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, 11 Feb 2021 18:59:45 +0100Mapping isomorphism for posets or graphshttps://ask.sagemath.org/question/55675/mapping-isomorphism-for-posets-or-graphs/I know that we can check if two posets/graphs are isomorphic using is_isomorphic(), but is there any way that I can get Sage to output a possible mapping between the two posets/graphs that are isomorphic?sunflowerThu, 11 Feb 2021 18:59:45 +0100https://ask.sagemath.org/question/55675/How to convert output of 'isomorphism_to' to transformation rulehttps://ask.sagemath.org/question/49149/how-to-convert-output-of-isomorphism_to-to-transformation-rule/Input:
C = EllipticCurve([0,0,0,-((250)/3),-(1249/27)])
print(C)
Cmin=C.minimal_model()
print(Cmin)
Cmin.isomorphism_to(C)
Output:
Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
Generic morphism:
From: Abelian group of points on Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
To: Abelian group of points on Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Via: (u,r,s,t) = (1, -1/3, 0, 0)
But I want explicit transformation like $(x,y) = (u^2 x+r , u^3 y + s u^2 x + t)$, in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.
EDIT:
What is wrong with the page? My question looked OK in preview window, but when sent there was gibberish inside $$.azerbajdzanMon, 23 Dec 2019 22:21:21 +0100https://ask.sagemath.org/question/49149/The question in the name of Normal Subgroup and Isomorphismhttps://ask.sagemath.org/question/49304/the-question-in-the-name-of-normal-subgroup-and-isomorphism/Let **$A$** and **$B$** be two groups.
Show that set **$N$ = { $(a,1): a \in A $ }** is the normal subgroup of **$A$ x $B$** and
that the **$A$ x $B$ $/ N$** quotient group is isomorph to **$B$**.
if you help me, i'll be exulted. hayyambeyWed, 01 Jan 2020 16:04:29 +0100https://ask.sagemath.org/question/49304/Birational transformation of general genus 1 curve to Weierstrass formhttps://ask.sagemath.org/question/49231/birational-transformation-of-general-genus-1-curve-to-weierstrass-form/> Is it possible to **birationally** transform general
> curve of genus 1 of any degree to
> Weierstrass form using Sage?
Example of curve of degree $12$ which has genus $1$ and has rational point $(-3, -\frac{17}{5})$.
Input:
x,y,z = QQ['x,y,z'].gens()
C = Curve(x^9*y^3 + 9*x^9*y^2*z + 9*x^8*y^3*z + 27*x^9*y*z^2 + 81*x^8*y^2*z^2 + 35*x^7*y^3*z^2 +
27*x^9*z^3 + 243*x^8*y*z^3 + 318*x^7*y^2*z^3 + 74*x^6*y^3*z^3 + 243*x^8*z^4 +
963*x^7*y*z^4 + 687*x^6*y^2*z^4 + 90*x^5*y^3*z^4 + 972*x^7*z^5 + 2124*x^6*y*z^5 +
871*x^5*y^2*z^5 + 67*x^4*y^3*z^5 + 2187*x^6*z^6 + 2799*x^5*y*z^6 + 692*x^4*y^2*z^6 +
39*x^3*y^3*z^6 + 2988*x^5*z^7 + 2358*x^4*y*z^7 + 415*x^3*y^2*z^7 + 21*x^2*y^3*z^7 +
2655*x^4*z^8 + 1466*x^3*y*z^8 + 211*x^2*y^2*z^8 + 4*x*y^3*z^8 + 1717*x^3*z^9 +
723*x^2*y*z^9 + 47*x*y^2*z^9 - 3*y^3*z^9 + 840*x^2*z^10 + 180*x*y*z^10 - 20*y^2*z^10 +
228*x*z^11 - 40*y*z^11 - 20*z^12)
C.genus()
Output:
1azerbajdzanFri, 27 Dec 2019 18:32:29 +0100https://ask.sagemath.org/question/49231/How to defining a twist on an elliptic curvehttps://ask.sagemath.org/question/39597/how-to-defining-a-twist-on-an-elliptic-curve/Hey,
I would like to do map points of the ellitptic curve $E(\mathbb F_{p^{k}})$ to its twist. I am able to define the twist on a mathematical way, but it returns always errors. I will give you a M(n)WE:
Aim: Get a generator of a r-torsion subgroup of E, lift that to E16 and twist it down to E4, to get a r-torsion subgroup-generator of E4.
#MWE
## Mathematical definition:
$E(\mathbb F_{p^{16}}): y^2=x^3+x$ and its quartic twist $E'(\mathbb F_{p^4}): y^2=x^3+2^{-1/4}x$. The point mapping is defined as $\psi: E\to E', (x,y,z)\mapsto (2^{-1/2}x, 2^{-3/4}y, z)$.
