On Mar 26, 2:15 pm, Alan Bromborsky <abro...@verizon.net> wrote:
> I have copied the trigsimp code from simplify.py and modified it to work
> with hyperbolic trig functions (see below). I am not ready to submit it
> as a patch yet. I want to get more complicated examples of hyperbolic
> trig simplification (ones that require the recursion option) and would
> also like to get examples that contain both trig and hyperbolic trig
> functions to see if sequential application of trigsimp and
> hyperbolicsimp would work and if the order of application is important.
> Would anyone who have any possible examples please post them (or just
> take the code below and run their own examples).
>
> from sympy import SYMPY_DEBUG
>
> from sympy.core import Basic, S, C, Add, Mul, Pow, Rational, Integer, \
> Derivative, Wild, Symbol, sympify
>
> from sympy.core.numbers import igcd
>
> from sympy.utilities import make_list, all
> from sympy.functions import gamma, exp, sqrt
>
> from sympy.simplify.cse_main import cse
>
> from sympy.polys import Poly
>
> import sympy.mpmath as mpmath
>
> from sympy import *
>
> def hyperbolicsimp(expr, deep=False, recursive=False):
> """
> Usage
> =====
> hyperbolicsimp(expr) -> reduces expression by using known
> hyperbolic trig identities
>
> Notes
> =====
>
> deep ........ apply hyperbolicsimp inside functions
> recursive ... use common subexpression elimination (cse()) and apply
> hyperbolicsimp recursively (recursively==True is quite
> expensive
> operation of the expression is large)
>
> Examples
> ========
> >>> from sympy import *
> >>> x = Symbol('x')
> >>> y = Symbol('y')
> >>> e = 2*cosh(x)**2 - 2*sinh(x)**2
> >>> hyperbolicsimp(e)
> 2
> >>> hyperbolicsimp(log(e))
> log(2*cosh(x)**2 - 2*sinh(x)**2)
> >>> hyperbolicsimp(log(e), deep=True)
> log(2)
> """
> if recursive:
> w, g = cse(expr)
> g = hyperbolicsimp_nonrecursive(g[0])
> for sub in reversed(w):
> g = g.subs(sub[0], sub[1])
> g = hyperbolicsimp_nonrecursive(g)
> return(g)
> else:
> return hyperbolicsimp_nonrecursive(expr, deep)
>
> def hyperbolicsimp_nonrecursive(expr, deep=False):
> """
> A nonrecursive hyperbolic trig simplifier, used from hyperbolicsimp.
>
> Usage
> =====
> hyperbolicsimp_nonrecursive(expr) -> reduces expression by
> using known hyperbolic trig identities
>
> Notes
> =====
>
> deep ........ apply hyperbolicsimp inside functions
>
> Examples
> ========
> >>> from sympy import *
> >>> x = Symbol('x')
> >>> y = Symbol('y')
> >>> e = 2*cosh(x)**2 - 2*sinh(x)**2
> >>> hyperbolicsimp(e)
> 2
> >>> hyperbolicsimp(log(e))
> log(2*cosh(x)**2 - 2*sinh(x)**2)
> >>> hyperbolicsimp(log(e), deep=True)
> log(2)
> """
> from sympy.core.basic import S
> sinh, cosh, tanh, coth = C.sinh, C.cosh, C.tanh, C.coth
>
> #XXX this stopped working:
> if expr == 1 - 1/cosh(Symbol("x"))**2:
> return tanh(Symbol("x"))**2
^^^
I think this should rather use pattern matching for the sake of not
only working with cosh(x).
Vinzent
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