@ -1005,19 +1007,19 @@ 
        Documentation Version
        
 
 
        
 
        
-highest_root()[source]
        
+highest_root()[source]
 
        Returns the highest weight root for A_n
        
 
        
 
 
        
 
        
-lie_algebra()[source]
        
+lie_algebra()[source]
 
        Returns the Lie algebra associated with A_n
        
 
        
 
 
        
 
        
-positive_roots()[source]
        
+positive_roots()[source]
 
        This method generates all the positive roots of
 A_n.  This is half of all of the roots of A_n;
 by multiplying all the positive roots by -1 we
@@ -1034,13 +1036,13 @@ 
        Documentation Version
        
 
 
        
 
        
-roots()[source]
        
+roots()[source]
 
        Returns the total number of roots for A_n
        
 
        
 
 
        
 
        
-simple_root(i)[source]
        
+simple_root(i)[source]
 
        Every lie algebra has a unique root system.
 Given a root system Q, there is a subset of the
 roots such that an element of Q is called a
@@ -1066,10 +1068,10 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.type_b.TypeB(n)[source]
        
+class sympy.liealgebras.type_b.TypeB(n)[source]
 
        
 
        
-basic_root(i, j)[source]
        
+basic_root(i, j)[source]
 
        This is a method just to generate roots
 with a 1 iin the ith position and a -1
 in the jth position.
        
@@ -1077,13 +1079,13 @@ 
        Documentation Version
        
 
 
        
 
        
-basis()[source]
        
+basis()[source]
 
        Returns the number of independent generators of B_n
        
 
        
 
 
        
 
        
-cartan_matrix()[source]
        
+cartan_matrix()[source]
 
        Returns the Cartan matrix for B_n.
 The Cartan matrix matrix for a Lie algebra is
 generated by assigning an ordering to the simple
@@ -1104,7 +1106,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dimension()[source]
        
+dimension()[source]
 
        Dimension of the vector space V underlying the Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_type import CartanType
@@ -1117,13 +1119,13 @@ 
        Documentation Version
        
 
 
        
 
        
-lie_algebra()[source]
        
+lie_algebra()[source]
 
        Returns the Lie algebra associated with B_n
        
 
        
 
 
        
 
        
-positive_roots()[source]
        
+positive_roots()[source]
 
        This method generates all the positive roots of
 A_n.  This is half of all of the roots of B_n;
 by multiplying all the positive roots by -1 we
@@ -1140,13 +1142,13 @@ 
        Documentation Version
        
 
 
        
 
        
-roots()[source]
        
+roots()[source]
 
        Returns the total number of roots for B_n”
        
 
        
 
 
        
 
        
-simple_root(i)[source]
        
+simple_root(i)[source]
 
        Every lie algebra has a unique root system.
 Given a root system Q, there is a subset of the
 roots such that an element of Q is called a
@@ -1174,22 +1176,22 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.type_c.TypeC(n)[source]
        
+class sympy.liealgebras.type_c.TypeC(n)[source]
 
        
 
        
-basic_root(i, j)[source]
        
+basic_root(i, j)[source]
 
        Generate roots with 1 in ith position and a -1 in jth position
        
 
        
 
 
        
 
        
-basis()[source]
        
+basis()[source]
 
        Returns the number of independent generators of C_n
        
 
        
 
 
        
 
        
-cartan_matrix()[source]
        
+cartan_matrix()[source]
 
        The Cartan matrix for C_n
        
 
        The Cartan matrix matrix for a Lie algebra is
 generated by assigning an ordering to the simple
@@ -1210,7 +1212,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dimension()[source]
        
+dimension()[source]
 
        Dimension of the vector space V underlying the Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_type import CartanType
@@ -1223,13 +1225,13 @@ 
        Documentation Version
        
 
 
        
 
        
-lie_algebra()[source]
        
+lie_algebra()[source]
 
        Returns the Lie algebra associated with C_n”
        
 
        
 
 
        
 
        
-positive_roots()[source]
        
+positive_roots()[source]
 
        Generates all the positive roots of A_n
        
 
        This is half of all of the roots of C_n; by multiplying all the
 positive roots by -1 we get the negative roots.
        
@@ -1245,13 +1247,13 @@ 
        Documentation Version
        
 
 
        
 
        
-roots()[source]
        
+roots()[source]
 
        Returns the total number of roots for C_n”
        
 
        
 
 
        
 
        
-simple_root(i)[source]
        
+simple_root(i)[source]
 
        The ith simple root for the C series
        
 
        Every lie algebra has a unique root system.
 Given a root system Q, there is a subset of the
@@ -1279,10 +1281,10 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.type_d.TypeD(n)[source]
        
+class sympy.liealgebras.type_d.TypeD(n)[source]
 
        
 
        
-basic_root(i, j)[source]
        
+basic_root(i, j)[source]
 
        This is a method just to generate roots
 with a 1 iin the ith position and a -1
 in the jth position.
        
@@ -1290,13 +1292,13 @@ 
        Documentation Version
        
 
 
        
 
        
-basis()[source]
        
+basis()[source]
 
        Returns the number of independent generators of D_n
        
 
        
 
 
        
 
        
-cartan_matrix()[source]
        
+cartan_matrix()[source]
 
        Returns the Cartan matrix for D_n.
 The Cartan matrix matrix for a Lie algebra is
 generated by assigning an ordering to the simple
@@ -1317,7 +1319,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dimension()[source]
        
+dimension()[source]
 
        Dmension of the vector space V underlying the Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_type import CartanType
@@ -1330,13 +1332,13 @@ 
        Documentation Version
        
 
 
        
 
        
-lie_algebra()[source]
        
+lie_algebra()[source]
 
        Returns the Lie algebra associated with D_n”
        
 
        
 
 
        
 
        
-positive_roots()[source]
        
+positive_roots()[source]
 
        This method generates all the positive roots of
 A_n.  This is half of all of the roots of D_n
 by multiplying all the positive roots by -1 we
@@ -1353,13 +1355,13 @@ 
        Documentation Version
        
 
 
        
 
        
-roots()[source]
        
+roots()[source]
 
        Returns the total number of roots for D_n”
        
 
        
 
 
        
 
        
-simple_root(i)[source]
        
+simple_root(i)[source]
 
        Every lie algebra has a unique root system.
 Given a root system Q, there is a subset of the
 roots such that an element of Q is called a
@@ -1387,10 +1389,10 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.type_e.TypeE(n)[source]
        
+class sympy.liealgebras.type_e.TypeE(n)[source]
 
        
 
        
-basic_root(i, j)[source]
        
+basic_root(i, j)[source]
 
        This is a method just to generate roots
 with a -1 in the ith position and a 1
 in the jth position.
        
@@ -1398,13 +1400,13 @@ 
        Documentation Version
        
 
 
        
 
        
-basis()[source]
        
+basis()[source]
 
        Returns the number of independent generators of E_n
        
 
        
 
 
        
 
        
-cartan_matrix()[source]
        
+cartan_matrix()[source]
 
        Returns the Cartan matrix for G_2
 The Cartan matrix matrix for a Lie algebra is
 generated by assigning an ordering to the simple
@@ -1425,7 +1427,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dimension()[source]
        
+dimension()[source]
 
        Dimension of the vector space V underlying the Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_type import CartanType
@@ -1438,7 +1440,7 @@ 
        Documentation Version
        
 
 
        
 
        
-positive_roots()[source]
        
+positive_roots()[source]
 
        This method generates all the positive roots of
 A_n.  This is half of all of the roots of E_n;
 by multiplying all the positive roots by -1 we
@@ -1455,13 +1457,13 @@ 
        Documentation Version
        
 
 
        
 
        
-roots()[source]
        
+roots()[source]
 
        Returns the total number of roots of E_n
        
 
        
 
 
        
 
        
-simple_root(i)[source]
        
+simple_root(i)[source]
 
        Every Lie algebra has a unique root system.
 Given a root system Q, there is a subset of the
 roots such that an element of Q is called a
@@ -1484,22 +1486,22 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.type_f.TypeF(n)[source]
        
+class sympy.liealgebras.type_f.TypeF(n)[source]
 
        
 
        
-basic_root(i, j)[source]
        
+basic_root(i, j)[source]
 
        Generate roots with 1 in ith position and -1 in jth position
        
 
        
 
 
        
 
        
-basis()[source]
        
+basis()[source]
 
        Returns the number of independent generators of F_4
        
 
        
 
 
        
 
        
-cartan_matrix()[source]
        
+cartan_matrix()[source]
 
        The Cartan matrix for F_4
        
 
        The Cartan matrix matrix for a Lie algebra is
 generated by assigning an ordering to the simple
@@ -1520,7 +1522,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dimension()[source]
        
+dimension()[source]
 
        Dimension of the vector space V underlying the Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_type import CartanType
@@ -1533,7 +1535,7 @@ 
        Documentation Version
        
 
 
        
 
        
-positive_roots()[source]
        
+positive_roots()[source]
 
        Generate all the positive roots of A_n
        
 
        This is half of all of the roots of F_4; by multiplying all the
 positive roots by -1 we get the negative roots.
        
@@ -1549,13 +1551,13 @@ 
        Documentation Version
        
 
 
        
 
        
-roots()[source]
        
+roots()[source]
 
        Returns the total number of roots for F_4
        
 
        
 
 
        
 
        
-simple_root(i)[source]
        
+simple_root(i)[source]
 
        The ith simple root of F_4
        
 
        Every lie algebra has a unique root system.
 Given a root system Q, there is a subset of the
@@ -1578,16 +1580,16 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.type_g.TypeG(n)[source]
        
+class sympy.liealgebras.type_g.TypeG(n)[source]
 
        
 
        
-basis()[source]
        
+basis()[source]
 
        Returns the number of independent generators of G_2
        
 
        
 
 
        
 
        
-cartan_matrix()[source]
        
+cartan_matrix()[source]
 
        The Cartan matrix for G_2
        
 
        The Cartan matrix matrix for a Lie algebra is
 generated by assigning an ordering to the simple
@@ -1606,7 +1608,7 @@ 
        Documentation Version
        
 
 
        
 
        
-dimension()[source]
        
+dimension()[source]
 
        Dimension of the vector space V underlying the Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_type import CartanType
@@ -1619,7 +1621,7 @@ 
        Documentation Version
        
 
 
        
 
        
-positive_roots()[source]
        
+positive_roots()[source]
 
        Generate all the positive roots of A_n
        
 
        This is half of all of the roots of A_n; by multiplying all the
 positive roots by -1 we get the negative roots.
        
@@ -1635,13 +1637,13 @@ 
        Documentation Version
        
 
 
        
 
        
-roots()[source]
        
+roots()[source]
 
        Returns the total number of roots of G_2”
        
 
        
 
 
        
 
        
-simple_root(i)[source]
        
+simple_root(i)[source]
 
        The ith simple root of G_2
        
 
        Every lie algebra has a unique root system.
 Given a root system Q, there is a subset of the
@@ -1664,7 +1666,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.weyl_group.WeylGroup(cartantype)[source]
        
+class sympy.liealgebras.weyl_group.WeylGroup(cartantype)[source]
 
        For each semisimple Lie group, we have a Weyl group.  It is a subgroup of
 the isometry group of the root system.  Specifically, it’s the subgroup
 that is generated by reflections through the hyperplanes orthogonal to
@@ -1672,7 +1674,7 @@ 
        Documentation Version
        
 group is a finite Coxeter group.
        
