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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Why am I getting $n=2$?

I'm putting together a collection of tables of orders of certain groups and there's a theorem that specifies that some of those groups are infinite. It is Theorem 3(5) of M. I. Prischepov, "Asphericity, atoricity, and symmetrically presented…
Shaun
  • 44,997
3
votes
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Constructing the automorphism group of an algebra in GAP

First of all, if one needs to run this code correctly, one should read in a file in order to make the command NaturalHomomorphismByIdeal run correctly as explained in the answer here. This is the original setup: x := X(Rationals, "x");; y :=…
3
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Gap groups commands

I'm always needing to learn more about GAP. Can anyone help me on the following question? Question: I have a list of 500 sublists where each sublist consists of six groups. Is there a command to display or renumber only those sublists with trivial…
user5802
3
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2 answers

$p$-subgroups in $\mathtt{GAP}$

My question is fairly simple. Given a finite group $G$ and a prime $p$ dividing the order of $G$, I'd like to ask $\mathtt{GAP}$ to provide two lists: one with every subgroup of $G$ that is a $p$-group, and one with every $p$-subgroup lying in a…
the_fox
  • 5,805
3
votes
2 answers

Permutability Graph with GAP

Could someone suggest a piece of code that will produce the subgroup permutability graph of a finite group? There is more than one way this graph can be defined. The one I have in mind has the non-normal subgroups of the group as vertices and two…
the_fox
  • 5,805
3
votes
1 answer

Serialising objects from the GAP computer algebra system

Note: I have asked a related question on stackoverflow, for the practical purpose of developing a web application that needs to export and import objects to/from the GAP computer algebra system, and push/pull to a relational database and the web. …
ramius
  • 153
2
votes
1 answer

Calculate reduced table of marks

Given a list of conjugacy classes of subgroups genlist of the symmetric group $S_n$. I want to compute the reduced table of marks of $S_n$ with the conjugacy classes of subgroups genlist. That means that I want to obtain a Size(genlist) $\times$…
2
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1 answer

finding code of a function in GAP packages

How can I find the codes related to a function in GAP? When I use "??" in front of the name of function there is no help, so I want to find the code of function among packages.
2
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2 answers

Filtered Usage in GAP

if I have a list of elements FV:= [[ 1, 2, 4 ], [ 2, 4 ], [ 3, 1, 2, 4 ], [ 5, 3, 1, 2, 4 ], [ 15, 16, 18 ], [ 16, 18 ], [ 17, 15, 16, 18 ],[ 19, 17, 15, 16, 18 ], [ 29, 30, 32 ], [ 30, 32 ], [ 31, 29, 30, 32 ], [ 33, 31, 29, 30, 32 ],…
S786
  • 1,001
2
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1 answer

wreath product function in GAP

Can we compute the wreath product of two arbitrary groups in GAP? There exists the following function : WreathProduct( G, H[, hom] ), but I do not how I can use that for two arbitrary groups?
Nil
  • 1,306
2
votes
1 answer

Matrices' outputs in GAP

Does anyone know whether is a function in GAP via I would be able to change elements of matrices over GF(2) to the form 0 and 1. need to say, in GAP, outputs for elements of matrices defined over GF(2) are in these form: Z(2)^0 and 0*Z(2). Is it…
Nil
  • 1,306
2
votes
1 answer

Sum of some columns of Character Table in GAP

Let $CT$ be the character table of the finite group $G$ and let $x$ and $y$ are two elements in distinct conjugacy classes. I want to add two columns in $CT$ corresponding to $x$ and $y$ together and then add some rows of the obtained table. It is…
2
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1 answer

Is there a better way to input an $n$-cycle in GAP?

In GAP, we can generate permutations using, for example alpha:=(1,2,3,4,5); But, this method is not usable if we want to input the permutation $$(1,2,\ldots,n)$$ for some variable $n$. It is possible to use alpha:=PermList(List([1..n],i->(i mod…
2
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1 answer

Conjugacy classes in GAP

Let $V(FA_4)$ be normalized unit group of group algebra $FA_4$, where $F$ is a field containing 4 elements and $A_4$ is alternating group on $4$ symbols. How can I find conjugacy classes of elements of $V$ using GAP commands? ( Since GAP has most…
HIMANSHU
  • 196
2
votes
1 answer

orthogonalization in GAP

I'm using Eigenvectors in GAP to diagonalize a matrix $M$. The matrix is guaranteed to be diagonalizable and in fact it should be so by an orthogonal transformation. This works fine and $D$ is the desired diagonal matrix…
unknown
  • 1,018