On Sat, Aug 25, 2012 at 4:39 AM, Volker Braun <vbraun.n...@gmail.com> wrote:
> The <> notation creates Python variables of the same name, so you shouldn't
> use it together with the PolynomialRing(..., "e") constructor. Basically,
> you need to be aware that the the string label "a" can be attached to
> multiple Python variable names (its OK to do so for the computer but you
> will get confused):
>
> sage: p.parent()
> Multivariate Polynomial Ring in a, b, c, d, e over Multivariate Polynomial
> Ring in a, b, c, d over Rational Field
>
> sage: preparse("R.<a,b,c,d,e> =
> PolynomialRing(PolynomialRing(QQ,'a,b,c,d'),'e',sparse=True)")
> "R = PolynomialRing(PolynomialRing(QQ,'a,b,c,d'),'e',sparse=True,
> names=('a', 'b', 'c', 'd', 'e',)); (a, b, c, d, e,) = R._first_ngens(5)"

Thanks for the clarification.

> As for the second part, searching solutions over floating-point numbers
> should be avoided. You probably want to first figure out if your system is
> over/underdetermined and compute a lexicographic order Groebner basis:
>
> http://ask.sagemath.org/question/403/method-for-solving-a-large-system-of-under

By the reals I meant the actual reals, not the floating point numbers.
 Thanks for the link!

Geoffrey

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