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.Tue, 18 Jun 2019 22:18:20 +0200how to generate Cayleygraphhttps://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/Hello,
how can I generate a cayleygraph for
y^2 = x^3+ax ;
a, could be 1 or 2 or 3 ;
p = 17
The producer points should be identifiable in this graph.
ThanksMon, 17 Jun 2019 13:08:42 +0200https://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/Answer by John Palmieri for <p>Hello,</p>
<p>how can I generate a cayleygraph for </p>
<p>y^2 = x^3+ax ;</p>
<p>a, could be 1 or 2 or 3 ;</p>
<p>p = 17</p>
<p>The producer points should be identifiable in this graph.</p>
<p>Thanks</p>
https://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/?answer=46926#post-id-46926Does this give what you want?
sage: E = EllipticCurve(GF(17), [1, 0]) # [1,0] -> coefficient of x, constant term
sage: E
Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 17
sage: A = E.abelian_group()
sage: G = A.permutation_group()
sage: G.cayley_graph()
Digraph on 16 verticesTue, 18 Jun 2019 06:52:54 +0200https://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/?answer=46926#post-id-46926Comment by manni for <p>Does this give what you want?</p>
<pre><code>sage: E = EllipticCurve(GF(17), [1, 0]) # [1,0] -> coefficient of x, constant term
sage: E
Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 17
sage: A = E.abelian_group()
sage: G = A.permutation_group()
sage: G.cayley_graph()
Digraph on 16 vertices
</code></pre>
https://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/?comment=46938#post-id-46938Thanks!!
Can it be modified to see the points and subgroups?
For example "Elliptic Curve defined by y^2 = x^3 + 6*x over Finite Field of size 7"
Group "(4,2)" --> (1,0) --> (4,5) --> {} -->Tue, 18 Jun 2019 21:11:27 +0200https://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/?comment=46938#post-id-46938Comment by John Palmieri for <p>Does this give what you want?</p>
<pre><code>sage: E = EllipticCurve(GF(17), [1, 0]) # [1,0] -> coefficient of x, constant term
sage: E
Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 17
sage: A = E.abelian_group()
sage: G = A.permutation_group()
sage: G.cayley_graph()
Digraph on 16 vertices
</code></pre>
https://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/?comment=46939#post-id-46939I don't know. You can look at the documentation for the cayley_graph method: http://doc.sagemath.org/html/en/reference/categories/sage/categories/semigroups.html#sage.categories.semigroups.Semigroups.ParentMethods.cayley_graphTue, 18 Jun 2019 22:18:20 +0200https://ask.sagemath.org/question/46925/how-to-generate-cayleygraph/?comment=46939#post-id-46939