 
        
 
        
-coxeter_diagram()[source]
        
+coxeter_diagram()[source]
 
        This method returns the Coxeter diagram corresponding to a Weyl group.
 The Coxeter diagram can be obtained from a Lie algebra’s Dynkin diagram
 by deleting all arrows; the Coxeter diagram is the undirected graph.
@@ -1693,7 +1695,7 @@ 
        Documentation Version
        
 
 
        
 
        
-delete_doubles(reflections)[source]
        
+delete_doubles(reflections)[source]
 
        This is a helper method for determining the order of an element in the
 Weyl group of G2.  It takes a Weyl element and if repeated simple reflections
 in it, it deletes them.
        
@@ -1701,7 +1703,7 @@ 
        Documentation Version
        
 
 
        
 
        
-element_order(weylelt)[source]
        
+element_order(weylelt)[source]
 
        This method returns the order of a given Weyl group element, which should
 be specified by the user in the form of products of the generating
 reflections, i.e. of the form r1*r2 etc.
        
@@ -1719,7 +1721,7 @@ 
        Documentation Version
        
 
 
        
 
        
-generators()[source]
        
+generators()[source]
 
        This method creates the generating reflections of the Weyl group for
 a given Lie algebra.  For a Lie algebra of rank n, there are n
 different generating reflections.  This function returns them as
@@ -1735,7 +1737,7 @@ 
        Documentation Version
        
 
 
        
 
        
-group_name()[source]
        
+group_name()[source]
 
        This method returns some general information about the Weyl group for
 a given Lie algebra.  It returns the name of the group and the elements
 it acts on, if relevant.
        
@@ -1743,7 +1745,7 @@ 
        Documentation Version
        
 
 
        
 
        
-group_order()[source]
        
+group_order()[source]
 
        This method returns the order of the Weyl group.
 For types A, B, C, D, and E the order depends on
 the rank of the Lie algebra.  For types F and G,
@@ -1759,7 +1761,7 @@ 
        Documentation Version
        
 
 
        
 
        
-matrix_form(weylelt)[source]
        
+matrix_form(weylelt)[source]
 
        This method takes input from the user in the form of products of the
 generating reflections, and returns the matrix corresponding to the
 element of the Weyl group.  Since each element of the Weyl group is
@@ -1783,23 +1785,23 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.liealgebras.cartan_type.CartanType_generator[source]
        
+class sympy.liealgebras.cartan_type.CartanType_generator[source]
 
        Constructor for actually creating things
        
 
        
 
 
        
 
        
-class sympy.liealgebras.cartan_type.Standard_Cartan(series, n)[source]
        
+class sympy.liealgebras.cartan_type.Standard_Cartan(series, n)[source]
 
        Concrete base class for Cartan types such as A4, etc
        
 
        
 
        
-rank()[source]
        
+rank()[source]
 
        Returns the rank of the Lie algebra
        
 
        
 
 
        
 
        
-series()[source]
        
+series()[source]
 
        Returns the type of the Lie algebra
        
 
        
 
@@ -1807,7 +1809,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.liealgebras.dynkin_diagram.DynkinDiagram(t)[source]
        
+sympy.liealgebras.dynkin_diagram.DynkinDiagram(t)[source]
 
        Display the Dynkin diagram of a given Lie algebra
        
 
        Works by generating the CartanType for the input, t, and then returning the
 Dynkin diagram method from the individual classes.
        
@@ -1827,7 +1829,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.liealgebras.cartan_matrix.CartanMatrix(ct)[source]
        
+sympy.liealgebras.cartan_matrix.CartanMatrix(ct)[source]
 
        Access the Cartan matrix of a specific Lie algebra
        
 
        Examples
        
 
        >>> from sympy.liealgebras.cartan_matrix import CartanMatrix
diff --git a/dev/modules/logic.html b/dev/modules/logic.html
index 62ea2c3fe82..b0622e5829b 100644
--- a/dev/modules/logic.html
+++ b/dev/modules/logic.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
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    • Assumptions
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      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -804,7 +806,7 @@
        Documentation Version

        Parsing Functions Reference

        -sympy.parsing.sympy_parser.parse_expr(s: str, local_dict: ~typing.Dict[str, ~typing.Any] | None = None, transformations: ~typing.Tuple[~typing.Callable[[~typing.List[~typing.Tuple[int, str]], ~typing.Dict[str, ~typing.Any], ~typing.Dict[str, ~typing.Any]], ~typing.List[~typing.Tuple[int, str]]], ...] | str = (<function lambda_notation>, <function auto_symbol>, <function repeated_decimals>, <function auto_number>, <function factorial_notation>), global_dict: ~typing.Dict[str, ~typing.Any] | None = None, evaluate=True)[source]
        +sympy.parsing.sympy_parser.parse_expr(s: str, local_dict: ~typing.Dict[str, ~typing.Any] | None = None, transformations: ~typing.Tuple[~typing.Callable[[~typing.List[~typing.Tuple[int, str]], ~typing.Dict[str, ~typing.Any], ~typing.Dict[str, ~typing.Any]], ~typing.List[~typing.Tuple[int, str]]], ...] | str = (<function lambda_notation>, <function auto_symbol>, <function repeated_decimals>, <function auto_number>, <function factorial_notation>), global_dict: ~typing.Dict[str, ~typing.Any] | None = None, evaluate=True)[source]

        Converts the string s to a SymPy expression, in local_dict.

        Parameters:
        @@ -944,7 +946,7 @@

        Parsing Functions Referencetransformations: Tuple[Callable[[List[Tuple[int, str]], Dict[str, Any], Dict[str, Any]], List[Tuple[int, str]]], ...],

        -) → str[source] +) → str[source]

        Converts the string s to Python code, in local_dict

        Generally, parse_expr should be used.

        @@ -959,19 +961,19 @@

        Parsing Functions Referenceglobal_dict: Dict[str, Any], -)[source] +)[source]

        Evaluate Python code generated by stringify_expr.

        Generally, parse_expr should be used.

        -sympy.parsing.maxima.parse_maxima(str, globals=None, name_dict={})[source]
        +sympy.parsing.maxima.parse_maxima(str, globals=None, name_dict={})[source]
        -sympy.parsing.mathematica.parse_mathematica(s)[source]
        +sympy.parsing.mathematica.parse_mathematica(s)[source]

        Translate a string containing a Wolfram Mathematica expression to a SymPy expression.

        If the translator is unable to find a suitable SymPy expression, the @@ -1044,7 +1046,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any],

        -)[source] +)[source]

        Splits symbol names for implicit multiplication.

        Intended to let expressions like xyz be parsed as x*y*z. Does not split Greek character names, so theta will not become @@ -1060,7 +1062,7 @@

        Parsing Transformations Referencepredicate: Callable[[str], bool],

        -)[source] +)[source]

        Creates a transformation that splits symbol names.

        predicate should return True if the symbol name is to be split.

        For instance, to retain the default behavior but avoid splitting certain @@ -1091,7 +1093,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any],

        -) → List[Tuple[int, str]][source] +) → List[Tuple[int, str]][source]

        Makes the multiplication operator optional in most cases.

        Use this before implicit_application(), otherwise expressions like sin 2x will be parsed as x * sin(2) rather than sin(2*x).

        @@ -1115,7 +1117,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any],

        -) → List[Tuple[int, str]][source] +) → List[Tuple[int, str]][source]

        Makes parentheses optional in some cases for function calls.

        Use this after implicit_multiplication(), otherwise expressions like sin 2x will be parsed as x * sin(2) rather than @@ -1140,7 +1142,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any],

        -)[source] +)[source]

        Allows functions to be exponentiated, e.g. cos**2(x).

        Examples

        >>> from sympy.parsing.sympy_parser import (parse_expr,
@@ -1162,7 +1164,7 @@ 
        Parsing Transformations Referenceglobal_dict: Dict[str, Any],
        -) → List[Tuple[int, str]][source] +) → List[Tuple[int, str]][source]

        Allows a slightly relaxed syntax.

        • Parentheses for single-argument method calls are optional.

          • @@ -1192,7 +1194,7 @@

          Parsing Transformations Referenceglobal_dict: Dict[str, Any],

        -)[source] +)[source]

        Converts floats into Rational. Run AFTER auto_number.

        @@ -1206,7 +1208,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any], -)[source] +)[source]

        Treats XOR, ^, as exponentiation, **.

        @@ -1223,7 +1225,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any], -)[source] +)[source]

        Substitutes “lambda” with its SymPy equivalent Lambda(). However, the conversion does not take place if only “lambda” is passed because that is a syntax error.

        @@ -1239,7 +1241,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any],

        -)[source] +)[source]

        Inserts calls to Symbol/Function for undefined variables.

        @@ -1253,7 +1255,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any], -)[source] +)[source]

        Allows 0.2[1] notation to represent the repeated decimal 0.2111… (19/90)

        Run this before auto_number.

        @@ -1268,7 +1270,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any], -)[source] +)[source]

        Converts numeric literals to use SymPy equivalents.

        Complex numbers use I, integer literals use Integer, and float literals use Float.

        @@ -1284,7 +1286,7 @@

        Parsing Transformations Referenceglobal_dict: Dict[str, Any],

        -)[source] +)[source]

        Allows standard notation for factorial.

        @@ -1300,7 +1302,7 @@

        Experimental \(\mathrm{\LaTeX}\)<

        \(\mathrm{\LaTeX}\) Parsing Functions Reference

        -sympy.parsing.latex.parse_latex(s, strict=False, backend='antlr')[source]
        +sympy.parsing.latex.parse_latex(s, strict=False, backend='antlr')[source]

        Converts the input LaTeX string s to a SymPy Expr.

        Parameters:
        @@ -1474,7 +1476,7 @@

        Lark \(\mathrm{\LaTeX}\) P

        Lark \(\mathrm{\LaTeX}\) Parser Functions

        -sympy.parsing.latex.parse_latex_lark(s: str)[source]
        +sympy.parsing.latex.parse_latex_lark(s: str)[source]

        Experimental LaTeX parser using Lark.

        This function is still under development and its API may change with the next releases of SymPy.

        @@ -1494,7 +1496,7 @@

        Lark \(\mathrm{\LaTeX}\) P
        transformer=None,

        -)[source] +)[source]

        Class for converting input \(\mathrm{\LaTeX}\) strings into SymPy Expressions. It holds all the necessary internal data for doing so, and exposes hooks for customizing its behavior.

        @@ -1527,7 +1529,7 @@

        Lark \(\mathrm{\LaTeX}\) P
        -class sympy.parsing.latex.lark.TransformToSymPyExpr[source]
        +class sympy.parsing.latex.lark.TransformToSymPyExpr[source]

        Returns a SymPy expression that is generated by traversing the lark.Tree passed to the .transform() function.

