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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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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? Would running ...
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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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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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MAGMA question concerning the order of conjugacy classes of a group

When I enter a group $G$ in MAGMA and ask MAGMA for the character table $ct$ of $G$, is then the order of the conjugacy classes of $ct$ always the same as the order of the conjugacy classes of $G$, ...
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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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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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Build up function for finite field element representation in Magma

Is there a built-in function in MAGMA which can represent the element $x\in GF(2^3)$ as $(x_1,x_2,x_3)\in (GF(2))^3$? I need this for the multidimensional Walsh transform.
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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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Type casting in Magma

I'm doing a Magma implementation of the Camellia block chiper for an university project. I'm facing an annoying problem, I have a sequence, representing a binary value, that I need to convert to an ...
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66 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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45 views

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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336 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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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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182 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 ...
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112 views

MAGMA: coercing matrix group to permutation group

I'm just starting out with using the MAGMA computer algebra system, and can't figure out how to tell MAGMA to consider $GL(3,2)$ as a permutation group, using the natural action on $(\mathbb F_2)^3$. ...
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Can MAGMA tell me the explicit matrices that define a module it computed?

I have been using MAGMA to compute the radical layers of the indecomposable projective modules of $G=F_8$ (Frobenius group of order $56$) in characteristic $2$ (note that MAGMA automatically extends ...
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How to compute the ray class field of $\mathbb{Q}(i)$?

I want to verify Thm 5.6 in Silvermans Advanced Topics in the Arithmetic of Elliptic Curves that says $K(j(E),h(E[\mathbb{c}])$ is the ray class filed of $K$ modulo $\mathbb{c}$. I choose $K= \mathbb{...
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Permutation modules in MAGMA

I had a question about MAGMA: Let's say we have a permutation group $G$ acting on $\{1,2,\dots ,n\}$, and we construct the permutation module over a field $F$, by using $V:=PermutationModule(G,F);$. ...
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Checking types in MAGMA

In using MAGMA, I always get type errors. How do you find out what the type of something is? For example, I have made an empty set $e := []$, how would I make MAGMA print out the type of $e$? Also, ...
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Matrix representation for PGL(n,q) in Magma

In Magma (Computational Algebra System), we can define both groups $GL(n,K)$ and $PGL(n,k)$. For instance: $K:=GF(7)$; $G:=GL(2,K)$; $G1:=PGL(2,K)$; Now, one can easily construct a subgroup $H$ ...
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representation of the dihedral group $D_3$

I'm very new with representations of groups. Here it is a non-commutative group with $6$ elements defined by $D_3 = \langle p,q\ |\ p^3 = q^2 = (pq)^2 = 1\rangle$ The representation I'm interested ...
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Boston's “Spaces of constant rank matrices over $\mathrm{GF}(2)$”

Let’s recall what is spaces of matrices of constant rank, that is, in spaces of matrices in which every nonzero matrix has the same rank. The case is, i’m reading journal by NIGEL BOSTON titled “...
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Defining a matrix in Magma with finite field entries

Consider the following matrix $$ G:=\left[ \begin {array}{cccccccc} 1&0&0&0&\alpha&\alpha+1&1&1\\ 0&1&0&0&1&\alpha&\alpha+1&1\\ 0&0&...
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Determining ring of integers using Computer Algebra Systems

I am working on ring of integers of given number fields. Are there any computer algebra systems that I can use to determine the ring of integers $O_K$ of a number field $K$? I am aware that I can ask ...
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Constructing a semidirect product in MAGMA

I am trying to construct in MAGMA the group $$ (C_3 \times C_3) \rtimes Q_8$$ in which the action of $Q_8$ on $C_3 \times C_3$ is given by the center $Z(Q_8)$ acting trivially, and the quotient $Q_8 /...
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GAP/Magma-cas: Suppose $H<S_n$ (given by generators): Does either system make it easy to find the maximal subgroup containing $H$?

I am not sure that this is the right forum, but anyhow: Suppose I have a subgroup $H$ of $S_n$ (given by generators). Does either system make it easy to find the maximal subgroup containing $H$?
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Printing p-adic matrices in Magma CAS

I would like to print some p-adic matrices into a file that can then be read by magma. In theory this should be possible by using PrintFileMagma(..) but the problem I'm having is that the matrices are ...
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How to create a circulant matrix in Magma CAS

How can one create a circulant matrix using the Magma computational algebra system? I have the row $(1,2,3,4,5,6)$ and I would like to use this row to generate the circulant matrix $$ \begin{...
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Set a time limit for computations in Magma CAS

I'm new to Magma CAS and looking for a way to abort a computation if Magma exceeds a given time limit. I know that Singular CAS calls this watchdog, but I couldn't find something similar in the Magma ...
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enumerating elements of a group in Magma

Let's say we have a permutation group in Magma. Let me write a concrete group, say $G:=$PermutationGroup$<16|(1,2,3,4,5,6,7,8),(1,2)(9,11)>$. If it's given in this format, is there a quick way ...
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Hadamard (entrywise) product in the Magma computer algebra system

Is it possible to efficiently compute the Hadamard product (= entrywise product) of 2 matrices in MAGMA? I can't find anything in the documentation. The best thing I can come up with is computing it ...
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Why are quotients of polynomial rings called “affine algebras” in Magma?

Although quotients of polynomials rings are affine algebras (in the sense that they are coordinate rings of affine schemes), they are not the only ones, right?
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How to save a pc-group in MAGMA?

I have a group $M$, which is a large matrix group. Using the command $\texttt{LMGSolubleRadical(M)}$ I obtained $R\cong M$, where $R$ is of type $\texttt{Grppc}$, and an isomorphism $M\to R$ called $\...
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How to get the coefficient of the constant part of a multivariate polynomial in MAGMA?

In the MAGMA software package, given a multivariate polynomial $f$ in some polynomial ring , how do we get its constant part? For univariate polynomials the method ConstantCoefficient(f) returns (...
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138 views

Print LIST of polynomials in Magma in one line instead of multiline

Suppose I have list of two polynomials and want to print it. I will get multi line output: ...
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181 views

Questions that SAGE, MAGMA can answer?

I practice theoretical mathematics and I know (almost) nothing about SAGE, MAGMA. I would like to know (in general) what type of questions can I ask SAGE to do? For example, I know that given an ...