Re: [Axiom-developer] Re: My Maxima Zeilberger

[William Sit]

Tim Daly wrote:
> 
> Fabrizio wrote:
> >
> >I am now working on optimizations
> >and I still have to check the results of my benchmark
> >against Mathematica's equivalent package.
> >
> >
> >Was the "fast_linsolve" command ever implemented
> >in MaXima?
> 
> I've never used any solution package in Maxima.
> 
> >This command could make hypergeometric summation
> >in Maxima MUCH faster because the bottle of the
> >algorithm is a sparse system of linear equations
> >with polynomial/rational coefficients.
> 
> I believe that PLEQN might do what you want.

As the author of PLEQN (in Axiom), I am sorry to say that the package is not
suitable for any large system, even if it is sparse. Certain subroutines in that
package would need to be made more efficient to take care of the sparse
structure (not just sparseness). For example, if your system is sparse and
bilinear (that is the coefficients are linear in their variables), you may try a
heuristic algorithm. Fritz Schwartz has done something like that in his LODO
package (in Axiom, and perhaps also in Reduce), I believe. I think Thomas Wolf
also has some package (in Maple?). Clemens Ballarin has done some comparisons.

Mathematica also has a decent command Reduce that may work, but I do not know
what algorithm is used.

William

-- 
William Sit
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