        @@ -1554,7 +1556,7 @@

        Lark \(\mathrm{\LaTeX}\) P

        \(\mathrm{\LaTeX}\) Parsing Exceptions Reference

        -class sympy.parsing.latex.LaTeXParsingError[source]
        +class sympy.parsing.latex.LaTeXParsingError[source]
        @@ -1562,7 +1564,7 @@

        \(\mathrm{\LaTeX}\) Parsin

        SymPy Expression Reference

        -class sympy.parsing.sym_expr.SymPyExpression(source_code=None, mode=None)[source]
        +class sympy.parsing.sym_expr.SymPyExpression(source_code=None, mode=None)[source]

        Class to store and handle SymPy expressions

        This class will hold SymPy Expressions and handle the API for the conversion to and from different languages.

        @@ -1633,7 +1635,7 @@

        \(\mathrm{\LaTeX}\) Parsin
        -convert_to_c()[source]
        +convert_to_c()[source]

        Returns a list with the c source code for the SymPy expressions

        Examples

        >>> from sympy.parsing.sym_expr import SymPyExpression
@@ -1655,7 +1657,7 @@ 
        \(\mathrm{\LaTeX}\) Parsin
 
 
        
 
        
-convert_to_expr(src_code, mode)[source]
        
+convert_to_expr(src_code, mode)[source]
 
        Converts the given source code to SymPy Expressions
        
 
        Examples
        
 
        >>> from sympy.parsing.sym_expr import SymPyExpression
@@ -1694,7 +1696,7 @@ 
        \(\mathrm{\LaTeX}\) Parsin
 
 
        
 
        
-convert_to_fortran()[source]
        
+convert_to_fortran()[source]
 
        Returns a list with the fortran source code for the SymPy expressions
        
 
        Examples
        
 
        >>> from sympy.parsing.sym_expr import SymPyExpression
@@ -1715,7 +1717,7 @@ 
        \(\mathrm{\LaTeX}\) Parsin
 
 
        
 
        
-convert_to_python()[source]
        
+convert_to_python()[source]
 
        Returns a list with Python code for the SymPy expressions
        
 
        Examples
        
 
        >>> from sympy.parsing.sym_expr import SymPyExpression
@@ -1736,7 +1738,7 @@ 
        \(\mathrm{\LaTeX}\) Parsin
 
 
        
 
        
-return_expr()[source]
        
+return_expr()[source]
 
        Returns the expression list
        
 
        Examples
        
 
        >>> from sympy.parsing.sym_expr import SymPyExpression
diff --git a/dev/modules/physics/biomechanics/api/activation.html b/dev/modules/physics/biomechanics/api/activation.html
index 71d425809e0..00f913721e2 100644
--- a/dev/modules/physics/biomechanics/api/activation.html
+++ b/dev/modules/physics/biomechanics/api/activation.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •

      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -811,7 +813,7 @@
        Documentation Version
        module.

        -class sympy.physics.biomechanics.activation.ActivationBase(name)[source]
        +class sympy.physics.biomechanics.activation.ActivationBase(name)[source]

        Abstract base class for all activation dynamics classes to inherit from.

        Notes

        Instances of this class cannot be directly instantiated by users. However, @@ -925,7 +927,7 @@

        Documentation Version
        -abstract rhs()[source]
        +abstract rhs()[source]

        Explanation

        The solution to the linear system of ordinary differential equations governing the activation dynamics:

        @@ -943,7 +945,7 @@
        Documentation Version
        -abstract classmethod with_defaults(name)[source]
        +abstract classmethod with_defaults(name)[source]

        Alternate constructor that provides recommended defaults for constants.

        @@ -970,7 +972,7 @@
        Documentation Version
        smoothing_rate=None,
        -)[source] +)[source]

        First-order activation dynamics based on De Groote et al., 2016 [R720].

        Explanation

        Gives the first-order activation dynamics equation for the rate of change @@ -1103,7 +1105,7 @@

        Documentation Version
        -rhs()[source]
        +rhs()[source]

        Ordered column matrix of equations for the solution of M x' = F.

        Explanation

        The solution to the linear system of ordinary differential equations @@ -1154,7 +1156,7 @@

        Documentation Version
        name,
        -)[source] +)[source]

        Alternate constructor that will use the published constants.

        Explanation

        Returns an instance of FirstOrderActivationDeGroote2016 using the @@ -1178,7 +1180,7 @@

        Documentation Version
        -class sympy.physics.biomechanics.activation.ZerothOrderActivation(name)[source]
        +class sympy.physics.biomechanics.activation.ZerothOrderActivation(name)[source]

        Simple zeroth-order activation dynamics mapping excitation to activation.

        Explanation

        @@ -1282,7 +1284,7 @@
        Documentation Version
        -rhs()[source]
        +rhs()[source]

        Ordered column matrix of equations for the solution of M x' = F.

        Explanation

        The solution to the linear system of ordinary differential equations @@ -1307,7 +1309,7 @@

        Documentation Version
        -classmethod with_defaults(name)[source]
        +classmethod with_defaults(name)[source]

        Alternate constructor that provides recommended defaults for constants.

        Explanation

        diff --git a/dev/modules/physics/biomechanics/api/curve.html b/dev/modules/physics/biomechanics/api/curve.html index 14ee35d2272..df94696d03b 100644 --- a/dev/modules/physics/biomechanics/api/curve.html +++ b/dev/modules/physics/biomechanics/api/curve.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -815,13 +817,13 @@
        Documentation Version
        fiber_force_velocity_inverse: CharacteristicCurveFunction,
        -)[source] +)[source]

        Simple data container to group together related characteristic curves.

        -class sympy.physics.biomechanics.curve.CharacteristicCurveFunction[source]
        +class sympy.physics.biomechanics.curve.CharacteristicCurveFunction[source]

        Base class for all musculotendon characteristic curve functions.

        @@ -845,7 +847,7 @@
        Documentation Version
        c11,
        -)[source] +)[source]

        Active muscle fiber force-length curve based on De Groote et al., 2016 [R721].

        Explanation

        @@ -948,7 +950,7 @@
        Documentation Version
        **hints,
        -)[source] +)[source]

        Evaluate the expression defining the function.

        Parameters:
        @@ -993,7 +995,7 @@
        Documentation Version
        c11,
        -)[source] +)[source]

        Evaluation of basic inputs.

        Parameters:
        @@ -1073,7 +1075,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Derivative of the function with respect to a single argument.

        Parameters:
        @@ -1095,7 +1097,7 @@
        Documentation Version
        l_M_tilde,
        -)[source] +)[source]

        Recommended constructor that will use the published constants.

        Parameters:
        @@ -1137,7 +1139,7 @@
        Documentation Version
        c1,
        -)[source] +)[source]

        Passive muscle fiber force-length curve based on De Groote et al., 2016 [R722].

        Explanation

        @@ -1220,7 +1222,7 @@
        Documentation Version
        **hints,
        -)[source] +)[source]

        Evaluate the expression defining the function.

        Parameters:
        @@ -1255,7 +1257,7 @@
        Documentation Version
        c1,
        -)[source] +)[source]

        Evaluation of basic inputs.

        Parameters:
        @@ -1285,7 +1287,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Derivative of the function with respect to a single argument.

        Parameters:
        @@ -1307,7 +1309,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Inverse function.

        Parameters:
        @@ -1327,7 +1329,7 @@
        Documentation Version
        l_M_tilde,
        -)[source] +)[source]

        Recommended constructor that will use the published constants.

        Parameters:
        @@ -1358,7 +1360,7 @@
        Documentation Version
        c1,
        -)[source] +)[source]

        Inverse passive muscle fiber force-length curve based on De Groote et al., 2016 [R723].

        Explanation

        @@ -1435,7 +1437,7 @@
        Documentation Version
        **hints,
        -)[source] +)[source]

        Evaluate the expression defining the function.

        Parameters:
        @@ -1470,7 +1472,7 @@
        Documentation Version
        c1,
        -)[source] +)[source]

        Evaluation of basic inputs.

        Parameters:
        @@ -1500,7 +1502,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Derivative of the function with respect to a single argument.

        Parameters:
        @@ -1522,7 +1524,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Inverse function.

        Parameters:
        @@ -1542,7 +1544,7 @@
        Documentation Version
        fl_M_pas,
        -)[source] +)[source]

        Recommended constructor that will use the published constants.

        Parameters:
        @@ -1576,7 +1578,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Muscle fiber force-velocity curve based on De Groote et al., 2016 [R724].

        Explanation

        Gives the normalized muscle fiber force produced as a function of @@ -1662,7 +1664,7 @@

        Documentation Version
        **hints,
        -)[source] +)[source]

        Evaluate the expression defining the function.

        Parameters:
        @@ -1699,7 +1701,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Evaluation of basic inputs.

        Parameters:
        @@ -1733,7 +1735,7 @@
        Documentation Version
        -fdiff(argindex=1)[source]
        +fdiff(argindex=1)[source]

        Derivative of the function with respect to a single argument.

        Parameters:
        @@ -1749,7 +1751,7 @@
        Documentation Version
        -inverse(argindex=1)[source]
        +inverse(argindex=1)[source]

        Inverse function.

        Parameters:
        @@ -1769,7 +1771,7 @@
        Documentation Version
        v_M_tilde,
        -)[source] +)[source]

        Recommended constructor that will use the published constants.

        Parameters:
        @@ -1803,7 +1805,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Inverse muscle fiber force-velocity curve based on De Groote et al., 2016 [R725].

        Explanation

        @@ -1879,7 +1881,7 @@
        Documentation Version
        **hints,
        -)[source] +)[source]

        Evaluate the expression defining the function.

        Parameters:
        @@ -1916,7 +1918,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Evaluation of basic inputs.

        Parameters:
        @@ -1957,7 +1959,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Derivative of the function with respect to a single argument.

        Parameters:
        @@ -1979,7 +1981,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Inverse function.

        Parameters:
        @@ -1999,7 +2001,7 @@
        Documentation Version
        fv_M,
        -)[source] +)[source]

        Recommended constructor that will use the published constants.

        Parameters:
        @@ -2034,7 +2036,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Tendon force-length curve based on De Groote et al., 2016 [R726].

        Explanation

        Gives the normalized tendon force produced as a function of normalized @@ -2121,7 +2123,7 @@

        Documentation Version
        **hints,
        -)[source] +)[source]

        Evaluate the expression defining the function.

        Parameters:
        @@ -2158,7 +2160,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Evaluation of basic inputs.

        Parameters:
        @@ -2192,7 +2194,7 @@
        Documentation Version
        -fdiff(argindex=1)[source]
        +fdiff(argindex=1)[source]

        Derivative of the function with respect to a single argument.

        Parameters:
        @@ -2208,7 +2210,7 @@
        Documentation Version
        -inverse(argindex=1)[source]
        +inverse(argindex=1)[source]

        Inverse function.

        Parameters:
        @@ -2228,7 +2230,7 @@
        Documentation Version
        l_T_tilde,
        -)[source] +)[source]

        Recommended constructor that will use the published constants.

