Dox a écrit :
Hi guys! I have an easy question... got an expression with
exponentials, say exp(x)+exp(-x), How can I get the result in terms of
hyperbolic functions
1/ First you can use the expr.subs method :
y=exp(x)+exp(-x)
y.subs(exp(x)==sinh(x)+cosh(x)).subs(exp(-x)=cosh(x)-sinh(x))
[You must call subs for all subexpressions : exp(x) and (exp(-x)]
2/ Second you can also play with match, find and subs :
w0=SR.wild(0) # w0 is now a matching subexpression
y.subs(exp(w0)==cosh(w0)+sinh(w0))
The result is sinh(-x) + sinh(x) + cosh(-x) + cosh(x)
And then y.subs(exp(w0)==cosh(w0)+sinh(w0)).simplify() is pretty.
I think it's impossible to subs the function exp to the other (sum of)
function(s) exp=cosh+sinh.
You must use the regular subexpression SR.wild(0) [look at help about
find, subs and match]
3/ Third, you can use the outside Sage function rewrite published at
http://wiki.sagemath.org/symbolics/rewrite and get the attachement file
rewriteXXXX.sage, load it.
and call rewrite (y, rules="exp2sinhcosh").
Choice what you prefer !
F.
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