ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 09 Jul 2018 06:33:30 -0500How to define a polynomial A(x,y) that (x,y) satisfying y^2+y=x^3http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/I am working on a elliptic curve like `y^2+y=x^3` over `GF(2^6)`
and i want to define a polynomial `A(x,y)` over `GF(2^6)` that `x,y` satisfying `y^2+y=x^3`
Hope to get your help, thank you!Sat, 07 Jul 2018 03:59:55 -0500http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/Comment by albertcz for <p>I am working on a elliptic curve like <code>y^2+y=x^3</code> over <code>GF(2^6)</code></p>
<p>and i want to define a polynomial <code>A(x,y)</code> over <code>GF(2^6)</code> that <code>x,y</code> satisfying <code>y^2+y=x^3</code></p>
<p>Hope to get your help, thank you!</p>
http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42868#post-id-42868This is what i need! thank you!Mon, 09 Jul 2018 06:33:30 -0500http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42868#post-id-42868Comment by vdelecroix for <p>I am working on a elliptic curve like <code>y^2+y=x^3</code> over <code>GF(2^6)</code></p>
<p>and i want to define a polynomial <code>A(x,y)</code> over <code>GF(2^6)</code> that <code>x,y</code> satisfying <code>y^2+y=x^3</code></p>
<p>Hope to get your help, thank you!</p>
http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42865#post-id-42865A polynomial function on your curve is given by an element in the quotient K[x,y] / (y^2 + y - x^3). The answer to your question really depends on what you want to do with such function.Sun, 08 Jul 2018 10:40:37 -0500http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42865#post-id-42865Comment by albertcz for <p>I am working on a elliptic curve like <code>y^2+y=x^3</code> over <code>GF(2^6)</code></p>
<p>and i want to define a polynomial <code>A(x,y)</code> over <code>GF(2^6)</code> that <code>x,y</code> satisfying <code>y^2+y=x^3</code></p>
<p>Hope to get your help, thank you!</p>
http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42857#post-id-42857I have reorganize my language. Thank you a lot for your attentionSat, 07 Jul 2018 21:02:34 -0500http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42857#post-id-42857Comment by dan_fulea for <p>I am working on a elliptic curve like <code>y^2+y=x^3</code> over <code>GF(2^6)</code></p>
<p>and i want to define a polynomial <code>A(x,y)</code> over <code>GF(2^6)</code> that <code>x,y</code> satisfying <code>y^2+y=x^3</code></p>
<p>Hope to get your help, thank you!</p>
http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42855#post-id-42855Please describe mathematically the situation. It is hard to figure out the "map between variables", so maybe we have a map $f$ from a polynomial ring $R$ to some other ring $S$, and the map $f:R\to S$ is determined by the images through $f$ of the generators of $R$.Sat, 07 Jul 2018 11:37:06 -0500http://ask.sagemath.org/question/42854/how-to-define-a-polynomial-axy-that-xy-satisfying-y2yx3/?comment=42855#post-id-42855