Hi Volker,
first of all, to the OP, sorry that the original topic of the thread has changed.
On 2014-12-29, Volker Braun <
vbrau...@gmail.com> wrote:
> On Monday, December 29, 2014 2:27:49 AM UTC+1, Simon King wrote:
>>
>> In fact, a year or two ago, I had experimental code where I did follow
>> the aproach to use Python objects (of course cythoned). It tought me much
>> (about theory), but it wasn't really competitive.
>>
>
> Competitive relative to what?
1.
Task: Computation of Gröbner bases for modules over path algebras.
Competitor: Letterplace (distributed with Singular), which deals with homogeneous
two-sided ideals in free algebras.
Aim: Be faster. Include the non-homogeneous and the one-sided case (of course,
finite Gröbner bases will not always exist). Work over path algebras, which are
more general than free algebras. Avoid a memory leak that appears in Letterplace
(or its Sage wrapper, not sure where the problem lies).
2.
Task: Computation of minimal generating sets for modules over basic algebras,
with an application to the computation of minimal projective resolutions for
basic algebras.
Competitor: David Green's C programs for the computation of minimal projective
resolutions for modular group algebras of prime power groups (distributed in
my optional group cohomology spkg).
Aim: Be faster. Work over basic algebras, which are more general than
modular group algebras of prime power groups. Compute Loewy layers for
modules over basic algebras, which is more general than computing a minimal
generating set.
3.
Task: Compute Ext algebras of basic algebras.
Competitor: Robert Michael Pawloski's programs.
Aim: Be faster and deal with bigger examples than what he describes in
his PhD thesis.
4.
"Holy grail": Compute the modular cohomology rings of Mathieu group M_{24}
(that's too big for the current group cohomology spkg).
> If you are just doubling the number of Python
> objects then how is that not just a factor of 2 in the worst case?
What do you mean by doubling the number of Python objects? Do you mean:
"The coefficients are Python objects anyway, so, what's the problem if
the terms become Python objects, too?"
> Hence geobuckets where each bucket is typically implemented as
> memory-contiguous array, no?
My reference is "The Geobucket Data Structure for Polynomials" of Thomas
Yan. His buckets are decreasingly sorted lists of terms. He doesn't
mention arrays. Do you have a different reference in mind? Or do you
think I misunderstood what he means (I thought "sorted list" would be
implemented as a linked list, not as an array)?
Best regards,
Simon