Daniel Krenn wrote:
> I want to solve polynomial equations and in order
> to do so, I do something like:
> sage: R.<x,y> = PolynomialRing(QQ, order='lex')
> sage: I = R.ideal([x*y-1, x^2-y^2])
> sage: I.groebner_basis()
> [x - y^3, y^4 - 1]
and then wrote:
> Meanwhile, I found, which seems to do what I want:
>
> sage: I.variety()
> [{y: -1, x: -1}, {y: 1, x: 1}]
> sage: I.variety(ring=QQbar)
> [{y: -1, x: -1}, {y: -1*I, x: 1*I}, {y: 1*I, x: -1*I}, {y: 1, x: 1}]
> sage: I.variety(ring=ZZ)
> [{y: -1, x: -1}, {y: 1, x: 1}]
On a related note, see the following at ask-sage:
http://ask.sagemath.org/question/8224/system-of-nonlinear-equations/
http://ask.sagemath.org/question/11070/find-algebraic-solutions-to-system-of-polynomial-equations/
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