## Define the fields and curves
p= 13
r=5
R=GF(p)
_.<x> = PolynomialRing(R)
R4.<x> = R.extension(x^4 - 2, 'x')
_.<y> = PolynomialRing(R)
R16.<y> = R.extension(y^16 -2, 'y')
_.<z> = PolynomialRing(R4)
R16_over_R4.<z> = R4.extension(z^4-x, 'z')
E = EllipticCurve(R, [1,0]) # y^2 = x^3+x
E4 = EllipticCurve(R4, [x,0])
E16 = EllipticCurve(R16, [1,0])
## Defining the point and pre-computations
k= ZZ(E.order()/r) # since E.order()*P = (0:1:0), we can trick with that
b=R16(2^(-1)); b= sqrt(sqrt(2)) #the twisting parameter, that is a square in R4 and R16
P= E.gens()[0]
Q=k*P # check if Q != E((0,1,0)), if yes its a r-torsion point.
Q16 = E16(Q) #raise Q
## The not working twist
#twist
E4( (Q16[0]*b^2, Q16[1]*b^3))
Sage is able to compute the quartic twist of its own, but I do not recieve the right twist, that I had computed by hand ( $E'$ ). Using
E4.quartic_twist(v^-1)ShalecThu, 16 Nov 2017 11:43:57 +0100https://ask.sagemath.org/question/39597/Generating graph families in Sagehttps://ask.sagemath.org/question/33040/generating-graph-families-in-sage/ I am trying to figure out how to generate strongly regular graphs with parameter (25,12,5,6). I need all 15 ( I believe) of the Paulus graphs with 25 vertices and the other 10 with 26 vertices to be generated. I know how to generate one of each that is in the database however, I need to generate the others to test my algorithm. I just need a nudge in the right direction. Thank you.fireydragonFri, 08 Apr 2016 01:57:33 +0200https://ask.sagemath.org/question/33040/Using nauty_geng with variable number of verticeshttps://ask.sagemath.org/question/11026/using-nauty_geng-with-variable-number-of-vertices/I am trying to use the nauty graph generator to count the number of non-isomorphic graphs with specified properties, but I am hindered by the fact that it seems nauty_geng only allows a fixed number of vertices.
For example, the following code counts the number of (non-isomorphic) connected graphs on 5 vertices:
count = 0
for g in graphs.nauty_geng("5 -c"):
count += 1
print count
The Sage output is: 21.
However, if I try to count the number of connected graphs on *n* vertices for *n* in a certain range, say *n*=3,4,5,6, as with the following code,
for n in range(3,7):
count = 0
for g in graphs.nauty_geng("n -c"):
count += 1
print (n,count)
,the count remains equal to zero for each *n*, and the situation is the same for all similar codes I have tried. The result is that in order to see what happens for multiple values of *n*, I must manually change all occurrences of *n* in the code.
1. Is this the meaning of "At a minimum, you must pass the number of vertices you desire," a statement in the help box?
2. Is there any way around this?
Thanks for any help with this!Emperor's_New_ClothesWed, 12 Feb 2014 13:39:09 +0100https://ask.sagemath.org/question/11026/Distinct (nonisomorphic) treeshttps://ask.sagemath.org/question/9993/distinct-nonisomorphic-trees/"Construct all non-isomorphic trees of order 7"
How to do that in Sage ?!
Please helpMohabSun, 07 Apr 2013 14:24:14 +0200https://ask.sagemath.org/question/9993/Does sage have analog of magma function IsIsomorphic?https://ask.sagemath.org/question/9651/does-sage-have-analog-of-magma-function-isisomorphic/Does Sage have analog of magma function [IsIsomorphic for curves](http://magma.maths.usyd.edu.au/magma/handbook/text/1253#13614)
> IsIsomorphic(C, D) : Crv, Crv -> BoolElt,MapSch
> Given irreducible curves C and D this
> function returns true is C and D are
> isomorphic over their common base
> field. If so, it also returns a scheme
> map giving an isomorphism between
> them. The curves C and D must be
> reduced. Currently the function
> requires that the curves are not both
> genus 0 nor both genus 1 unless the
> base field is finite.
or [IsIsomorphic for hyperelliptic curves](http://magma.maths.usyd.edu.au/magma/handbook/text/1391#15274)?
> IsIsomorphic(C1, C2) : CrvHyp, CrvHyp
> -> BoolElt, MapIsoSch
>
> SetVerbose("CrvHypIso", n): Maximum: 3
>
> This function returns true if and only if the hyperelliptic curves C1
> and C2 are isomorphic over their
> common base field. If the curves are
> isomorphic, an isomorphism is
> returned.petRUShkaWed, 26 Dec 2012 07:56:53 +0100https://ask.sagemath.org/question/9651/