# simplify sinh expression

I guess I just ran up against one of those maxima things again, but I thought I would signal the problem anyway.

I would have expected Sage to simplify

sinh(log(1+sqrt(2)))

(it is 1), but Sage doesn't. It doesn't return True to the following either

arcsinh(1)==1+sqrt(2)

or am I missing something?

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sinh(log(1+sqrt(2))).n() 1.00000000000000

( 2013-01-20 04:49:07 -0600 )edit

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Wouldn't be the worst thing in the world if someone had a look at our simplification heuristics. In the meantime:

sage: y = sinh(log(1+sqrt(2)))
sage: y.simplify_full()
sinh(log(sqrt(2) + 1))
sage: y.maxima_methods().exponentialize()
-1/2/(sqrt(2) + 1) + 1/2*sqrt(2) + 1/2
sage: y.maxima_methods().exponentialize().simplify_full()
1
more

Really, we have to decide if we want complete granularity like Maxima, which leads to things without ambiguity because you would choose whether to use methods that "simplify" multivalued functions like log, or to continue our current point of adding more and more methods to simplification. I lean toward the latter, but maybe it's time to think about that again.

( 2013-01-21 01:51:44 -0600 )edit