ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 07 Aug 2019 18:14:35 -0500Define the affine variety $X = V (y − x^2, y − x + 1)$.http://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.ArnabWed, 07 Aug 2019 18:14:35 -0500http://ask.sagemath.org/question/47429/The perimeter of a rectangle is 600 yards. What are the dimensions of the rectangle if the length is 10 yards more than the width?http://ask.sagemath.org/question/35036/the-perimeter-of-a-rectangle-is-600-yards-what-are-the-dimensions-of-the-rectangle-if-the-length-is-10-yards-more-than-the-width/The perimeter of a rectangle is 600 yards. What are the dimensions of the rectangle if the length is 10 yards more than the width? mgraceb16Mon, 03 Oct 2016 00:58:44 -0500http://ask.sagemath.org/question/35036/