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.Sun, 15 Dec 2019 21:30:46 +0100- Orbit "OnSets" in Sagehttps://ask.sagemath.org/question/49044/orbit-onsets-in-sage/I have the following code from GAP which works in Sage 8.9 using gap.eval:
gap.eval("grp := Group([ (1,2,3,4,5), (1,2,4,3) ])")
gap.eval("els := Elements(grp)")
gap.eval("aut := AutomorphismGroup(grp)")
gap.eval("forbidden_orbit := Orbit(aut, els{[1,2,3,4]}, OnSets)")
F_orbit = gap.new("forbidden_orbit")
I'd like to do this directly in Sage. However, is there a Sage function analogous to Gap's "AutomorphismGroup()" and is there a Sage function analogous to how I'm using the "Orbit" function in GAP? I can't seem to find one that outputs the same as above, which should be:
[ [ (), (2,3,5,4), (2,4,5,3), (2,5)(3,4) ],
[ (), (1,2,4,3), (1,3,4,2), (1,4)(2,3) ],
[ (), (1,2)(3,5), (1,3,2,5), (1,5,2,3) ],
[ (), (1,3)(4,5), (1,4,3,5), (1,5,3,4) ],
[ (), (1,2,5,4), (1,4,5,2), (1,5)(2,4) ] ]DanPSun, 15 Dec 2019 21:30:46 +0100https://ask.sagemath.org/question/49044/
- How can I compute the orbits of an automorphism group?https://ask.sagemath.org/question/43283/how-can-i-compute-the-orbits-of-an-automorphism-group/ I am new on automorphisms, need to know how to compute the orbits of an automorphism group in Sage.ASHWed, 08 Aug 2018 10:31:56 +0200https://ask.sagemath.org/question/43283/
- Semimonomial transformation grouphttps://ask.sagemath.org/question/34134/semimonomial-transformation-group/I have a subgroup of the semimonomial transformation group which is implemented in Sage and would like to be able to use for example the Orbit-functions in GAP, any ideas of how to do this?
Below I compute the full automorphism group of a linear [8,5] code over GF(4), with its generators stored in the variable "Gautgens".
f.<w>=GF(4,'x')
G=matrix(f,[[1,0],[w,1]])
Gt=reduce(lambda x,y:x.tensor_product(y,subdivide=False),[G]*3)
C=LinearCode(Gt[range(3,8)])
Gautgens=C.automorphism_group_gens()[0]
What I would like to do is to use the Orbits-function in GAP to find the orbits of some vectors in GF(4)^8 (v1,v2,v3,...) under the action of the automorphism group above. That is, something like:
gap.Orbits(gap.Group(Gautgens),[v1,v2,v3,..],"On....")
But I don't know how to make the automorphism group a group in GAP.
An alternative solution for me would be to map the automorphism group to an isomorphic permutation group acting on points. That is I would number all the vectors in GF(4)^8 and the automorphism group would then act as a permutation group on this indexing.AxelDTue, 19 Jul 2016 17:57:35 +0200https://ask.sagemath.org/question/34134/
- Counting cycles of induced permutationshttps://ask.sagemath.org/question/31888/counting-cycles-of-induced-permutations/In order to do some sophisticated counting in graph theory, I need to count the cycles of some particular permutations.
In my situation, $n$ is an integer greater than 1, and $K_n$ is the set of all two-element sets {a,b} with $a, b$ being integers not greater than $n$. Now any element $\pi$ of the symmetric group $S_n$ induces a permutation $\overline{\pi}$ of $K_n$ in a natural way, i.e. $\overline{\pi}$ maps any set {a,b} of $K_n$ onto {$\pi(a)$, $\pi(b)$}. What I want to figure out with the help of SAGE is the number of cycles that the permutation $\overline{\pi}$ has.
If you can help me, please do not forget to mention those little extra things that need to be done and that might appear obvious to you (e.g. importing packages and so forth), since I am a relative novice to SAGE.
Thank you very much.
MalteMalteMon, 28 Dec 2015 17:56:15 +0100https://ask.sagemath.org/question/31888/
- Random orbithttps://ask.sagemath.org/question/10585/random-orbit/Hi! I have to create a list for a random orbit [p1,p2,..pi] where each pi equals to the image of pi-1, and i have 3 diffĂ©rent functions that can be chosen randomly. I have to generate 50k points.miouchaThu, 19 Dec 2013 18:00:11 +0100https://ask.sagemath.org/question/10585/