Indeed when I added equations like b*bb-1 == 0, to forbid b from being zero, the resulting ideal is 0 dimensional (which means that there are only a finite number of solutions over C). The groebner basis (in lex order) has 225 elements. Right now I'm attempting to calculate the radical and primary decomposition. Victor On Wed, Aug 24, 2011 at 12:09 PM, Victor Miller <victorsmiller@gmail.com> wrote:
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
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