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.

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Installing a new function in GAP

I have written the following snippet of code to compute the subgroup permutability degree of a finite group $G$. spd := function(G) local allsubs, subreps, count, H, K, index; subreps := Flat(List(ConjugacyClassesSubgroups(G),Representative));…
the_fox
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compute the action and the orbits of a finite set

If $X$ is a set of 183 points and if the group $S_4$ acts on $\{1,2,3,4\}$ and fixes the other points. How can compute the action and the orbits in GAP?
user23
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About a presentation of a FpGroup

I'm studying a group in GAP, and I have a list of relators of this finited presented group. My trouble is, this group has too many relations (actually more than 500), and GAP gives me these relations (maybe not) randomly. I want to write the…
none
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Intersection of Ideal in Gap(QPA)

I'm New to Gap(QPA). I'm trying to intersect Ideal in Gap and find their generators. For example here I construct some trivially intersecting ideals, Q:=…
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What does the ouput of StructureDescription mean in GAP?

gap> StructureDescription(G); Gives: "(C5 x C5) : C12" How exactly should this output be interpreted?
Numeral
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Can GAP compute logarithms?

I have been using GAP lately and I know how to compute logarithms, but only in some cases by using the function LogInt(n,b). So for example if $n=5^8$ and $b=5$, then LogInt($5^8$, $5$)=$8$. But imagine I want to compute $\log_3(5)=1,46...$. If I…
Gillyweeds
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how to save a structure in gap

Is there a way to save a structure to a file in GAP? For example : data:=rec(); data.Name:="random matrix"; data.Value:=RandomMat(3,4); data.Rank:=2; How would I save "data" to a file so it can be read from GAP at a future session? and how would I…
unknown
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Code for LCM of order of element in GAP

Is there an easier way to write the LCM part of this code? Gap only allows two arguments for LCM_INT. SigmaSet := function(GROUP, g1, g2) local S, g3; S := [ ]; g3:= g2^-1 * g1^-1; g_elts := [g1, g2, g3]; for g in GROUP do for j in [0..LCM_INT(…
ChrisG
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Reloading a package

I have the following question concerning loading of GAP packages (concerns in the same way both Linux and Windows). Suppose I have a package named "SamplePackage" located in the pkg directory. After launching a GAP session I load the SamplePackage…
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GAP: construct projection operator onto subspace

In GAP, I would like to check if a vector $v$ has a non-vanishing overlap with a given subspace $U$. Consider a linear subspace $U \subset V$ and its complement $U^\perp$ with respect to a non-degenerate inner product. Thus one has $U + U^\perp =…
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Constructing Invertible 0-1-matrices

I am looking for effective algorithmic solutions for the following two problems: Question 1: Is there a quick way to obtain for a given $n$ the list of all integer $n \times n$ matrices having only entries 0 and 1 that are invertible? Question 2:…
Mare
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Exceeded the Permitted Memory

I have been trying to program with large matrices, but unfortunately I have been getting an error that my permitted memory has been exceeded. I have read various ways online that it is possible to increase the permitted memory using Command Line…
spadey
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Monoid of ideals in GAP

Given a finite dimensional algebra $A$ and a set of twosided ideals $\{I_1, I_2,...,I_n \}$. Let $G$ be the monoid (or sometimes group) generated by those ideals. Is there a way to obtain this monoid via GAP (or a package like qpa) and check what…
Mare
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Problem with matrices with entries in the family of rational functions

I have the following setup: gap> a := X(Rationals,"a");; b := X(Rationals,"b");;c := X(Rationals,"c");; gap> M := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], > [ -b, -a, -1, -a, -1, 0 ], [ -a, -1, 0, -1, 0, 0 ], > [ b, a, 1, 0, 0, 0 ], […
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Why does this gap programm not work?

DeclareOperation("helpfunction", [IsList]); InstallMethod(helpfunction, "for a representation of a quiver",[IsList],0,function(L) local list, n, i, j, f, temp, temp2, temp3, u; n:=L[1]; s:=L[2]; l:=L[3]; …
Mare
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