        Parameters:
        @@ -2262,7 +2264,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Inverse tendon force-length curve based on De Groote et al., 2016 [R727].

        Explanation

        Gives the normalized tendon length that produces a specific normalized @@ -2338,7 +2340,7 @@

        Documentation Version
        **hints,
        -)[source] +)[source]

        Evaluate the expression defining the function.

        Parameters:
        @@ -2375,7 +2377,7 @@
        Documentation Version
        c3,
        -)[source] +)[source]

        Evaluation of basic inputs.

        Parameters:
        @@ -2415,7 +2417,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Derivative of the function with respect to a single argument.

        Parameters:
        @@ -2437,7 +2439,7 @@
        Documentation Version
        argindex=1,
        -)[source] +)[source]

        Inverse function.

        Parameters:
        @@ -2457,7 +2459,7 @@
        Documentation Version
        fl_T,
        -)[source] +)[source]

        Recommended constructor that will use the published constants.

        Parameters:
        diff --git a/dev/modules/physics/biomechanics/api/index.html b/dev/modules/physics/biomechanics/api/index.html index 7ddb94bd200..b764fafb7bd 100644 --- a/dev/modules/physics/biomechanics/api/index.html +++ b/dev/modules/physics/biomechanics/api/index.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -803,7 +805,7 @@
        Documentation Version

        Clebsch-Gordon Coefficients.

        -class sympy.physics.quantum.cg.CG(j1, m1, j2, m2, j3, m3)[source]
        +class sympy.physics.quantum.cg.CG(j1, m1, j2, m2, j3, m3)[source]

        Class for Clebsch-Gordan coefficient.

        Parameters:
        @@ -866,7 +868,7 @@
        Documentation Version
        -class sympy.physics.quantum.cg.Wigner3j(j1, m1, j2, m2, j3, m3)[source]
        +class sympy.physics.quantum.cg.Wigner3j(j1, m1, j2, m2, j3, m3)[source]

        Class for the Wigner-3j symbols.

        Parameters:
        @@ -911,7 +913,7 @@
        Documentation Version
        -class sympy.physics.quantum.cg.Wigner6j(j1, j2, j12, j3, j, j23)[source]
        +class sympy.physics.quantum.cg.Wigner6j(j1, j2, j12, j3, j, j23)[source]

        Class for the Wigner-6j symbols

        See also

        @@ -924,7 +926,7 @@
        Documentation Version
        -class sympy.physics.quantum.cg.Wigner9j(j1, j2, j12, j3, j4, j34, j13, j24, j)[source]
        +class sympy.physics.quantum.cg.Wigner9j(j1, j2, j12, j3, j4, j34, j13, j24, j)[source]

        Class for the Wigner-9j symbols

        See also

        @@ -937,7 +939,7 @@
        Documentation Version
        -sympy.physics.quantum.cg.cg_simp(e)[source]
        +sympy.physics.quantum.cg.cg_simp(e)[source]

        Simplify and combine CG coefficients.

        Explanation

        This function uses various symmetry and properties of sums and diff --git a/dev/modules/physics/quantum/circuitplot.html b/dev/modules/physics/quantum/circuitplot.html index 6e3ed0fcae5..2c0c2051f0e 100644 --- a/dev/modules/physics/quantum/circuitplot.html +++ b/dev/modules/physics/quantum/circuitplot.html @@ -329,18 +329,20 @@

      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      -class sympy.physics.quantum.circuitplot.CircuitPlot(c, nqubits, **kwargs)[source]
      +class sympy.physics.quantum.circuitplot.CircuitPlot(c, nqubits, **kwargs)[source]

      A class for managing a circuit plot.

      @@ -828,43 +830,43 @@
      Documentation Version
      max_wire,
      -)[source] +)[source]

      Draw a vertical control line.

      -control_point(gate_idx, wire_idx)[source]
      +control_point(gate_idx, wire_idx)[source]

      Draw a control point.

      -not_point(gate_idx, wire_idx)[source]
      +not_point(gate_idx, wire_idx)[source]

      Draw a NOT gates as the circle with plus in the middle.

      -one_qubit_box(t, gate_idx, wire_idx)[source]
      +one_qubit_box(t, gate_idx, wire_idx)[source]

      Draw a box for a single qubit gate.

      -swap_point(gate_idx, wire_idx)[source]
      +swap_point(gate_idx, wire_idx)[source]

      Draw a swap point as a cross.

      -two_qubit_box(t, gate_idx, wire_idx)[source]
      +two_qubit_box(t, gate_idx, wire_idx)[source]

      Draw a box for a two qubit gate. Does not work yet.

      -update(kwargs)[source]
      +update(kwargs)[source]

      Load the kwargs into the instance dict.

      @@ -872,13 +874,13 @@
      Documentation Version
      -sympy.physics.quantum.circuitplot.CreateCGate(name, latexname=None)[source]
      +sympy.physics.quantum.circuitplot.CreateCGate(name, latexname=None)[source]

      Use a lexical closure to make a controlled gate.

      -class sympy.physics.quantum.circuitplot.Mx(*args, **kwargs)[source]
      +class sympy.physics.quantum.circuitplot.Mx(*args, **kwargs)[source]

      Mock-up of an x measurement gate.

      This is in circuitplot rather than gate.py because it’s not a real gate, it just draws one.

      @@ -886,7 +888,7 @@
      Documentation Version
      -class sympy.physics.quantum.circuitplot.Mz(*args, **kwargs)[source]
      +class sympy.physics.quantum.circuitplot.Mz(*args, **kwargs)[source]

      Mock-up of a z measurement gate.

      This is in circuitplot rather than gate.py because it’s not a real gate, it just draws one.

      @@ -894,7 +896,7 @@
      Documentation Version
      -sympy.physics.quantum.circuitplot.circuit_plot(c, nqubits, **kwargs)[source]
      +sympy.physics.quantum.circuitplot.circuit_plot(c, nqubits, **kwargs)[source]

      Draw the circuit diagram for the circuit with nqubits.

      Parameters:
      @@ -913,7 +915,7 @@
      Documentation Version
      -sympy.physics.quantum.circuitplot.labeller(n, symbol='q')[source]
      +sympy.physics.quantum.circuitplot.labeller(n, symbol='q')[source]

      Autogenerate labels for wires of quantum circuits.

      Parameters:
      diff --git a/dev/modules/physics/quantum/commutator.html b/dev/modules/physics/quantum/commutator.html index 88a411f6f7a..3a86547c243 100644 --- a/dev/modules/physics/quantum/commutator.html +++ b/dev/modules/physics/quantum/commutator.html @@ -329,18 +329,20 @@
    • Linearized Carvallo-Whipple Bicycle Model
    • +
  • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
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      +
    +
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    • -
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      +
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    • -
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      +
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    • +
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    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      -class sympy.physics.quantum.gate.CGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.CGate(*args, **kwargs)[source]

      A general unitary gate with control qubits.

      A general control gate applies a target gate to a set of targets if all of the control qubits have a particular values (set by @@ -837,13 +839,13 @@

      Documentation Version
      -decompose(**options)[source]
      +decompose(**options)[source]

      Decompose the controlled gate into CNOT and single qubits gates.

      -eval_controls(qubit)[source]
      +eval_controls(qubit)[source]

      Return True/False to indicate if the controls are satisfied.

      @@ -869,7 +871,7 @@
      Documentation Version
      -plot_gate(circ_plot, gate_idx)[source]
      +plot_gate(circ_plot, gate_idx)[source]

      Plot the controlled gate. If simplify_cgate is true, simplify C-X and C-Z gates into their more familiar forms.

      @@ -884,20 +886,20 @@
      Documentation Version
      -class sympy.physics.quantum.gate.CGateS(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.CGateS(*args, **kwargs)[source]

      Version of CGate that allows gate simplifications. I.e. cnot looks like an oplus, cphase has dots, etc.

      -sympy.physics.quantum.gate.CNOT[source]
      +sympy.physics.quantum.gate.CNOT[source]

      alias of CNotGate

      -class sympy.physics.quantum.gate.CNotGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.CNotGate(*args, **kwargs)[source]

      Two qubit controlled-NOT.

      This gate performs the NOT or X gate on the target qubit if the control qubits all have the value 1.

      @@ -946,7 +948,7 @@
      Documentation Version
      -class sympy.physics.quantum.gate.Gate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.Gate(*args, **kwargs)[source]

      Non-controlled unitary gate operator that acts on qubits.

      This is a general abstract gate that needs to be subclassed to do anything useful.

      @@ -960,7 +962,7 @@
      Documentation Version
      -get_target_matrix(format='sympy')[source]
      +get_target_matrix(format='sympy')[source]

      The matrix representation of the target part of the gate.

      Parameters:
      @@ -996,13 +998,13 @@
      Documentation Version
      -sympy.physics.quantum.gate.H[source]
      +sympy.physics.quantum.gate.H[source]

      alias of HadamardGate

      -class sympy.physics.quantum.gate.HadamardGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.HadamardGate(*args, **kwargs)[source]

      The single qubit Hadamard gate.

      Parameters:
      @@ -1029,7 +1031,7 @@
      Documentation Version
      -class sympy.physics.quantum.gate.IdentityGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.IdentityGate(*args, **kwargs)[source]

      The single qubit identity gate.

      Parameters:
      @@ -1043,19 +1045,19 @@
      Documentation Version
      -class sympy.physics.quantum.gate.OneQubitGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.OneQubitGate(*args, **kwargs)[source]

      A single qubit unitary gate base class.

      -sympy.physics.quantum.gate.Phase[source]
      +sympy.physics.quantum.gate.Phase[source]

      alias of PhaseGate

      -class sympy.physics.quantum.gate.PhaseGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.PhaseGate(*args, **kwargs)[source]

      The single qubit phase, or S, gate.

      This gate rotates the phase of the state by pi/2 if the state is |1> and does nothing if the state is |0>.

      @@ -1071,19 +1073,19 @@
      Documentation Version
      -sympy.physics.quantum.gate.S[source]
      +sympy.physics.quantum.gate.S[source]

      alias of PhaseGate

      -sympy.physics.quantum.gate.SWAP[source]
      +sympy.physics.quantum.gate.SWAP[source]

      alias of SwapGate

      -class sympy.physics.quantum.gate.SwapGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.SwapGate(*args, **kwargs)[source]

      Two qubit SWAP gate.

      This gate swap the values of the two qubits.

      @@ -1096,7 +1098,7 @@
      Documentation Version
      -decompose(**options)[source]
      +decompose(**options)[source]

      Decompose the SWAP gate into CNOT gates.

      @@ -1104,13 +1106,13 @@
      Documentation Version
      -sympy.physics.quantum.gate.T[source]
      +sympy.physics.quantum.gate.T[source]

      alias of TGate

      -class sympy.physics.quantum.gate.TGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.TGate(*args, **kwargs)[source]

      The single qubit pi/8 gate.

      This gate rotates the phase of the state by pi/4 if the state is |1> and does nothing if the state is |0>.

