math prompt improvements

reasoning_gym/algebra/intermediate_integration.py

@@ -77,9 +77,10 @@ def __init__(self, config: IntermediateIntegrationConfig):
             "Evaluate the indefinite integral: ∫ {integrand} dx",
         ]
         self.added_instruction = """
-In addition, when doing calculation, use the following instructions together with your mathematical ingenuity to solve the integral problems
-## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
-## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
+When performing calculations, please follow these guidelines:
+1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
+2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
+3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).
 """
 
     def _get_outer_constant(self, rng: random.Random) -> int:

reasoning_gym/algebra/polynomial_multiplication.py

@@ -69,9 +69,9 @@ def __init__(self, config: PolynomialMultiplicationConfig):
             "Calculate the following: {polynomial_expr}",
         ]
         self.added_instruction = """
-In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
-## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
-## 2. Always use * when doing all sorts of multiplcation in your reasoning steps and even in reporting answers.
+When performing calculations, please follow these guidelines:
+1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
+2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
 """
         super().__init__(config=config, seed=config.seed, size=config.size)
 

reasoning_gym/algebra/simple_integration.py

@@ -42,9 +42,9 @@ def __init__(self, config: SimpleIntegrationConfig):
             "Evaluate the indefinite integral: ∫ {integrand} dx",
         ]
         self.added_instruction = """
-In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
-## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
-## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
+When performing calculations, please follow these guidelines:
+1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
+2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
 """
         super().__init__(config=config, seed=config.seed, size=config.size)