ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 11 Sep 2016 03:35:37 -0500Division polynomials just a function of x !https://ask.sagemath.org/question/34794/division-polynomials-just-a-function-of-x/ I evaluated Divison polynomials using
R.<A,B>=PolynomialRing(ZZ)
E = EllipticCurve([A,B])
g = E.division_polynomial(k)
The results i noticed were just function of $x$ , In theory i saw that division polynomials for k even depends on y. In there something I am unable to notice.
For example : ` E.division_polynomial(k)` returned `4*x^3 + 4*A*x + 4*B ` but theory says it is `2y`.
From this one can get a intuition that may be we are squaring them.
But ` E.division_polynomial(8)` returned a degree $33$ polynomial which means that clearly we are not squaring things.Sun, 11 Sep 2016 01:13:41 -0500https://ask.sagemath.org/question/34794/division-polynomials-just-a-function-of-x/Comment by FrédéricC for <p>I evaluated Divison polynomials using </p>
<pre><code>R.<A,B>=PolynomialRing(ZZ)
E = EllipticCurve([A,B])
g = E.division_polynomial(k)
</code></pre>
<p>The results i noticed were just function of $x$ , In theory i saw that division polynomials for k even depends on y. In there something I am unable to notice.</p>
<p>For example : <code>E.division_polynomial(k)</code> returned <code>4*x^3 + 4*A*x + 4*B</code> but theory says it is <code>2y</code>.
From this one can get a intuition that may be we are squaring them. </p>
<p>But <code>E.division_polynomial(8)</code> returned a degree $33$ polynomial which means that clearly we are not squaring things.</p>
https://ask.sagemath.org/question/34794/division-polynomials-just-a-function-of-x/?comment=34796#post-id-34796Could you just read the documentation: E.division_polynomial?Sun, 11 Sep 2016 03:35:37 -0500https://ask.sagemath.org/question/34794/division-polynomials-just-a-function-of-x/?comment=34796#post-id-34796Comment by vishb for <p>I evaluated Divison polynomials using </p>
<pre><code>R.<A,B>=PolynomialRing(ZZ)
E = EllipticCurve([A,B])
g = E.division_polynomial(k)
</code></pre>
<p>The results i noticed were just function of $x$ , In theory i saw that division polynomials for k even depends on y. In there something I am unable to notice.</p>
<p>For example : <code>E.division_polynomial(k)</code> returned <code>4*x^3 + 4*A*x + 4*B</code> but theory says it is <code>2y</code>.
From this one can get a intuition that may be we are squaring them. </p>
<p>But <code>E.division_polynomial(8)</code> returned a degree $33$ polynomial which means that clearly we are not squaring things.</p>
https://ask.sagemath.org/question/34794/division-polynomials-just-a-function-of-x/?comment=34795#post-id-34795Are we replacing $y$ by $x^2+ax+b$ everywhere ?Sun, 11 Sep 2016 01:25:52 -0500https://ask.sagemath.org/question/34794/division-polynomials-just-a-function-of-x/?comment=34795#post-id-34795