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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MAGMA question concerning the ordering of Irr($G\times H$)

Let $G$ and $H$ be finite groups. Denote the ordinary character table of $G$ by ctG and the ordinary character table of $H$ by ctH. Then, it is well-known how to get the ordinary character table of $...
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Does MAGMA automatically identify $G$ and $G^\text{op}$?

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 $G$. Let $...
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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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54 views

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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42 views

“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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1answer
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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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Construction of a group in Magma

I need to construct the following group in Magma: given $H=(C_2)^3 \rtimes (C_7 \rtimes C_3) \times C_3$ (so $\operatorname{SmallGroup}(168,43)\times C_3$), there is a non-split central extension by $...
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How to find the irreducible constituents of a Brauer character with MAGMA?

I'd like to ask the following MAGMA-question: How to find the irreducible constituents of a Brauer character with MAGMA? Let $G$ be a finite group. Moreover, let $k$ be a finite field of ...
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Workaround for Windows Magma Memory Limit [duplicate]

I found this question which said that Magma for Windows has a strict memory limit of 1.3 GB as a consequence of something weird with long ints. Is there any known workaround for this on a Windows ...
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Construction of a field with roots of unity in MAGMA

I would like to construct a field (NumberField) that contains a (primitive) $n$-th root of unity and $i = \sqrt{-1}$ using a computer algebra system MAGMA, i.e. $\mathbb{Q}(\zeta_n, i)$. I tried ...
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104 views

Cartesian Product over a list of objects in MAGMA

I'm currently trying to create the Cartesian Product of certain objects (namely: Character Tables of different finite groups). However, it seems like I don't really understand the car<$...$> ...
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232 views

Using Velu's formulas in MAGMA

Most isogeny-based cryptographic schemes rely on constructing an isogeny having a given kernel. That is, given an elliptic curve $E$ and a subgroup $G$ of points of $E$, there is interest in ...
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1answer
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Pre-image of element in quaternion algebra

Let $A$ be an indefinite quaternion algebra (e.g. $(2,5)_\mathbb{Q}$), let $M$ be a maximal order in $A$ and let $\Gamma$ be the Fuchsian group derived from $M$. We will denote the group of units of $...
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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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249 views

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 ...
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Are all quaternion algebras over the rationals skew fields?

If I understand correctly, any quaternion algebra over the rationals is a noncommutative associative division algebra. I am currently working with implementations of quaternion algebras in MAGMA and ...
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Solving linear systems for integer values in MAGMA

Say we are given a quaternion algebra D over a number field F as well as a maximal $\mathcal{O}_F$-order $\Delta$ $\subseteq$ D and say we have a $\mathbb{Z}$-basis $\omega_1, . . . , \omega_n$ for $\...
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Computing the inverse of a full lattice in a quaternion algebra

Let $D$ be quaternion algebra over a number field $F$. Let $\Delta\subseteq D$ be a maximal $\mathcal{O}_{F}$-order. Let $\mathfrak{b}$ be a fractional left $\Delta$-ideal. In his book "Maximal Orders"...
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Define a vector space for a given set on Magma.

This is probably an easy question, but I have been looking for hours before posting it. I want for a given finite set say $S$ (in particular a set of homogeneous polynomials), to define the vector ...
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Artin Representations in MAGMA

Here's a toy example of the difficulty I'm having... Let $K/\mathbb{Q}$ be a Galois extension of degree 3. There are two non-trivial irreducible characters on Gal$(K/\mathbb{Q}),$ call them $\chi_1$ ...
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1answer
698 views

How do I copy an output of magma to a .txt file? [closed]

While I have created a function to compute something on magma, when am running the computations the list of things I take back is so big, that I can't see them all when I scroll up on magma, it ...
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Why did Magma had an error(?) for $x\big(x+807^2\big) \big(x+811^2\big) = y^2$

In this post, we considered the elliptic curve, $$x\big(x+(m-1)^2\big) \big(x+(m+1)^2\big) = y^2\tag1$$ Online Magma was able to solve the case $m=2^7$ but timed-out on $m=5^7$, $$x\big(x+78124^2\...
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An elliptic curve $x(x - 78126^2)(x - 4\times5^7) = y^2$ for $x_1^7+x_2^7+\dots +x_8^7= x_9^7$

Ajai Choudhry found an infinite number of primitive solutions to, $$x_1^7+x_2^7+\dots +x_8^7= x_9^7$$ by using an elliptic curve with a parameter $m=2$. There are variants, the one I used is, $$x(x ...
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MAGMA - construct local field as a quotient of polynomial ring over local field

I'm dealing with the following problem: I have a local field K_v, which is defined by the completion of a number field K at the place v. Moreover, I have an irreducibe polynomial f in K_v[x]. I want ...
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2answers
62 views

Generate some sort of “graph” of specific subgroups

I need to look at all the conjugacy classes of subgroups of odd order in $\operatorname{GL}_6(2)$, and understand the respective inclusions. I was hoping to generate some sort of lattice of those ...
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MAGMA: One-sided ideals in finitely presented algebras

So I have the following code in MAGMA to obtain a right ideal in the free algebra: K := RationalField(); F<x> := FreeAlgebra(K,1); I := rideal<F|x^2>; ...
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260 views

How to reduce a polynomial over an extension field (with or without MAGMA)

I have the elements $u^{4770}$ and $u^{7489}$ lying in the finite field $\mathbb{F}_{29^3} = \mathbb{F}_{29}[u]$ where $u^3+2u+27=0$. I'd like to find equivalent values with lower degrees so that I ...