On Sat, Apr 28, 2012 at 12:42 AM, Tom Bachmann <e_mc...@web.de> wrote:
> On 28.04.2012 02:42, Aaron Meurer wrote:
>>
>> On Fri, Apr 27, 2012 at 2:46 PM, Tom Bachmann<e_mc...@web.de> wrote:
>>>
>>> A quick update:
>>>
>>> I implemented a much better selection strategy for the groebner basis
>>> algorithm ("sugar cube"), implemented the "extended version" (with
>>> trasformation matrix) and improved the algorithm to compute module
>>> quotients
>>> to use only one groebner basis computation. This sped up the
>>> implementation
>>> of the "rational simplification algorithm 1" quite significantly.
>>>
>>> All of this is in my agca8 branch which has no pull request, yet. Testing
>>> is
>>> a bit difficult since trigsimp_groebner is not in master, yet.
>>
>>
>> So let's get it merged. The issue I see is that we need to come up
>> with a good default/heuristics for the parameters (esp. polynomial and
>> hints). Any thoughts on that?
>>
>
> Yes, that's definitely a usability issue. I'm not quite sure how to go about
> it.
>
>
>> And I guess it should be integrated with trigsimp() better. How do
>> you think the existing algorithm should fit into things? We'll also
>> want to integrate it with the recursive version, so that it can
>> simplify trig expressions that are nested in other trig expressions,
>> and also make it so it can simplify things like sin(x)**2 + cos(x)**2
>> + sqrt(sin(x)) (take out the non-rational function parts).
>>
>
> Yes, absolutely. I'll see what I can do.
>
>
>> Do you know of any other issues that should prevent it from being merged?
>>
>
> Nothing I can think of.
>
>
>> Regarding cancel() being slow, this might be the dense representation
>> again, though I think also the PRS algorithm used to compute the gcd
>> of multivariate polynomials occasionally hits a worse-case complexity.
>>
>
> Hm. Note that the denominator is 1, so really there should not be anything
> fancy happening wrt multivariate polynomial algorithms. What it *does* do is
> take out denominators, for which factorizations over the integers are
> necessary. Not sure how fast that should be (integer gcd is very fast, but
> naively I would expect the required number of gcd computations to blow up
> quickly).
So all it's doing is computing the lcm of the coefficients? I don't
see how that would take so much time. If this is true, then I suppose
an option could be added to cancel to disable this, as it's not really
necessary.
Aaron Meurer
>
>
>> Aaron Meurer
>>
>>>
>>>
>>> On 23.04.2012 22:02, Tom Bachmann wrote:
>>>>>
>>>>>
>>>>> The first algorithm in the paper where ratsimpmodprime was taken from
>>>>> should
>>>>> probably do quite well - as far as I can tell it shoud be about as fast
>>>>> as polynomial=True (maybe two or three times slower, or something of
>>>>> that order - not 100 times), and work quite well (it minimizes the
>>>>> maximum of the degrees of numerator and denominator). Will take a bit
>>>>> of
>>>>> work to implement, though (although it will nicely show of my
>>>>> commutative algebra module :D).
>>>>
>>>>
>>>>
>>>> I implemented this in agca8 (no pull request, yet). It works, but I
>>>> think its probably not very fast since my algorithms are not
>>>> particularly optimized. When we push the trigsimp PR I will see how it
>>>> goes with the other algorithm.
>>>>
>>>
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>>
>
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