#572 trigsimp exponentially slow on lists

[Stavros Macrakis]

trigsimp of a [] list can sometimes take time exponential
in the length of the list.

For example:

trigsimp(makelist(sin(i)^2+cos(i)^2,i,1,N))

for N=4,5,... takes 0.12, 0.52, 1.50, 4.45, 13.97 secs.

Also for sin(i)^2.

Of course, it should take linear time.

This doesn't happen

[Stavros Macrakis]

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Oops, "this doesn't happen" should continue... in other cases,
like sin(1)^2, sin(x)^2+cos(x)^2, etc.

[Raymond Toy]

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This is probably due to the way trigsimp1 and improve work
(share/trigonometry/trgsmp.mac).

It looks like caused by trigsimp1 and improve, which cause
quadratic behavior, I think.

I think if trigsimp3 is modified to map(trigsimp1,
num(expn))/map(trigsimp1,denom(expn), things will work much
faster. Some care must be taken in case expn is not a list,
but that's not too difficult.

[Raymond Toy]

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Fixed. trigsimp3 modified to handle each element of the
list one at a time instead of trying to do the entire list
all at once.