On 21.04.2012 20:52, Aaron Meurer wrote:
I didn't enable cython in the polys, but for me,
trigsimp_groebner(smallExpr, quick=True, hints=[2]) takes 194 seconds
in your latest branch. On the other hand,
smallExpr.rewrite(exp).expand().rewrite(cos).cancel() takes 12
seconds, and produces the same answer.
Well that is embarassing *g*. But I don't think ratsimpmodprime can beat
this. The point is that expand, rewrite etc is very directed, whereas
ratsimpmodprime essentially just does a "dumb" search. That's also why
it gets so slow as soon as the number of generators increases.
So there's still some work to be done.
Aaron Meurer
On Sat, Apr 21, 2012 at 6:20 AM, Tom Bachmann<e_mc...@web.de> wrote:
Ok, so I pushed the changes to my trigsimp branch. There are two commits,
WIP and WIP2.
The basic idea is the following: suppose there are two sets of variables,
x1,..., xn, y1, .., yn, such that none of the xi appears in the generators
of the ideal -- they are "free" generators. Then really we have not much
hope of ever getting rid of xi-s in the fraction. Specifically, if the
fraction is actually a polynomial is the xis, then we cannot ever do better
than simplifying just the coefficients.
That what WIP implements.
Another obervation is that if the coefficients involve different subsets of
the the yi-s, then the ratsimp can be sped up further by using only the
relevant variables. In fact the groebner basis computed for all variables
together can (under reasonable assumptions on the groebner basis computation
algorithm) be split according to these disjoint subsets. This is what WIP2
implements (you will notice that doing this splitting is quite a bit of
work).
Running trigsimp(smallExpr, quick=True, hints=[2]) takes 200 seconds with
WIP2 (both ideas), and 250 seconds with WIP (only the first idea).
We end up with expressions like sin(q2)*cos(2*q3)*cos(q4) - sin(q2)*cos(q4).
Trigsimp_groebner takes forever on this sort of expression - it's just too
many variables. There are simpler expressions involving sin(q2+q3) etc, but
trigsimp_groebner is bad at finding them (you have to provide them in the
hints, essentially...).
On 21.04.2012 09:20, Tom Bachmann wrote:
Hi,
I implemented some optimizations (not yet pushed) which allowed me to run
trigsimp_groebner(smallExpr, quick=True, hints=[2])
in "reasonable" time (~5 minutes).
The result is this:
ddq1*(sin(q2)*sin(q4)*cos(2*q3) + cos(q2)*cos(q3)*cos(q4)) -
ddq2*sin(2*q3)*sin(q4) + ddq3*cos(q3)*cos(q4) + ddq4*sin(q3)*sin(q4) +
dq1**2*(-sin(2*q2)*sin(2*q3)*sin(q4)/2 - sin(q3)*cos(2*q2)*cos(q4)) +
dq1*dq3*(-2*sin(q2)*sin(2*q3)*sin(q4) - 2*sin(q3)*cos(q2)*cos(q4)) +
dq1*dq4*(sin(q2)*cos(2*q3)*cos(q4) - sin(q2)*cos(q4)) -
2*dq2*dq3*sin(q4)*cos(2*q3) - dq2*dq4*sin(2*q3)*cos(q4) -
dq3**2*sin(q3)*cos(q4) + dq4**2*sin(q3)*cos(q4)
(len(str(smallExpr))/len(str(this)) is about 30!)
It seems quite possible to run trigsimp_groebner with more aggressive
parameters on this much shorter expression ... but I'll have breakfast
now :-).
On 20.04.2012 02:22, Aaron Meurer wrote:
Great. I think the best way to demonstrate new functionality like
this is to just create a special function that does it (like
trigsimp_groebner) in some branch, and add that to __init__.py. Then,
when it is ready to go in, remove it from __init__.py and integrate it
directly into the main function (in this case trigsimp). This is how
I've done things with risch_integrate in my integration3 branch, and I
plan to remove it and just put it in integrate() when I'm done.
I tried the expressions from
https://groups.google.com/d/topic/sympy/3y6orHV2_4k/discussion (see
the tarball linked to in the first post). I just tried the small
expression with n=1, but it just hung on the reduction step. Any
thoughts on how to make this faster? Those expressions would make good
stress tests for this.
Aaron Meurer
On Thu, Apr 19, 2012 at 3:03 PM, Tom Bachmann<e_mc...@web.de> wrote:
I have pushed a more usable trigsimp_groebner to my new trigsimp
branch. It
is probably buggy, but I've had enough for today. Just to let anyone
know
who might wish to try it out :).
Best,
Tom
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