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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display output completely in GAP

If GAP computes large output it will be shortenend by ( [...] ). How can I display the whole output? Unfortunately I have not found an answer yet. Thanks!
Franco
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Lie algebra of the group generators in GAP

I have generators for my group in GAP. Additionally, I possess a specific unitary element and wish to determine whether this unitary element arises from the Lie algebra of my group's generators. Initially, I considered a brute-force approach,…
j.doe
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DirectSumMat for general fields in GAP

The GAP-command DirectSumMat allows to take the direct sum of matrices over (only certain?) fields. Now I did the following in…
Mare
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GAP code to construct a faithful permutation representation using three subgroups

I'm new to GAP, and I tried to adjust the code that ahulpke wrote at the link: Faithful permutation representation to construct a faithful representation of the group $C_2\times (C_4\rtimes C_4)$ using "three orbits". I adujested the code by adding…
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PointGroup command doesn't work for a group created with the SmallGeneratingSet of an AffineCrystGroup.

I test the following code snippet in GAP: M:=[[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], [[0, 1, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [1/4, 1/4, 1/4, 1]], [[-1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 1, 0], [0, 1/2, 1/2, 1]], [[0, -1, 0, 0],…
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Express an arbitrary rotation matrix in GAP.

It is well known that the rotation matrix has the formula described here. I wonder how can I express these matrices in GAP with arbitrary rotating angles. Edit: Dear Max Horn, thank you for your comments. But based on the description here: I…
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How can I check if an ideal has a direct sum decomposition? [GAP]

I need a function to check if a left ideal of a Group Algebra has a direct sum decomposition or not. So, I need a function that return true if the left ideal has a direct sum decomposition or false if the left ideal doesn't have a direct sum…
Amanda
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Find all subgroups of GL(3,7) with a Sylow 3-subgroup of order 27

I want to use GAP to study all subgroups of GL(3,7) with a Sylow 3-subgroup of order 27. How can I do it? Thanks.
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Sporadic simple groups in GAP

I sincerely apologize in advance for this simple question. I recently started learning GAP and I am having difficulties finding Sporadic simple groups in GAP. For example, if I want to find the order of the symmetric group $S_{10}$, I know that…
user824863
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Problem with sorting inside a loop in GAP

I'm very new to GAP, and I'm struggling with SortBy. Starting with a list of lists, I want to sort each list by AbsoluteValue in GAP. However, I can only get Sort or SortBy to work outside of a loop. The problem exists already in this tiny…
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Obtaining maps of rings in gap

Given a finite ring $A$ (a finite group would be enough actually as we do not use multiplication of the ring). Is it possible to obtain the ring $R$ (with usual addition and multiplication being given by composition) of all maps (not structure…
Mare
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Finding a certain set of matrices with GAP

Call a $n \times n$-matrix $A=(a_{i,j})$ with entries only 0 or 1 "cool" in case it has the following properties: -We have $a_{i,j}=0$ in case $i>j$. -It has only 1 on the diagonal -It has only 1 in the first row. (call it "supercool" if additional…
Mare
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GAP — null multidimensional array

I need to create an $n\times a \times b$ array in GAP. How do I do that fast? I tried putting e := NullMat(a,b); Array := []; for i in [1..n] do Array[i] := e; od; However, then when I try to change a single entry, GAP changes it in every copy of…
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Finding right transversals using GAP

I am new to the GAP software and I am following the GAP manual. I have found one right transversal to a subgroup of a group. Now i want to know if we can find all the right transversals of a subgroup in a group. If yes, how can we do so?
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Store GAP REPL representation of expression in string

I have noticed that the representation that is displayed by the GAP REPL (read-evaluate-print loop) when an expression is evaluated sometimes differs from the result of printing that same expression, e.g.: gap>…
Peter
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