On Sat, Jan 24, 2009 at 10:39:03AM +0100, Andrej Vodopivec wrote:
> > /* A tough example learned from Cox */
> > poly_grobner([x^5+y^4+z^3-1,x^3+y^3+z^2-1], [x,y,z]);
> >
> > takes 1mn30s
>
> You should compile the grobner package if you wish to compare it to
> the compiled affine package.
Indeed, you are completely right:
on the same machine, with grobner.x86f
(%i4) poly_monomial_order: grlex;
Evaluation took 0.0000 seconds (0.0000 elapsed) using 32 bytes.
(%o4) grlex
(%i5) poly_reduced_grobner([x^5+y^4+z^3-1,x^3+y^3+z^2-1], [x,y,z])$
Evaluation took 0.0000 seconds (0.0000 elapsed) using 111.523 KB.
(%i6) poly_monomial_order: lex;
Evaluation took 0.0000 seconds (0.0000 elapsed) using 8 bytes.
(%o6) lex
(%i7) poly_reduced_grobner([x^5+y^4+z^3-1,x^3+y^3+z^2-1], [x,y,z])$
Evaluation took 2.4200 seconds (2.4200 elapsed) using 142.060 MB.
and with affine:
(%i8) grobner_basis([x^5+y^4+z^3-1,x^3+y^3+z^2-1])$
....
Evaluation took 0.1700 seconds (0.1700 elapsed) using 8.723 MB.
So with compiled grobner package, maxima is faster than maple using
the same type of ordering (total degree, and then lexical), since maple
uses around 1.5 s. I must say that compiling is incredibly efficient here,
since uncompiled package takes 1mn30s.
As a practical conclusion, i think maxima would appear in a better light
if the install procedure systematically compiled such packages which are
widely used by people doing heavy formal computations. I have colleagues
involved in such work who complained that maxima is too slow, idem
for mathematica, so are using maple or specialized faster software.
As a workaround the documentation should mention to compile such packages,
and to do it as root once because of permission problems.
--
Michel TALON