      @@ -1126,13 +1128,13 @@
      Documentation Version
      -class sympy.physics.quantum.gate.TwoQubitGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.TwoQubitGate(*args, **kwargs)[source]

      A two qubit unitary gate base class.

      -class sympy.physics.quantum.gate.UGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.UGate(*args, **kwargs)[source]

      General gate specified by a set of targets and a target matrix.

      Parameters:
      @@ -1146,7 +1148,7 @@
      Documentation Version
      -get_target_matrix(format='sympy')[source]
      +get_target_matrix(format='sympy')[source]

      The matrix rep. of the target part of the gate.

      Parameters:
      @@ -1168,13 +1170,13 @@
      Documentation Version
      -sympy.physics.quantum.gate.X[source]
      +sympy.physics.quantum.gate.X[source]

      alias of XGate

      -class sympy.physics.quantum.gate.XGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.XGate(*args, **kwargs)[source]

      The single qubit X, or NOT, gate.

      Parameters:
      @@ -1188,13 +1190,13 @@
      Documentation Version
      -sympy.physics.quantum.gate.Y[source]
      +sympy.physics.quantum.gate.Y[source]

      alias of YGate

      -class sympy.physics.quantum.gate.YGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.YGate(*args, **kwargs)[source]

      The single qubit Y gate.

      Parameters:
      @@ -1208,13 +1210,13 @@
      Documentation Version
      -sympy.physics.quantum.gate.Z[source]
      +sympy.physics.quantum.gate.Z[source]

      alias of ZGate

      -class sympy.physics.quantum.gate.ZGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.gate.ZGate(*args, **kwargs)[source]

      The single qubit Z gate.

      Parameters:
      @@ -1228,7 +1230,7 @@
      Documentation Version
      -sympy.physics.quantum.gate.gate_simp(circuit)[source]
      +sympy.physics.quantum.gate.gate_simp(circuit)[source]

      Simplifies gates symbolically

      It first sorts gates using gate_sort. It then applies basic simplification rules to the circuit, e.g., XGate**2 = Identity

      @@ -1236,7 +1238,7 @@
      Documentation Version
      -sympy.physics.quantum.gate.gate_sort(circuit)[source]
      +sympy.physics.quantum.gate.gate_sort(circuit)[source]

      Sorts the gates while keeping track of commutation relations

      This function uses a bubble sort to rearrange the order of gate application. Keeps track of Quantum computations special commutation @@ -1247,7 +1249,7 @@

      Documentation Version
      -sympy.physics.quantum.gate.normalized(normalize)[source]
      +sympy.physics.quantum.gate.normalized(normalize)[source]

      Set flag controlling normalization of Hadamard gates by \(1/\sqrt{2}\).

      This is a global setting that can be used to simplify the look of various expressions, by leaving off the leading \(1/\sqrt{2}\) of the Hadamard gate.

      @@ -1280,7 +1282,7 @@
      Documentation Version
      <class 'sympy.physics.quantum.gate.SwapGate'>),
      -)[source] +)[source]

      Return a random circuit of ngates and nqubits.

      This uses an equally weighted sample of (X, Y, Z, S, T, H, CNOT, SWAP) gates.

      diff --git a/dev/modules/physics/quantum/grover.html b/dev/modules/physics/quantum/grover.html index 8efff891184..c2448374cf8 100644 --- a/dev/modules/physics/quantum/grover.html +++ b/dev/modules/physics/quantum/grover.html @@ -329,18 +329,20 @@
    • Linearized Carvallo-Whipple Bicycle Model
    • +
  • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      -class sympy.physics.quantum.grover.OracleGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.grover.OracleGate(*args, **kwargs)[source]

      A black box gate.

      The gate marks the desired qubits of an unknown function by flipping the sign of the qubits. The unknown function returns true when it @@ -856,7 +858,7 @@

      Documentation Version
      -class sympy.physics.quantum.grover.WGate(*args, **kwargs)[source]
      +class sympy.physics.quantum.grover.WGate(*args, **kwargs)[source]

      General n qubit W Gate in Grover’s algorithm.

      The gate performs the operation 2|phi><phi| - 1 on some qubits. |phi> = (tensor product of n Hadamards)*(|0> with n qubits)

      @@ -872,7 +874,7 @@
      Documentation Version
      -sympy.physics.quantum.grover.apply_grover(oracle, nqubits, iterations=None)[source]
      +sympy.physics.quantum.grover.apply_grover(oracle, nqubits, iterations=None)[source]

      Applies grover’s algorithm.

      Parameters:
      @@ -903,7 +905,7 @@
      Documentation Version
      -sympy.physics.quantum.grover.grover_iteration(qstate, oracle)[source]
      +sympy.physics.quantum.grover.grover_iteration(qstate, oracle)[source]

      Applies one application of the Oracle and W Gate, WV.

      Parameters:
      @@ -939,7 +941,7 @@
      Documentation Version
      -sympy.physics.quantum.grover.superposition_basis(nqubits)[source]
      +sympy.physics.quantum.grover.superposition_basis(nqubits)[source]

      Creates an equal superposition of the computational basis.

      Parameters:
      diff --git a/dev/modules/physics/quantum/hilbert.html b/dev/modules/physics/quantum/hilbert.html index 8e559a93d9f..e49ae7c01a5 100644 --- a/dev/modules/physics/quantum/hilbert.html +++ b/dev/modules/physics/quantum/hilbert.html @@ -329,18 +329,20 @@
    • Linearized Carvallo-Whipple Bicycle Model
    • +
  • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -806,7 +808,7 @@
        Documentation Version
        * Matt Curry

        -class sympy.physics.quantum.hilbert.ComplexSpace(dimension)[source]
        +class sympy.physics.quantum.hilbert.ComplexSpace(dimension)[source]

        Finite dimensional Hilbert space of complex vectors.

        The elements of this Hilbert space are n-dimensional complex valued vectors with the usual inner product that takes the complex conjugate @@ -837,7 +839,7 @@

        Documentation Version
        -class sympy.physics.quantum.hilbert.DirectSumHilbertSpace(*args)[source]
        +class sympy.physics.quantum.hilbert.DirectSumHilbertSpace(*args)[source]

        A direct sum of Hilbert spaces [R766].

        This class uses the + operator to represent direct sums between different Hilbert spaces.

        @@ -869,7 +871,7 @@
        Documentation Version
        -classmethod eval(args)[source]
        +classmethod eval(args)[source]

        Evaluates the direct product.

        @@ -883,7 +885,7 @@
        Documentation Version
        -class sympy.physics.quantum.hilbert.FockSpace[source]
        +class sympy.physics.quantum.hilbert.FockSpace[source]

        The Hilbert space for second quantization.

        Technically, this Hilbert space is a infinite direct sum of direct products of single particle Hilbert spaces [R767]. This is a mess, so we have @@ -909,7 +911,7 @@

        Documentation Version
        -class sympy.physics.quantum.hilbert.HilbertSpace[source]
        +class sympy.physics.quantum.hilbert.HilbertSpace[source]

        An abstract Hilbert space for quantum mechanics.

        In short, a Hilbert space is an abstract vector space that is complete with inner products defined [R768].

        @@ -938,7 +940,7 @@
        Documentation Version
        -class sympy.physics.quantum.hilbert.L2(interval)[source]
        +class sympy.physics.quantum.hilbert.L2(interval)[source]

        The Hilbert space of square integrable functions on an interval.

        An L2 object takes in a single SymPy Interval argument which represents the interval its functions (vectors) are defined on.

        @@ -958,7 +960,7 @@
        Documentation Version
        -class sympy.physics.quantum.hilbert.TensorPowerHilbertSpace(*args)[source]
        +class sympy.physics.quantum.hilbert.TensorPowerHilbertSpace(*args)[source]

        An exponentiated Hilbert space [R769].

        Tensor powers (repeated tensor products) are represented by the operator ** Identical Hilbert spaces that are multiplied together @@ -1000,7 +1002,7 @@

        Documentation Version
        -class sympy.physics.quantum.hilbert.TensorProductHilbertSpace(*args)[source]
        +class sympy.physics.quantum.hilbert.TensorProductHilbertSpace(*args)[source]

        A tensor product of Hilbert spaces [R770].

        The tensor product between Hilbert spaces is represented by the operator * Products of the same Hilbert space will be combined into @@ -1045,7 +1047,7 @@

        Documentation Version
        -classmethod eval(args)[source]
        +classmethod eval(args)[source]

        Evaluates the direct product.

        diff --git a/dev/modules/physics/quantum/index.html b/dev/modules/physics/quantum/index.html index 0db6902bc8b..1e8e023f67b 100644 --- a/dev/modules/physics/quantum/index.html +++ b/dev/modules/physics/quantum/index.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
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    • -
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      +
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    • -
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      +
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    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      -class sympy.physics.quantum.operator.DifferentialOperator(*args, **kwargs)[source]
      +class sympy.physics.quantum.operator.DifferentialOperator(*args, **kwargs)[source]

      An operator for representing the differential operator, i.e. d/dx

      It is initialized by passing two arguments. The first is an arbitrary expression that involves a function, such as Derivative(f(x), x). The @@ -925,7 +927,7 @@

      Documentation Version
      -class sympy.physics.quantum.operator.HermitianOperator(*args, **kwargs)[source]
      +class sympy.physics.quantum.operator.HermitianOperator(*args, **kwargs)[source]

      A Hermitian operator that satisfies H == Dagger(H).

      Parameters:
      @@ -947,7 +949,7 @@
      Documentation Version
      -class sympy.physics.quantum.operator.IdentityOperator(*args, **kwargs)[source]
      +class sympy.physics.quantum.operator.IdentityOperator(*args, **kwargs)[source]

      An identity operator I that satisfies op * I == I * op == op for any operator op.

      @@ -969,7 +971,7 @@
      Documentation Version
      -class sympy.physics.quantum.operator.Operator(*args, **kwargs)[source]
      +class sympy.physics.quantum.operator.Operator(*args, **kwargs)[source]

      Base class for non-commuting quantum operators.

      An operator maps between quantum states [R772]. In quantum mechanics, observables (including, but not limited to, measured physical values) are @@ -1044,7 +1046,7 @@

      Documentation Version
      -class sympy.physics.quantum.operator.OuterProduct(*args, **old_assumptions)[source]
      +class sympy.physics.quantum.operator.OuterProduct(*args, **old_assumptions)[source]

      An unevaluated outer product between a ket and bra.

      This constructs an outer product between any subclass of KetBase and BraBase as |a><b|. An OuterProduct inherits from Operator as they act as @@ -1124,7 +1126,7 @@

      Documentation Version
      -class sympy.physics.quantum.operator.UnitaryOperator(*args, **kwargs)[source]
      +class sympy.physics.quantum.operator.UnitaryOperator(*args, **kwargs)[source]

      A unitary operator that satisfies U*Dagger(U) == 1.

      Parameters:
      diff --git a/dev/modules/physics/quantum/operatorset.html b/dev/modules/physics/quantum/operatorset.html index e9a88dd95f9..147c1175b22 100644 --- a/dev/modules/physics/quantum/operatorset.html +++ b/dev/modules/physics/quantum/operatorset.html @@ -329,18 +329,20 @@
    • Linearized Carvallo-Whipple Bicycle Model
    • +
  • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
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      +
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    • -
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      +
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    • +
  • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -807,7 +809,7 @@
        Documentation Version
        * Update tests.

