Why abs(sin(pi/n)) is not simplified by sin(pi/n) when n>2
I try to simplify an expression but Sage can't to do so.
This is my code :
sage: n= var("n")
sage: assume(n,'integer',n>2)
sage: show((abs(sin(pi/n))).simplify_full().simplify_trig())
But this code :
sage: show((abs(pi/n)).simplify())
gives "of course" the good result :
pi/n
Can someone explain to me what is happening?
The most one can say here is that Maxima doesn't "know" that sin(pi/n) is, in fact, positive. The assumptions framework in Maxima (and hence Sage) is acknowledged to be fairly weak.
It is unfortunate because for more complicated expressions that simplify a lot, we can not rely on Sage for such simplification. Thanks Krisman for your help!