When you set b=1 SAGE (actually Singular) almost immediately calculates the primary decomposition: [Ideal (f, e, b - 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (f, c, b - 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (e, c, b - 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (f - 1, e - 1, d - 1, b - 1, c^2 + 5*c + 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (f - 1, d - 1, c - 1, b - 1, e^2 + 5*e + 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (e - 1, d - 1, c - 1, b - 1, f^2 + 5*f + 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (e, d, b - 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (f - 1, e - 1, c - 1, b - 1, d^2 + 5*d + 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (f, d, b - 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field, Ideal (d, c, b - 1) of Multivariate Polynomial Ring in b, c, d, e, f over Rational Field] I didn't put in equations to forbid b,c,d,e,f from being 0. That seems to be the source of the higher dimensionality. A typical non-spurious component is b=1,d=1,e=1,f=1, c^2 + 5*c + 1 = 0. On Wed, Aug 24, 2011 at 11:23 AM, Schroeppel, Richard <rschroe@sandia.gov> wrote:
Just add three more equations: Try b=c=d=1 first; if that's singular, try things like b=.6 or b+c=1.5.
Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] on behalf of Bill Gosper [billgosper@gmail.com] Sent: Tuesday, August 23, 2011 11:56 PM To: math-fun@mailman.xmission.com Subject: Re: [math-fun] computer algebra
Victor Miller> Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff
in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3.
I.e., triply underdetermined?
That scotches the plan to PSLQ the exact algebraics from 1000 digit approximations. --rwg
Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun