Looking for a 64-bit build with large memory limit
Subject: Looking for a 64-bit build with large memory limit
From: Barton Willis
Date: Thu, 6 Dec 2007 18:40:41 -0600
-----maxima-bounces at math.utexas.edu wrote: -----
>I played with your equations a bit, substituting vectors of random small
>integers for your parameters (
>e.g. A=[-1,2,3]). For example, with one set of random vectors, they look
>like:
>
> [-x*y*z-5*y*z+4*x*z+z+4*y-x,
> -3*x*y*z+x*z+z-x*y+2*y+x-4,
> -5*y*z-x*z+3*z+7*x*y-y-3*x+1]
>
>
>Applying "solve" to this results in numerical solutions, meaning that
>Maxima could not find a symbolic solution.
>
>Using Maxima, I also tried solving for x in eq1, back-substituting,
>solving for y, and back-substituting one solution. This gave me
>
>(7*z^3-69*z^2+102*z-36)*sqrt(241*z^4-1010*z^3+1433*z^2-856*z+208)-1007*z^5
>+3428*z^4-4303*z^3+2598*z^2-876*z+144
>which a priori does not look solvable in closed form. Using to_poly and
>resultant gives a 12th-degree polynomial which factors, the highest-degree
>factor being a 6th-degree irreducible polynomial.
Alternative:
(%i17) eqs;
(%o17) [-x*y*z-5*y*z+4*x*z+z+4*y-x,-3*x*y*z+x*z+z-x*y+2*y+x-4,-5
*y*z-x*z+3*z+7*x*y-y-3*x+1]
(%i18) load(grobner)$
Loading maxima-grobner $Revision: 1.3 $ $Date: 2007/04/14 21:23:05 $
(%i19) poly_reduced_grobner(eqs,[x,y,z]);
(%o19)
[17205125*z^5-66019450*z^4-21601255*z^3+159883808*z^2-182298800*z-320137*y+31598365,1225*z^6-5565*z^5+
1779*z^4+12472*z^3-21027*z^2+11409*z-1582,17513825
*z^5-77241430*z^4+13309663*z^3+184847004*z^2-263074071*z-
11009929*x+112124250]
The 2nd equation is degree 6 in z.
Barton