        -class sympy.physics.quantum.qubit.IntQubit(*args, **kwargs)[source]
        +class sympy.physics.quantum.qubit.IntQubit(*args, **kwargs)[source]

        A qubit ket that store integers as binary numbers in qubit values.

        The differences between this class and Qubit are:

          @@ -882,13 +884,13 @@
          Documentation Version
          -class sympy.physics.quantum.qubit.IntQubitBra(*args, **kwargs)[source]
          +class sympy.physics.quantum.qubit.IntQubitBra(*args, **kwargs)[source]

          A qubit bra that store integers as binary numbers in qubit values.

          -class sympy.physics.quantum.qubit.Qubit(*args, **kwargs)[source]
          +class sympy.physics.quantum.qubit.Qubit(*args, **kwargs)[source]

          A multi-qubit ket in the computational (z) basis.

          We use the normal convention that the least significant qubit is on the right, so |00001> has a 1 in the least significant qubit.

          @@ -945,7 +947,7 @@
          Documentation Version
          -class sympy.physics.quantum.qubit.QubitBra(*args, **kwargs)[source]
          +class sympy.physics.quantum.qubit.QubitBra(*args, **kwargs)[source]

          A multi-qubit bra in the computational (z) basis.

          We use the normal convention that the least significant qubit is on the right, so |00001> has a 1 in the least significant qubit.

          @@ -968,7 +970,7 @@
          Documentation Version
          -sympy.physics.quantum.qubit.matrix_to_density(mat)[source]
          +sympy.physics.quantum.qubit.matrix_to_density(mat)[source]

          Works by finding the eigenvectors and eigenvalues of the matrix. We know we can decompose rho by doing: sum(EigenVal*|Eigenvect><Eigenvect|)

          @@ -976,7 +978,7 @@
          Documentation Version
          -sympy.physics.quantum.qubit.matrix_to_qubit(matrix)[source]
          +sympy.physics.quantum.qubit.matrix_to_qubit(matrix)[source]

          Convert from the matrix repr. to a sum of Qubit objects.

          Parameters:
          @@ -1000,7 +1002,7 @@
          Documentation Version
          -sympy.physics.quantum.qubit.measure_all(qubit, format='sympy', normalize=True)[source]
          +sympy.physics.quantum.qubit.measure_all(qubit, format='sympy', normalize=True)[source]

          Perform an ensemble measurement of all qubits.

          Parameters:
          @@ -1041,7 +1043,7 @@
          Documentation Version
          -sympy.physics.quantum.qubit.measure_all_oneshot(qubit, format='sympy')[source]
          +sympy.physics.quantum.qubit.measure_all_oneshot(qubit, format='sympy')[source]

          Perform a oneshot ensemble measurement on all qubits.

          A oneshot measurement is equivalent to performing a measurement on a quantum system. This type of measurement does not return the probabilities @@ -1082,7 +1084,7 @@

          Documentation Version
          normalize=True,
          -)[source] +)[source]

          Perform a partial ensemble measure on the specified qubits.

          Parameters:
          @@ -1135,7 +1137,7 @@
          Documentation Version
          format='sympy',
          -)[source] +)[source]

          Perform a partial oneshot measurement on the specified qubits.

          A oneshot measurement is equivalent to performing a measurement on a quantum system. This type of measurement does not return the probabilities @@ -1171,7 +1173,7 @@

          Documentation Version
          -sympy.physics.quantum.qubit.qubit_to_matrix(qubit, format='sympy')[source]
          +sympy.physics.quantum.qubit.qubit_to_matrix(qubit, format='sympy')[source]

          Converts an Add/Mul of Qubit objects into it’s matrix representation

          This function is the inverse of matrix_to_qubit and is a shorthand for represent(qubit).

          diff --git a/dev/modules/physics/quantum/represent.html b/dev/modules/physics/quantum/represent.html index 8e9231eb144..9c2affb42c0 100644 --- a/dev/modules/physics/quantum/represent.html +++ b/dev/modules/physics/quantum/represent.html @@ -329,18 +329,20 @@
        • Linearized Carvallo-Whipple Bicycle Model
        +
      • Control Tutorials
      • -
    • How-to Guides
        +
      +
      • +
    • How-to Guides
      • Assumptions
      • Symbolic and fuzzy booleans
      • Writing Custom Functions
        • -
      • Physics -
        • +
      • Physics
      • Solve Equations
        -sympy.physics.quantum.represent.enumerate_states(*args, **options)[source]
        +sympy.physics.quantum.represent.enumerate_states(*args, **options)[source]

        Returns instances of the given state with dummy indices appended

        Operates in two different modes:

          @@ -852,7 +854,7 @@
          Documentation Version
          **options,
        -)[source] +)[source]

        Returns a basis state instance corresponding to the basis specified in options=s. If no basis is specified, the function tries to form a default basis state of the given expression.

        @@ -899,7 +901,7 @@
        Documentation Version
        -sympy.physics.quantum.represent.integrate_result(orig_expr, result, **options)[source]
        +sympy.physics.quantum.represent.integrate_result(orig_expr, result, **options)[source]

        Returns the result of integrating over any unities (|x><x|) in the given expression. Intended for integrating over the result of representations in continuous bases.

        @@ -941,7 +943,7 @@
        Documentation Version
        -sympy.physics.quantum.represent.rep_expectation(expr, **options)[source]
        +sympy.physics.quantum.represent.rep_expectation(expr, **options)[source]

        Returns an <x'|A|x> type representation for the given operator.

        Parameters:
        @@ -966,7 +968,7 @@
        Documentation Version
        -sympy.physics.quantum.represent.rep_innerproduct(expr, **options)[source]
        +sympy.physics.quantum.represent.rep_innerproduct(expr, **options)[source]

        Returns an innerproduct like representation (e.g. <x'|x>) for the given state.

        Attempts to calculate inner product with a bra from the specified @@ -994,7 +996,7 @@

        Documentation Version
        -sympy.physics.quantum.represent.represent(expr, **options)[source]
        +sympy.physics.quantum.represent.represent(expr, **options)[source]

        Represent the quantum expression in the given basis.

        In quantum mechanics abstract states and operators can be represented in various basis sets. Under this operation the follow transforms happen:

        diff --git a/dev/modules/physics/quantum/shor.html b/dev/modules/physics/quantum/shor.html index d4a51b0bc09..b4c6e03c84b 100644 --- a/dev/modules/physics/quantum/shor.html +++ b/dev/modules/physics/quantum/shor.html @@ -329,18 +329,20 @@
      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      -class sympy.physics.quantum.shor.CMod(*args, **kwargs)[source]
      +class sympy.physics.quantum.shor.CMod(*args, **kwargs)[source]

      A controlled mod gate.

      This is black box controlled Mod function for use by shor’s algorithm. TODO: implement a decompose property that returns how to do this in terms @@ -836,7 +838,7 @@

      Documentation Version
      -sympy.physics.quantum.shor.period_find(a, N)[source]
      +sympy.physics.quantum.shor.period_find(a, N)[source]

      Finds the period of a in modulo N arithmetic

      This is quantum part of Shor’s algorithm. It takes two registers, puts first in superposition of states with Hadamards so: |k>|0> @@ -846,7 +848,7 @@

      Documentation Version
      -sympy.physics.quantum.shor.shor(N)[source]
      +sympy.physics.quantum.shor.shor(N)[source]

      This function implements Shor’s factoring algorithm on the Integer N

      The algorithm starts by picking a random number (a) and seeing if it is coprime with N. If it is not, then the gcd of the two numbers is a factor diff --git a/dev/modules/physics/quantum/spin.html b/dev/modules/physics/quantum/spin.html index f2d991130a4..aee7a64d497 100644 --- a/dev/modules/physics/quantum/spin.html +++ b/dev/modules/physics/quantum/spin.html @@ -329,18 +329,20 @@

    • Linearized Carvallo-Whipple Bicycle Model
    • +
  • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -803,13 +805,13 @@
        Documentation Version

        Quantum mechanical angular momemtum.

        -class sympy.physics.quantum.spin.J2Op(*args, **kwargs)[source]
        +class sympy.physics.quantum.spin.J2Op(*args, **kwargs)[source]

        The J^2 operator.

        -class sympy.physics.quantum.spin.JxBra(j, m)[source]
        +class sympy.physics.quantum.spin.JxBra(j, m)[source]

        Eigenbra of Jx.

        See JzKet for the usage of spin eigenstates.

        @@ -823,7 +825,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JxBraCoupled(j, m, jn, *jcoupling)[source]
        +class sympy.physics.quantum.spin.JxBraCoupled(j, m, jn, *jcoupling)[source]

        Coupled eigenbra of Jx.

        See JzKetCoupled for the usage of coupled spin eigenstates.

        @@ -837,7 +839,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JxKet(j, m)[source]
        +class sympy.physics.quantum.spin.JxKet(j, m)[source]

        Eigenket of Jx.

        See JzKet for the usage of spin eigenstates.

        @@ -851,7 +853,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JxKetCoupled(j, m, jn, *jcoupling)[source]
        +class sympy.physics.quantum.spin.JxKetCoupled(j, m, jn, *jcoupling)[source]

        Coupled eigenket of Jx.

        See JzKetCoupled for the usage of coupled spin eigenstates.

        @@ -865,7 +867,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JyBra(j, m)[source]
        +class sympy.physics.quantum.spin.JyBra(j, m)[source]

        Eigenbra of Jy.

        See JzKet for the usage of spin eigenstates.

        @@ -879,7 +881,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JyBraCoupled(j, m, jn, *jcoupling)[source]
        +class sympy.physics.quantum.spin.JyBraCoupled(j, m, jn, *jcoupling)[source]

        Coupled eigenbra of Jy.

        See JzKetCoupled for the usage of coupled spin eigenstates.

        @@ -893,7 +895,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JyKet(j, m)[source]
        +class sympy.physics.quantum.spin.JyKet(j, m)[source]

        Eigenket of Jy.

        See JzKet for the usage of spin eigenstates.

        @@ -907,7 +909,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JyKetCoupled(j, m, jn, *jcoupling)[source]
        +class sympy.physics.quantum.spin.JyKetCoupled(j, m, jn, *jcoupling)[source]

        Coupled eigenket of Jy.

        See JzKetCoupled for the usage of coupled spin eigenstates.

        @@ -921,7 +923,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JzBra(j, m)[source]
        +class sympy.physics.quantum.spin.JzBra(j, m)[source]

        Eigenbra of Jz.

        See the JzKet for the usage of spin eigenstates.

        @@ -935,7 +937,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JzBraCoupled(j, m, jn, *jcoupling)[source]
        +class sympy.physics.quantum.spin.JzBraCoupled(j, m, jn, *jcoupling)[source]

        Coupled eigenbra of Jz.

        See the JzKetCoupled for the usage of coupled spin eigenstates.

