Questions tagged [gap]

GAP (Groups, Algorithms and Programming) is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. It provides a programming language, a library of thousands of functions implementing algebraic algorithms, and large data libraries of algebraic objects.

Please note that GAP Forum or GAP Support may be more suitable places for questions about GAP: see http://www.gap-system.org/Contacts/Forum/forum.html

This is the tag for questions related to the computational algebra system GAP.

GAP (Groups, Algorithms and Programming) is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. It provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more.

Suggestions on using the gap tag:

  • please use it for new questions which explicitly ask something about the GAP system. This will help other GAP users who are reading math.SE to discover your question;

  • please don't use it for retrospective tagging of answered or commented questions where the answers/comments use GAP but most likely same calculation could be performed with any general-purpose computer algebra system;

  • in other cases, please use it with certain discretion, dependently on the potential learning value of the content of the discussion for other GAP users.

If you want to ask a question in this category, please note that there are well-established support channels for GAP users such as GAP Forum and GAP Support which may be more suitable places for such questions with a different (though possibly intersecting) audience, and with a different response rate (which may be faster or slower, dependently on your question). While there are certainly GAP users and some authors of GAP and/or its packages among the users of this Q&A site, please do not assume that the question on GAP asked here will necessarily be seen by the majority of GAP developers and package authors. On the other hand, research questions which may be of interest to wide ranks of GAP users are certainly welcomed here as well.

It may also happen that your question is already answered in the Frequently Asked Questions section of the GAP website or in the GAP Forum (to search GAP Forum archives, click here).

Finally, if you think that you have discovered a bug in the GAP system, the recommended way to report it is to use the GAP issue tracker on GitHub. Many packages have their own issue trackers, which you can find following the links here.

810 questions
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How is GAP generating all subgroups?

GAP can return all subgroups of $S_4$ pretty much instantaneously: gap> AllSubgroups(SymmetricGroup(4)); [ Group(()), Group([ (1,2)(3,4) ]), Group([ (1,3)(2,4) ]), Group([ (1,4)(2,3) ]), Group([ (3,4) ]), Group([ (2,3) ]), Group([ (2,4) ]),…
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Minimal Permutation Representation Degree of a group: GAP implementation

For a finite group $G$, let $\mu(G)$ be the least positive integer $n$ such that $G$ is embedded as a subgroup of the symmetric group on $n$ points. In other words, $\mu(G)$ is the minimal permutation representation degree of $G$. Note here that…
the_fox
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GAP Integrated Development Environment

Is there any fancy editor of GAP code or even some environment dedicated to it? I've been using Notepad++ for this purpose but it seems only to color the syntax. I would like to have more developmental features.
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Graphical interface in GAP

Is there any graphical interface in GAP? Something like RStudio for R or WxMaxima for Maxima. I'm using GAP under a Linux system. Thanks
4
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1 answer

Inputting a group into GAP

Can anyone tell me whether or not it is possible to input the following 2-group into GAP? The question is the order of element $a$ is $2^m$, where $m$ could be any integer $\geq 2$. For example, I input $a*b*a$, then the system returns…
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Check element membership in GAP

Does there exist a proper function in order to check a matrix belongs to GL(3,2) in GAP? I have already searched but I didn't find any function except "IsElementOfFpGroup". But GL(3,2) is not FpGroup.
Nil
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4
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Output Of Wreath product in GAP

The output of WreathProduct of two permutation groups in GAP is a permutation group, I want to compute the wreath product of two general linear groups. l:=group of 3x3 matrices of size 6 over GF(2) g:=GL(2,2) gap> WreathProduct(PSL(2,2),l);
Nil
  • 1,306
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1 answer

matrix representation of a permutation in GAP

I have wrote the following lines in GAP: $ gap> G:=PSL(4,4);\\ \\ gap> p:=SylowSubgroup(G,5);;\\ gap> e:=Elements(p);;\\ gap>…
Adeleh
  • 1,357
3
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Substituting values in multivariate polynomial in GAP

given a polynomial $p(x,y)$ from $\mathbb Z[x,y]$. I want to substitute $x=1$ leaving $y$ as it is. The command Value(p,[1,y]) does not work. Can you give me a hint? After that it gets a little more complicated. Let $$p(x,y)=x^6+y^6$$ After…
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How to quit GAP script?

I'm new to GAP and have some trouble with its script. Here is the script that I wrote: foo.gap #!/usr/bin/gap -q Display(1 + 1); quit; I expected if I type "./foo.gap" then it displays 2 and returns control: $ ./foo.gap 2 $ However it doesn't…
Orat
  • 4,065
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In GAP, how to generate a quotient automorphism group so that its elements are still maps?

For simplicity, I've tried to work with automorphism and inner automorphism groups by using the operator /. Although this attempt effectively computes the correct group, which is called the outer automorphism group, its elements do not show up as…
Cadenza
  • 535
3
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1 answer

application order in GAP multiplication

GAP multiplication of permutations $p1 * p2$ first applies $p1$, then applies $p2$ to the result. Many textbooks apply $p2$, then apply $p1$ to the result, which feels more consistent with composition of functions, so the action on set element $x$…
Danny Heap
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3
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Is there a function more general that DuplicateFreeList() in GAP?

The function DuplicateFreeList in GAP, which is the same a the function Unique, takes a list and returns all the elements of that list with duplicates removed. My problem is that this function checks for duplicates using =, whereas I want to remove…
Mike Pierce
  • 18,938
3
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1 answer

Obtaining the list of all transformations in GAP

Is there a command in GAP to obtain all transformations on $n$ symbols (so there should be $n^n$ of them). I can not find such a command in https://www.gap-system.org/Manuals/doc/ref/chap53.html#X7B51CE257B814B09 but I would think that there is such…
Mare
  • 2,332
3
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1 answer

Delta subgroup with GAP

This question is perhaps a bit silly, but I haven't figured out from the GAP manual how to do this. I want to create a function delta which takes as input a (finite) group $G$ and returns the full preimage of $Z(G/\Phi(G))$, where $\Phi(G)$ is the…
the_fox
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