# Questions tagged [magma-cas]

Magma is a computer algebra system distributed by the University of Sydney, and designed for solving problems in algebra, number theory, geometry and combinatorics.

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### How to use GAP/magma to list all the elements of some order in a finite group? [closed]

How to use GAP/magma to list all the elements of some order in a finite group? For example, let $G\cong \mathbb{Z}_2\times \mathbb{Z}_{24}$, how to use GAP/magma to list all the elements of order $24$?...
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### Can MAGMA compute pullbacks of $kG$-modules?

Let $G$ be a finite group and let $k$ be a finite field of characteristic $p>0$ such that $p\mid |G|$. Let $M_1, M_2$ and $M_3$ be finitely generated $kG$-modules. I read in the MAGMA online ...
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### Is there a CAS that can compute a direct product decomposition of modular group algebras?

Let $G$ be a finite group and $k$ be a finite field of characteristic $p>0$ such that $p\mid |G|$. Is there a computer algebra system which can compute a direct product decomposition of such ...
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### Compute the discriminant and the conductor of an elliptic curve using magma

To compute the minimal discriminant and the conductor of an elliptic curve using Magma, for example this elliptic curve, we use this command ...
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### Gap code for a certain property of subgroups

Let $G$ be a given finite group of order $n$. We would like to write a Gap code for: Step1. find all divisors $d$ of $n$ such that there is no any subgroup of order $d$ or $n/d$, Step2. for every $d$...
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### Partial sums of the Dedekind zeta function

Is there a way to find the partial sums of the Dedekind zeta function? In particular, I would like to find the sum $$\sum_{0 \neq I \subset\mathcal{O}_K \\N(I) \le n} \frac{1}{N(I)^s}$$ for a given $n$...
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### MAGMA-question concerning the multiplicity of indecomposable $kG$-modules in a decomposable $kG$-module

Let $G$ be a finite group and $p$ be a prime. Moreover, let $k$ be a finite field of characteristic $p$, such that $p$ divides $|G|$. Furthermore suppose that $k$ is a splitting field for $G$. ...
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### Coercion of roots of unities in MAGMA

In MAGMA, I want to do computations in $\bar{\mathbb{Q}}[x,y]$. Say I want to form elements such as $\zeta x$, where $\zeta$ is some root of unity. MAGMA doesn't automatically regard $\zeta$ as an ...
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### Computing explicit galois actions in Magma

In the computational algebra system Magma, given an (irreducible) univariate polynomial $f$ (defined over the rationals $\mathbb{Q}$, say), can one compute the action of an element $g$ of the galois ...
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### Embedding Subgroup in Direct Product in Magma

I am using magma and want to consider a group $H$ as a subgroup of the direct product $H \times G$, written in magma as DirectProduct(H,G). Right now I am having to use the subgroup generator ...
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### “No permutation group context” when using printf in MAGMA

I tried to write a very simple code in Magma to print a matrix in a way that can be copypasted directly in Latex. ...
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### Could we use Magma to calculate subgroups of a fixed order?

I know very little about the software Magma and I know it can be used in group theory. Here I have a problem, could someone tell me whether and how to calculate it using Magma? Here is the problem: ...
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### If then statements with two indices in Magma software

In Magma a single variable functions can be created for use, say, f:= func< n | n lt 2 select 2 else Self(n-1)*Self(n)+1 >; [f(n): n in [0..12]]; These are ...
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### MAGMA: Excluding LowIndexSubgroups containing some elements

In the GAP command LowIndexSubgroupsFpGroup there is an optional argument, a list of elements of the group, to restrict the search only to subgroups that do not ...
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### Expediting Groebner basis computation

I am trying to solve a bunch of homogenous polynomial equations in several variables, using Groebner basis method. I expect to get a unique rational solution. The problem is that the coefficients of ...
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### Decomposition/Cartan matrix of a block in Magma?

Given a group, you can compute its Cartan matrix with Magma using the command AbsoluteCartanMatrix(G,k); where $k$ is any field. You can also compute the ...
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### Can MAGMA compute Auslander-Reiten sequences in group algebras?

I'd like to ask the following MAGMA question: Given a non-projective $kG$-module $M$, where $G$ is a finite group and $k$ is a finite field whose characteristic divides $|G|$, can MAGMA compute the ...
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### Given an indecomposable $kG$-module $M$, can MAGMA compute a minimal projective cover of $M$?

I'd like to ask the following MAGMA question: Let $G$ be a finite group and let $k$ be a finite field, such that char$(k)$ divides $|G|$. Given an indecomposable $kG$-module $M$, can MAGMA compute ...
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### An error occurs when computing a decomposition matrix of a factor group with MAGMA

I'd like to ask, if anybody can help me with the following: I entered this in MAGMA, but an error message (see below) appeared. ...
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### Does MAGMA use a standard p-modular system?

I'd like to ask the following question: Are the Brauer character values of kG-modules (where k and G are finite) in MAGMA computed with respect to the standard p-modular system described in the ...
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### Magma function for modulo irreducible polynomial

So, I am trying to make a program in Magma which returns the value table of a given function F over a field $GF(2^n)$. To do so I need a irreducible polyomial. For example, I've considered $GF(2^3)$ ...
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### How to make a list of variables in Magma(computer algebra system)?

In sagemath, for making a list of variables like $Z=[z00,z01,z02, ... ,z97,z98,z99]$ we can use this code: ...
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### How to do inflation of $k(G/N)$-modules with MAGMA?

I'd like to ask the following MAGMA-question: Let $k$ be a field of characteristic $p$, $G$ be a finite group and $N$ a normal subgroup of $G$. Moreover, let $M$ be a $k(G/N)$-module. Is it ...
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### Writing a vector variable in Magma.

So let's assume I am working with $n$-dimensional functions. In Magma I have a code that goes like this: ...
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### Problem in Magma regarding truth table and ANF

So, I am trying to solve a problem in Magma, that is implement a program which gives me the ANF of a Boolean function if the input is given with the truth table. There is a really nice algorithm to do ...
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### How to construct $\mathbb{F}_p(\zeta)$ with MAGMA?

I'd like to ask the following question concerning a MAGMA command I'm probably not aware of. Is it possible to construct a field of the form $F=\mathbb{F}_p(\zeta)$ with MAGMA, where $\zeta$ ...
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### On IsSimple() in Magma. [closed]

It is known that $S_{11}$ is a Atlas group and is not a simple group. In Magma, IsSimple(ATLASGroup("S11")); Runtime error in 'IsSimple': Bad argument types Argument types given: ...
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### Order of roots in MAGMA and/or Pari for computing Galois groups

I am trying to understand the Galois group of splitting fields (over $\mathbb Q$) of some polynomials. Especially those for which the Galois group is not the full symmetric group. For instance the ...
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### How to use string operations on braid groups in MAGMA

I am currently learning to use the computer algebra program MAGMA. It might be a very basic question but I could not find anything about it. I am working with elements in braid groups and I want to ...