        @@ -949,7 +951,7 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JzKet(j, m)[source]
        +class sympy.physics.quantum.spin.JzKet(j, m)[source]

        Eigenket of Jz.

        Spin state which is an eigenstate of the Jz operator. Uncoupled states, that is states representing the interaction of multiple separate spin @@ -1065,7 +1067,7 @@

        Documentation Version
        -class sympy.physics.quantum.spin.JzKetCoupled(j, m, jn, *jcoupling)[source]
        +class sympy.physics.quantum.spin.JzKetCoupled(j, m, jn, *jcoupling)[source]

        Coupled eigenket of Jz

        Spin state that is an eigenket of Jz which represents the coupling of separate spin spaces.

        @@ -1183,13 +1185,13 @@
        Documentation Version
        -class sympy.physics.quantum.spin.JzOp(*args, **kwargs)[source]
        +class sympy.physics.quantum.spin.JzOp(*args, **kwargs)[source]

        The Jz operator.

        -class sympy.physics.quantum.spin.Rotation(*args, **kwargs)[source]
        +class sympy.physics.quantum.spin.Rotation(*args, **kwargs)[source]

        Wigner D operator in terms of Euler angles.

        Defines the rotation operator in terms of the Euler angles defined by the z-y-z convention for a passive transformation. That is the coordinate @@ -1251,7 +1253,7 @@

        Documentation Version
        -classmethod D(j, m, mp, alpha, beta, gamma)[source]
        +classmethod D(j, m, mp, alpha, beta, gamma)[source]

        Wigner D-function.

        Returns an instance of the WignerD class corresponding to the Wigner-D function specified by the parameters.

        @@ -1304,7 +1306,7 @@
        Documentation Version
        -classmethod d(j, m, mp, beta)[source]
        +classmethod d(j, m, mp, beta)[source]

        Wigner small-d function.

        Returns an instance of the WignerD class corresponding to the Wigner-D function specified by the parameters with the alpha and gamma angles @@ -1352,7 +1354,7 @@

        Documentation Version
        -class sympy.physics.quantum.spin.WignerD(*args, **hints)[source]
        +class sympy.physics.quantum.spin.WignerD(*args, **hints)[source]

        Wigner-D function

        The Wigner D-function gives the matrix elements of the rotation operator in the jm-representation. For the Euler angles \(\alpha\), @@ -1445,7 +1447,7 @@

        Documentation Version
        -sympy.physics.quantum.spin.couple(expr, jcoupling_list=None)[source]
        +sympy.physics.quantum.spin.couple(expr, jcoupling_list=None)[source]

        Couple a tensor product of spin states

        This function can be used to couple an uncoupled tensor product of spin states. All of the eigenstates to be coupled must be of the same class. It @@ -1504,7 +1506,7 @@

        Documentation Version
        -sympy.physics.quantum.spin.uncouple(expr, jn=None, jcoupling_list=None)[source]
        +sympy.physics.quantum.spin.uncouple(expr, jn=None, jcoupling_list=None)[source]

        Uncouple a coupled spin state

        Gives the uncoupled representation of a coupled spin state. Arguments must be either a spin state that is a subclass of CoupledSpinState or a spin diff --git a/dev/modules/physics/quantum/state.html b/dev/modules/physics/quantum/state.html index 0f6376e35ea..0f494c3cd7a 100644 --- a/dev/modules/physics/quantum/state.html +++ b/dev/modules/physics/quantum/state.html @@ -329,18 +329,20 @@

      • Linearized Carvallo-Whipple Bicycle Model
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -803,7 +805,7 @@
        Documentation Version

        Dirac notation for states.

        -class sympy.physics.quantum.state.Bra(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.Bra(*args, **kwargs)[source]

        A general time-independent Bra in quantum mechanics.

        Inherits from State and BraBase. A Bra is the dual of a Ket [R777]. This class and its subclasses will be the main classes that users will use for @@ -863,7 +865,7 @@

        Documentation Version
        -class sympy.physics.quantum.state.BraBase(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.BraBase(*args, **kwargs)[source]

        Base class for Bras.

        This class defines the dual property and the brackets for printing. This is an abstract base class and you should not instantiate it directly, @@ -872,7 +874,7 @@

        Documentation Version
        -class sympy.physics.quantum.state.Ket(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.Ket(*args, **kwargs)[source]

        A general time-independent Ket in quantum mechanics.

        Inherits from State and KetBase. This class should be used as the base class for all physical, time-independent Kets in a system. This class @@ -936,7 +938,7 @@

        Documentation Version
        -class sympy.physics.quantum.state.KetBase(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.KetBase(*args, **kwargs)[source]

        Base class for Kets.

        This class defines the dual property and the brackets for printing. This is an abstract base class and you should not instantiate it directly, instead @@ -945,13 +947,13 @@

        Documentation Version
        -class sympy.physics.quantum.state.OrthogonalBra(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.OrthogonalBra(*args, **kwargs)[source]

        Orthogonal Bra in quantum mechanics.

        -class sympy.physics.quantum.state.OrthogonalKet(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.OrthogonalKet(*args, **kwargs)[source]

        Orthogonal Ket in quantum mechanics.

        The inner product of two states with different labels will give zero, states with the same label will give one.

        @@ -969,19 +971,19 @@
        Documentation Version
        -class sympy.physics.quantum.state.OrthogonalState(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.OrthogonalState(*args, **kwargs)[source]

        General abstract quantum state used as a base class for Ket and Bra.

        -class sympy.physics.quantum.state.State(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.State(*args, **kwargs)[source]

        General abstract quantum state used as a base class for Ket and Bra.

        -class sympy.physics.quantum.state.StateBase(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.StateBase(*args, **kwargs)[source]

        Abstract base class for general abstract states in quantum mechanics.

        All other state classes defined will need to inherit from this class. It carries the basic structure for all other states such as dual, _eval_adjoint @@ -996,7 +998,7 @@

        Documentation Version
        -classmethod dual_class()[source]
        +classmethod dual_class()[source]

        Return the class used to construct the dual.

        @@ -1010,7 +1012,7 @@
        Documentation Version
        -class sympy.physics.quantum.state.TimeDepBra(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.TimeDepBra(*args, **kwargs)[source]

        General time-dependent Bra in quantum mechanics.

        This inherits from TimeDepState and BraBase and is the main class that should be used for Bras that vary with time. Its dual is a TimeDepBra.

        @@ -1043,7 +1045,7 @@
        Documentation Version
        -class sympy.physics.quantum.state.TimeDepKet(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.TimeDepKet(*args, **kwargs)[source]

        General time-dependent Ket in quantum mechanics.

        This inherits from TimeDepState and KetBase and is the main class that should be used for Kets that vary with time. Its dual is a @@ -1083,7 +1085,7 @@

        Documentation Version
        -class sympy.physics.quantum.state.TimeDepState(*args, **kwargs)[source]
        +class sympy.physics.quantum.state.TimeDepState(*args, **kwargs)[source]

        Base class for a general time-dependent quantum state.

        This class is used as a base class for any time-dependent state. The main difference between this class and the time-independent state is that this @@ -1115,7 +1117,7 @@

        Documentation Version
        -class sympy.physics.quantum.state.Wavefunction(*args)[source]
        +class sympy.physics.quantum.state.Wavefunction(*args)[source]

        Class for representations in continuous bases

        This class takes an expression and coordinates in its constructor. It can be used to easily calculate normalizations and probabilities.

        @@ -1285,7 +1287,7 @@
        Documentation Version
        -normalize()[source]
        +normalize()[source]

        Return a normalized version of the Wavefunction

        Examples

        >>> from sympy import symbols, pi
@@ -1304,7 +1306,7 @@ 
        Documentation Version
        
 
 
        
 
        
-prob()[source]
        
+prob()[source]
 
        Return the absolute magnitude of the w.f., \(|\psi(x)|^2\)
        
 
        Examples
        
 
        >>> from sympy import symbols, pi
diff --git a/dev/modules/physics/quantum/tensorproduct.html b/dev/modules/physics/quantum/tensorproduct.html
index 2cd2ad5a181..632648078b9 100644
--- a/dev/modules/physics/quantum/tensorproduct.html
+++ b/dev/modules/physics/quantum/tensorproduct.html
@@ -329,18 +329,20 @@
 
      • Linearized Carvallo-Whipple Bicycle Model
        •
      • +
    • Control Tutorials
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • -
  • How-to Guides
      +
    +
    • +
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
      • -
    • Physics -
      • +
    • Physics
    • Solve Equations
      • Solving Guidance
      • Solve an Equation Algebraically
        • @@ -805,7 +807,7 @@
        Documentation Version
        of Many-Particle Systems.”

        -class sympy.physics.secondquant.AnnihilateBoson(k)[source]
        +class sympy.physics.secondquant.AnnihilateBoson(k)[source]

        Bosonic annihilation operator.

        Examples

        >>> from sympy.physics.secondquant import B
@@ -816,7 +818,7 @@ 
        Documentation Version
        -apply_operator(state)[source]
        +apply_operator(state)[source]

        Apply state to self if self is not symbolic and state is a FockStateKet, else multiply self by state.

        Examples

        @@ -834,11 +836,11 @@
        Documentation Version
        -class sympy.physics.secondquant.AnnihilateFermion(k)[source]
        +class sympy.physics.secondquant.AnnihilateFermion(k)[source]

        Fermionic annihilation operator.

        -apply_operator(state)[source]
        +apply_operator(state)[source]

        Apply state to self if self is not symbolic and state is a FockStateKet, else multiply self by state.

        Examples

        @@ -946,7 +948,7 @@
        Documentation Version
        -class sympy.physics.secondquant.AntiSymmetricTensor(symbol, upper, lower)[source]
        +class sympy.physics.secondquant.AntiSymmetricTensor(symbol, upper, lower)[source]

        Stores upper and lower indices in separate Tuple’s.

        Each group of indices is assumed to be antisymmetric.

        Examples

        @@ -1016,37 +1018,37 @@
        Documentation Version
        -sympy.physics.secondquant.B[source]
        +sympy.physics.secondquant.B[source]

        alias of AnnihilateBoson

        -sympy.physics.secondquant.BBra[source]
        +sympy.physics.secondquant.BBra[source]

        alias of FockStateBosonBra

        -sympy.physics.secondquant.BKet[source]
        +sympy.physics.secondquant.BKet[source]

        alias of FockStateBosonKet

        -sympy.physics.secondquant.Bd[source]
        +sympy.physics.secondquant.Bd[source]

        alias of CreateBoson

        -class sympy.physics.secondquant.BosonicBasis[source]
        +class sympy.physics.secondquant.BosonicBasis[source]

        Base class for a basis set of bosonic Fock states.

        -class sympy.physics.secondquant.Commutator(a, b)[source]
        +class sympy.physics.secondquant.Commutator(a, b)[source]

        The Commutator: [A, B] = A*B - B*A

        The arguments are ordered according to .__cmp__()

        Examples

        @@ -1087,7 +1089,7 @@
        Documentation Version
        -doit(**hints)[source]
        +doit(**hints)[source]

        Enables the computation of complex expressions.

