From c4f1f2bb4fe9e7bf67baca7f90c3366e64caea78 Mon Sep 17 00:00:00 2001 From: rocky Date: Sat, 8 Jul 2023 19:52:11 -0400 Subject: [PATCH] ComplexExpand doc corrections/completions --- mathics/builtin/numbers/hyperbolic.py | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/mathics/builtin/numbers/hyperbolic.py b/mathics/builtin/numbers/hyperbolic.py index b0b1f6b60..774c0f386 100644 --- a/mathics/builtin/numbers/hyperbolic.py +++ b/mathics/builtin/numbers/hyperbolic.py @@ -261,6 +261,9 @@ class ComplexExpand(SympyFunction):
'ComplexExpand[$expr$]'
expands $expr$ assuming that all variables are real. + +
'ComplexExpand[$expr$,{$x1$,$x2$, ...}] +
expands $expr$ assuming that variables matching any of the $xi$ are complex.
Note: we get equivalent, but different results from WMA: @@ -268,7 +271,7 @@ class ComplexExpand(SympyFunction): >> ComplexExpand[3^(I x)] = 3 ^ (-Im[x]) Re[3 ^ (I Re[x])] + I Im[3 ^ (I Re[x])] 3 ^ (-Im[x]) - Assume that both and are real: + Assume that both $x$ and $y$ and are real: >> ComplexExpand[Sin[x + I y]] = Cosh[y] Sin[x] + I Cos[x] Sinh[y] @@ -289,7 +292,7 @@ class ComplexExpand(SympyFunction): >> ComplexExpand[Abs[2^z Log[2 z]], z] = Abs[I Arg[Re[z] + I Im[z]] + Log[4 Im[z] ^ 2 + 4 Re[z] ^ 2] / 2] 2 ^ Re[z] - Specify that a variable is take to be complex: + Specify that variable $z$ is taken to be complex: >> ComplexExpand[Re[2 z^3 - z + 1], z] = 1 - Re[z] + 2 Re[z] ^ 3 - 6 Im[z] ^ 2 Re[z] """