ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 08 Aug 2019 01:14:35 +0200Define the affine variety $X = V (y − x^2, y − x + 1)$.https://ask.sagemath.org/question/47429/define-the-affine-variety-x-v-y-x2-y-x-1/Define the affine variety
(a) $X = V (y − x^2, y − x + 1)$.
(b) Find all the rational points on X.
What I got in the examples is that we can use the code
sage: x,y,z = PolynomialRing(GF(5), 3, 'xyz').gens()
sage: C = Curve(y^2*z^7 - x^9 - x*z^8); C
sage: C.rational_points()
To get rational points over Finite Field of size 5. To calculate over rational we can replace $GF(5)$ by QQ but to get a finite result we have to have the intersection.
Later I also used:
sage: R.<x,y> = PolynomialRing(QQ)
sage: R
sage: I = R.ideal(y-x^2,y-x+1)
sage: I.variety()
But didn't get my result.ArnabThu, 08 Aug 2019 01:14:35 +0200https://ask.sagemath.org/question/47429/how can I Calculate grobner bases in this application?https://ask.sagemath.org/question/36407/how-can-i-calculate-grobner-bases-in-this-application/ I want to solve some questions ,which they need to find many Grobner Bases but I don't know how can I use this app to find Grobner Bases , I will be so Thanks full if some one helps me .mahyaSat, 28 Jan 2017 17:09:33 +0100https://ask.sagemath.org/question/36407/