        Examples

        >>> from sympy.physics.secondquant import Commutator, F, Fd
@@ -1103,7 +1105,7 @@ 
        Documentation Version
        
 
 
        
 
        
-classmethod eval(a, b)[source]
        
+classmethod eval(a, b)[source]
 
        The Commutator [A,B] is on canonical form if A < B.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import Commutator, F, Fd
@@ -1120,11 +1122,11 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.CreateBoson(k)[source]
        
+class sympy.physics.secondquant.CreateBoson(k)[source]
 
        Bosonic creation operator.
        
 
        
 
        
-apply_operator(state)[source]
        
+apply_operator(state)[source]
 
        Apply state to self if self is not symbolic and state is a FockStateKet, else
 multiply self by state.
        
 
        Examples
        
@@ -1142,11 +1144,11 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.CreateFermion(k)[source]
        
+class sympy.physics.secondquant.CreateFermion(k)[source]
 
        Fermionic creation operator.
        
 
        
 
        
-apply_operator(state)[source]
        
+apply_operator(state)[source]
 
        Apply state to self if self is not symbolic and state is a FockStateKet, else
 multiply self by state.
        
 
        Examples
        
@@ -1254,7 +1256,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.Dagger(arg)[source]
        
+class sympy.physics.secondquant.Dagger(arg)[source]
 
        Hermitian conjugate of creation/annihilation operators.
        
 
        Examples
        
 
        >>> from sympy import I
@@ -1269,7 +1271,7 @@ 
        Documentation Version
        
 
        
 
        
 
        
-classmethod eval(arg)[source]
        
+classmethod eval(arg)[source]
 
        Evaluates the Dagger instance.
        
 
        Examples
        
 
        >>> from sympy import I
@@ -1289,31 +1291,31 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.physics.secondquant.F[source]
        
+sympy.physics.secondquant.F[source]
 
        alias of AnnihilateFermion
        
 
        
 
 
        
 
        
-sympy.physics.secondquant.FBra[source]
        
+sympy.physics.secondquant.FBra[source]
 
        alias of FockStateFermionBra
        
 
        
 
 
        
 
        
-sympy.physics.secondquant.FKet[source]
        
+sympy.physics.secondquant.FKet[source]
 
        alias of FockStateFermionKet
        
 
        
 
 
        
 
        
-sympy.physics.secondquant.Fd[source]
        
+sympy.physics.secondquant.Fd[source]
 
        alias of CreateFermion
        
 
        
 
 
        
 
        
-class sympy.physics.secondquant.FixedBosonicBasis(n_particles, n_levels)[source]
        
+class sympy.physics.secondquant.FixedBosonicBasis(n_particles, n_levels)[source]
 
        Fixed particle number basis set.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import FixedBosonicBasis
@@ -1329,7 +1331,7 @@ 
        Documentation Version
        
 
        
 
        
 
        
-index(state)[source]
        
+index(state)[source]
 
        Returns the index of state in basis.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import FixedBosonicBasis
@@ -1342,7 +1344,7 @@ 
        Documentation Version
        
 
 
        
 
        
-state(i)[source]
        
+state(i)[source]
 
        Returns the state that lies at index i of the basis
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import FixedBosonicBasis
@@ -1357,7 +1359,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.FockState(occupations)[source]
        
+class sympy.physics.secondquant.FockState(occupations)[source]
 
        Many particle Fock state with a sequence of occupation numbers.
        
 
        Anywhere you can have a FockState, you can also have S.Zero.
 All code must check for this!
        
@@ -1366,7 +1368,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.FockStateBosonBra(occupations)[source]
        
+class sympy.physics.secondquant.FockStateBosonBra(occupations)[source]
 
        Describes a collection of BosonBra particles.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import BBra
@@ -1378,7 +1380,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.FockStateBosonKet(occupations)[source]
        
+class sympy.physics.secondquant.FockStateBosonKet(occupations)[source]
 
        Many particle Fock state with a sequence of occupation numbers.
        
 
        Occupation numbers can be any integer >= 0.
        
 
        Examples
        
@@ -1391,13 +1393,13 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.FockStateBra(occupations)[source]
        
+class sympy.physics.secondquant.FockStateBra(occupations)[source]
 
        Representation of a bra.
        
 
        
 
 
        
 
        
-class sympy.physics.secondquant.FockStateFermionBra(occupations, fermi_level=0)[source]
        
+class sympy.physics.secondquant.FockStateFermionBra(occupations, fermi_level=0)[source]
 
        Examples
        
 
        >>> from sympy.physics.secondquant import FBra
 >>> FBra([1, 2])
@@ -1412,7 +1414,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.FockStateFermionKet(occupations, fermi_level=0)[source]
        
+class sympy.physics.secondquant.FockStateFermionKet(occupations, fermi_level=0)[source]
 
        Many-particle Fock state with a sequence of occupied orbits.
        
 
        Explanation
        
 
        Each state can only have one particle, so we choose to store a list of
@@ -1431,13 +1433,13 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.FockStateKet(occupations)[source]
        
+class sympy.physics.secondquant.FockStateKet(occupations)[source]
 
        Representation of a ket.
        
 
        
 
 
        
 
        
-class sympy.physics.secondquant.InnerProduct(bra, ket)[source]
        
+class sympy.physics.secondquant.InnerProduct(bra, ket)[source]
 
        An unevaluated inner product between a bra and ket.
        
 
        Explanation
        
 
        Currently this class just reduces things to a product of
@@ -1460,7 +1462,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.KroneckerDelta(i, j, delta_range=None)[source]
        
+class sympy.physics.secondquant.KroneckerDelta(i, j, delta_range=None)[source]
 
        The discrete, or Kronecker, delta function.
        
 
        
 
        Parameters:
        
@@ -1511,7 +1513,7 @@ 
        Documentation Version
        
 
        
 
        
 
        
-classmethod eval(i, j, delta_range=None)[source]
        
+classmethod eval(i, j, delta_range=None)[source]
 
        Evaluates the discrete delta function.
        
 
        Examples
        
 
        >>> from sympy import KroneckerDelta
@@ -1708,7 +1710,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.NO(arg)[source]
        
+class sympy.physics.secondquant.NO(arg)[source]
 
        This Object is used to represent normal ordering brackets.
        
 
        i.e.  {abcd}  sometimes written  :abcd:
        
 
        Explanation
        
@@ -1733,7 +1735,7 @@ 
        Documentation Version
        
 Nothing more, nothing less.
        
 
        
 
        
-doit(**hints)[source]
        
+doit(**hints)[source]
 
        Either removes the brackets or enables complex computations
 in its arguments.
        
 
        Examples
        
@@ -1754,7 +1756,7 @@ 
        Documentation Version
        
 
 
        
 
        
-get_subNO(i)[source]
        
+get_subNO(i)[source]
 
        Returns a NO() without FermionicOperator at index i.
        
 
        Examples
        
 
        >>> from sympy import symbols
@@ -1814,7 +1816,7 @@ 
        Documentation Version
        
 
 
        
 
        
-iter_q_annihilators()[source]
        
+iter_q_annihilators()[source]
 
        Iterates over the annihilation operators.
        
 
        Examples
        
 
        >>> from sympy import symbols
@@ -1836,7 +1838,7 @@ 
        Documentation Version
        
 
 
        
 
        
-iter_q_creators()[source]
        
+iter_q_creators()[source]
 
        Iterates over the creation operators.
        
 
        Examples
        
 
        >>> from sympy import symbols
@@ -1860,12 +1862,12 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.PermutationOperator(i, j)[source]
        
+class sympy.physics.secondquant.PermutationOperator(i, j)[source]
 
        Represents the index permutation operator P(ij).
        
 
        P(ij)*f(i)*g(j) = f(i)*g(j) - f(j)*g(i)
        
 
        
 
        
-get_permuted(expr)[source]
        
+get_permuted(expr)[source]
 
        Returns -expr with permuted indices.
        
 
        Explanation
        
 
        >>> from sympy import symbols, Function
@@ -1882,7 +1884,7 @@ 
        Documentation Version
        
 
 
        
 
        
-class sympy.physics.secondquant.VarBosonicBasis(n_max)[source]
        
+class sympy.physics.secondquant.VarBosonicBasis(n_max)[source]
 
        A single state, variable particle number basis set.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import VarBosonicBasis
@@ -1894,7 +1896,7 @@ 
        Documentation Version
        
 
        
 
        
 
        
-index(state)[source]
        
+index(state)[source]
 
        Returns the index of state in basis.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import VarBosonicBasis
@@ -1912,7 +1914,7 @@ 
        Documentation Version
        
 
 
        
 
        
-state(i)[source]
        
+state(i)[source]
 
        The state of a single basis.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import VarBosonicBasis
@@ -1927,7 +1929,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.physics.secondquant.apply_operators(e)[source]
        
+sympy.physics.secondquant.apply_operators(e)[source]
 
        Take a SymPy expression with operators and states and apply the operators.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import apply_operators
@@ -1940,7 +1942,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.physics.secondquant.contraction(a, b)[source]
        
+sympy.physics.secondquant.contraction(a, b)[source]
 
        Calculates contraction of Fermionic operators a and b.
        
 
        Examples
        
 
        >>> from sympy import symbols
@@ -1977,7 +1979,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.physics.secondquant.evaluate_deltas(e)[source]
        
+sympy.physics.secondquant.evaluate_deltas(e)[source]
 
        We evaluate KroneckerDelta symbols in the expression assuming Einstein summation.
        
 
        Explanation
        
 
        If one index is repeated it is summed over and in effect substituted with
@@ -2037,7 +2039,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.physics.secondquant.matrix_rep(op, basis)[source]
        
+sympy.physics.secondquant.matrix_rep(op, basis)[source]
 
        Find the representation of an operator in a basis.
        
 
        Examples
        
 
        >>> from sympy.physics.secondquant import VarBosonicBasis, B, matrix_rep
@@ -2063,7 +2065,7 @@ 
        Documentation Version
        
 
        permutation_operators,
        
 
        
 
-)[source]
+)[source]
 
        Performs simplification by introducing PermutationOperators where appropriate.
        
 
        Explanation
        
 
        
@@ -2106,7 +2108,7 @@ 
        Documentation Version
        
 
        pretty_indices={},
        
 
        
 
-)[source]
+)[source]
 
        Collect terms by substitution of dummy variables.
        
 
        Explanation
        
 
        This routine allows simplification of Add expressions containing terms
@@ -2165,7 +2167,7 @@ 
        Documentation Version
        
 
 
        
 
        
-sympy.physics.secondquant.wicks(e, **kw_args)[source]
        
+sympy.physics.secondquant.wicks(e, **kw_args)[source]
 
        Returns the normal ordered equivalent of an expression using Wicks Theorem.
        
 
        Examples
        
 
        >>> from sympy import symbols, Dummy
diff --git a/dev/modules/physics/sho.html b/dev/modules/physics/sho.html
index e7f753f2d72..d22eb6c58a6 100644
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+++ b/dev/modules/physics/sho.html
@@ -329,18 +329,20 @@
 
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