On Sun, Aug 24, 2008 at 11:03 AM, Ryan <[EMAIL PROTECTED]> wrote:
>
> Thanks, both seem like workable options. A related question...
>
> There are alot of different simplify commands, but not one that seems
> to be effective for hyperbolic trig functions. For instance
>
> cosh(arcsinh(3/2)) simplifies to sqrt(13)/2
>
> but none of the simplify commands seem to produce this.
>
> Any thoughts?
>
Wait a little? In the new Ginac-based Sage symbolic
code that Burcin and I are implementing right now this works
automatically:
sage: x = var('x', ns=1); S = x.parent()
sage: S(3/2).arcsinh().cosh()
sqrt(13/4)
Keep your eye on
http://trac.sagemath.org/sage_trac/ticket/3872
Ginac is a very robust fast C++ library for symbolic manipulation
that will replace most of Sage's current dependence on Maxima
by something much better. http://www.ginac.de/
Sympy doesn't automatically do the above simplification (yet):
sage: import sympy
sage: Integer = sympy.Integer
sage: sympy.cosh(sympy.asinh(3/2))
cosh(asinh(3/2))
By the way, in ginac the C++ code that defines the above simplification
is here:
if (is_exactly_a<function>(x)) {
const ex &t = x.op(0);
// cosh(acosh(x)) -> x
if (is_ex_the_function(x, acosh))
return t;
// cosh(asinh(x)) -> sqrt(1+x^2)
if (is_ex_the_function(x, asinh))
return sqrt(_ex1+power(t,_ex2));
// cosh(atanh(x)) -> 1/sqrt(1-x^2)
if (is_ex_the_function(x, atanh))
return power(_ex1-power(t,_ex2),_ex_1_2);
}
It's in the file inifcns_trans.cpp in the ginac distribution.
William
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