From 689d2c8902f16fa460804847e9d3143a30cdc8f7 Mon Sep 17 00:00:00 2001
From: john verzani <jverzani@gmail.com>
Date: Thu, 25 Apr 2024 21:50:40 -0400
Subject: [PATCH] Lim (#66)
* different display for lim
* one more tweak
* doc string update
---
Project.toml | 2 +-
src/limits.jl | 145 +++++++++++++++++++++++++++++++++++++++-----------
2 files changed, 114 insertions(+), 33 deletions(-)
diff --git a/Project.toml b/Project.toml
index ec7eb6f..184f0c3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
name = "CalculusWithJulia"
uuid = "a2e0e22d-7d4c-5312-9169-8b992201a882"
-version = "0.2.2"
+version = "0.2.3"
[deps]
Base64 = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
diff --git a/src/limits.jl b/src/limits.jl
index 2e5a2c5..b2fdc2d 100644
--- a/src/limits.jl
+++ b/src/limits.jl
@@ -1,20 +1,41 @@
"""
- lim(f, c; n=5, dir="+")
+ lim(f, c; n=6, m=1, dir="+-")
lim(f, c, dir; n-5)
Means to generate numeric table of values of `f` as `h` gets close to `c`.
+* `n`, `m`: powers of `10` to add (subtract) to (from) `c`.
+* `dir`: Either `"+-"` (show left and right), `"+"` (right limit), or `"-"` (left limit). Can also use functions `+`, `-`, `±`.
+
Example:
+
```
-f(x) = sin(x) / x
-lim(f, 0)
+julia> f(x) = sin(x) / x
+f (generic function with 1 method)
+
+julia> lim(f, 0)
+ 0.1 0.9983341664682815
+ 0.01 0.9999833334166665
+ 0.001 0.9999998333333416
+ 0.0001 0.9999999983333334
+ 1.0e-5 0.9999999999833332
+ 1.0e-6 0.9999999999998334
+ ⋮ ⋮
+ c L?
+ ⋮ ⋮
+-1.0e-6 0.9999999999998334
+-1.0e-5 0.9999999999833332
+-0.0001 0.9999999983333334
+-0.001 0.9999998333333416
+-0.01 0.9999833334166665
+-0.1 0.9983341664682815
```
"""
-function lim(f::Function, c::Real; n::Int=6, m::Int=1, dir="+")
+function lim(f::Function, c::Real; n::Int=6, m::Int=1, dir="+-")
dir = string(dir)
Limit(f, c, n, m, dir)
end
-lim(f::Function, c::Real, dir; n::Integer=5, m::Integer=1) = lim(f,c; n, m, dir=string(dir))
+lim(f::Function, c::Real, dir; n::Int=6, m::Int=1) = lim(f,c; n, m, dir=string(dir))
struct Limit{F,R}
@@ -26,41 +47,101 @@ struct Limit{F,R}
end
# try to better align numbers
+_l8(x) = length(string(x)) ÷ 8
+
function Base.show(io::IO, L::Limit)
(; f,c,n,m,dir) = L
+
+ ms = maximum(length ∘ string, (c-1/10^n, c+1/10^n))
+ sc = (sign(c-m) * sign(c+m) < 0)
+
+ h = 1/10^n
+ nt = 2 + maximum(_l8, (c-h, c+h)) + (n ÷ 8)
+
+ if dir == "+" || dir == "+-" || dir == "±"
+ show₊(io, L; sc, ms)
+ end
+ print_dots(io, "c", "L?"; sc, ms)
+ if dir == "-" || dir == "--" || dir == "+-" || dir == "±"
+ show₋(io, L; sc, ms)
+ end
+ nothing
+end
+
+function show₊(io::IO, L::Limit; sc=false, ms=0)
+
+ (; f,c,n,m,dir) = L
+
hs = [1/10^i for i in m:n] # close to 0
- if dir == "+"
- xs = c .+ hs
- else
- xs = c .- hs
+ xsᵣ = c .+ hs
+ ysᵣ = string.(f.(xsᵣ))
+
+ last_y = nothing
+
+ for (x,y) ∈ zip(xsᵣ, ysᵣ)
+ print_next(io, x, y, last_y; sc, ms)
+ last_y = y
+ println(io, "")
end
- ys = string.(map(f, xs))
- _l8(x) = length(string(x)) ÷ 8
- nt = 2 + _l8(first(xs)) + (n ÷ 8)
- nl = false
+ print_dots(io; sc, ms)
+end
+
+# show - case
+function show₋(io::IO, L::Limit; sc=false, ms=0)
+ (; f,c,n,m,dir) = L
+
+ hs = [1/10^i for i in n:-1:m] # close to 0
+ xsₗ = c .- hs
+ ysₗ = string.(f.(xsₗ))
+
last_y = nothing
- for (x,y) ∈ zip(xs, ys)
- nl && println(io, "")
- nl = true
- print(io, x)
- m = _l8(x)
- print(io, "\t"^(nt-m))
- if isnothing(last_y)
- print(io, y)
+
+ i, l = 1, length(ysₗ)
+ nl = true
+ #dir == "-" && print_dots(io; sc, ms)
+ print_dots(io; sc, ms)
+ for (x, y) ∈ zip(xsₗ, ysₗ)
+ if i == l
+ last_y = nothing
+ nl = false
else
- flag = true
- ly = length(last_y)
- for (i,yᵢ) ∈ enumerate(y)
- if flag && i <= ly && yᵢ == last_y[i]
- printstyled(io, yᵢ; bold=true)
- else
- print(io, yᵢ)
- flag=false
- end
+ last_y = ysₗ[i+1]
+ i += 1
+ end
+ print_next(io, x, y, last_y; sc, ms)
+ nl && println(io, "")
+ end
+
+end
+
+# print dots or c L
+function print_dots(io::IO, l="⋮", r="⋮"; sc, ms)
+ d = ms ÷ 2
+ println(io, " "^d, l, " "^(4 +2d), r)
+end
+
+
+# print next number referring to last one for styling
+function print_next(io::IO, x, y, last_y=nothing; sc=false, ms=0)
+ xₛ = string(x)
+ sc && x > 0 && (xₛ = " " * xₛ)
+
+ print(io, xₛ)
+ l = length(xₛ)
+ print(io, " "^(ms - l + 5))
+ if isnothing(last_y)
+ print(io, y)
+ else
+ flag = true
+ ly = length(last_y)
+ for (i,yᵢ) ∈ enumerate(y)
+ if flag && i <= ly && yᵢ == last_y[i]
+ printstyled(io, yᵢ; bold=true)
+ else
+ print(io, yᵢ)
+ flag=false
end
end
- last_y = y
end
- nothing
end