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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Different number field discriminants in Sage and Magma

I have been working with towers of number fields. My problem is that when computing the absolute discriminant of such number fields, Sage and Magma give different values. You can see this by doing in ...
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33 views

How to print long strings in MAGMA?

I'm trying to print a very long list to a file using magma to make it "callable". The list is called F2, and the code I'm using to print this list to a file is the following ...
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Does Magma let you specify primary invariants?

I am cross-posting this question from scicomp.SE. The computer algebra system Magma can calculate primary invariants (i.e. a homogeneous system of parameters) in an invariant ring of a finite group ...
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How do i substitute a value into a polynomial in Magma (CAS)?

I have the following code R := PolynomialRing( Integers() ); i:=2^6-1; a:=Intseq(i,2); f:=Polynomial(a); f; //resulting in X^5 + X^4 + X^3 + X^2 + X + 1 I would like to replace the ...
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Some questions about (normal) subgroups of finite groups

If the number of subgroups $H$ of some finite group $G$ is mentioned, as far as I understood, all subgroups are considered, no matter whether two or more of them are isomorphic, whereas the number of ...
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33 views

Creating ideals of finitely presented algebras in MAGMA

I want to create (right, left, two-sided) ideals of a finitely-presented algebra in MAGMA. I know how to do this for a free algebra, and the magma handbook indicates that it's possible to do this for ...
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37 views

What exactly is the group Omega(n,q) in MAGMA?

Let $n>2$ and $q$ be a prime power. In MAGMA I'm having a lot of trouble identifying the group Omega(n,q). I'm trying to use a source that asserts that it is the group of $n\times n$ orthogonal ...
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42 views

Can MAGMA determine if a ring is free as a module over a subring?

Suppose I have constructed a pair of rings $R\subset S$ in Magma (the computer algebra system) and I know that $S$ is finitely generated as an $R$-module. Does Magma have a routine to determine if $S$ ...
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69 views

Calculating number of subgroups of explicit order in Magma Calculator

I have a group, given by direct product of $A_4$ and $D_6$. The exercise is to find all p-Sylow subgroups of $A_4 \times D_6$ without the use of 3rd Sylow theorem. I am confident I can find the ...
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106 views

Solve multivariate equations in MATLAB/MAGMA/GP-PARI/SAGE

I want to solve equations of the form $$a_1 x_1 + a_2 x_2 + a_3 x_3 + \dots + a_n x_n + b_1 x_1 x_2 + b_2 x_1 x_3 + \dots + b_n x_{n-1} x_n$$ where all the coefficients are in $GF(p)$ and variables ...
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How to create a ring in MAGMA with relations?

I'm using MAGMA221 and would like to create a ring over $GF(2)$ with respect to a list of relations. Here's what I have so far: $\mathtt{Z:=GF(2);} \\\mathtt{P<x,y,z>:=PolynomialRing(Z,3);}$ ...
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47 views

Computing group cohomology in magma?

I don't how to construct a group module in MAGMA. Can someone show me how to compute group cohomology using MAGMA? For example, I am interested in the action of finite p-groups on abelian p-groups, ...
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56 views

Can MAGMA write Groebner basis elements in terms of the original generators?

Consider the free algebra $F = \mathbb Q(a)\langle x, y, z\rangle$ and the ideal $$I = \langle xy - ayx, yz - zy, xz - zx - y\rangle$$ According to the following code $y^2 \in I$. ...
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281 views

Advantages to learning Sage?

I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search ...
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29 views

Prime subfield enveloping algebra in Magma

Given a matrix group G $\leq$ GL(d, K), I can create the subalgebra of Mat$_{d}$(K) consisting of all K-linear combinations of the elements of G using the MatrixAlgebra<K, d | L> constructor. I ...
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51 views

magma: singularity type (IsNode?)

Does magma know the singularity type of a point in a scheme? I've seen some functions but they all seem to be about curves. This is my context: I have a surface in $P^2\times P^1$ with zero ...
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95 views

Coercing elements into a set in MAGMA

Suppose I had a permutation group $G$ for example, that corresponded to the intersection of some elements of a list $H$ where the elements are groups. Then, if I wanted to create a set or some ...
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228 views

Algorithm design for enumerating pairs of noncommuting elements up to conjugacy

I am trying to write some Magma code that, given a group $G$, returns a list of pairs $(x,y)$ with $x,y\in G$ such that $[x,y]\neq 1$ and such that every pair $(z,w)$ in the group with $[z,w]\neq 1$ ...
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44 views

Writing a series of polynomial equations of certain degree from a sequence of binary bits using Magma

How do I write a series of polynomial equations of a specified degree from a sequence of binary bits using Magma. So far, I have the following code for converting a decimal sequence to binary. ...
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180 views

finding roots of polynomial in MAGMA or GAP

Please hint me. I want to find the roots of $x^3+(1-2n)x^2-(1+4n)x+8n^2-10n-1$ with Magma or GAP. In Magma: $P<x> := PolynomialRing(Rationals())$; $P<n>:= ...
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Regarding “hidden work” of MAGMA Order function

The computational algebra system MAGMA has a function called Order. What it does is find the multiplicative order of its argument, which must be a nonzero element ...
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MAGMA miscalculation of NilpotencyClass

I'm copying this question from over at SO, since there is no tag about the MAGMA cas over there, as I only just figured out. Hope someone can answer over here. Not asking for migration because I've ...
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64 views

MAGMA hom function

Suppose I have two fields E1 and E2. If I tell MAGMA to do: isom:=hom<E1->E2|b^7 ...
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Finding the $H$-orbit of $W$ using either Magma or Gap. [closed]

Let $G$ be a finite group and $H$ be a subgroup of $G$. Suppose that $W$ is a subset of $G$. How I could find the $H$-orbit of $W$ by using either Magma or Gap (where $G$ acts upon $W$ by ...
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60 views

Computer program for factorization into irreducible polynomials over $\mathbb{Z}_{p^k}$

Hensel's Lemma allows us to factor a polynomial uniquely into basic irreducible factors over $\mathbb{Z}_{p^k}$. Is there a SAGE or Magma command that gives this factorization? Or can anyone help in ...
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284 views

Output for places in Magma's online calculator

I'm using Magma's online calculator to study some algebraic fuction fields, places, etc. I know that for an algebraic function field $F/K$, the places $\mathbb{P}_F$ are principal ideals of the ...
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53 views

Help finding a summation using CAS

While approximating an integral by midpoint rule, I ended up with $$\iint_R f(x, y)\hspace{1mm}dA\approx \dfrac{1}{n^2}\sum_{i=0}^{n-1}\sum_{j=0}^{n-1} f\left[\dfrac{1}{2n}+\dfrac{i}{n},\hspace{3mm} ...
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1answer
85 views

schur index in GAP

What is the command for the Schur index in GAP? Let $χ$ be an irreducible (complex) character of a finite group, $G$. The Schur index $m_K(χ)$ of $χ$ over the field $K$ is the smallest positive ...
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137 views

Character Table of Finite Group In Magma

I want to get character table of following group for some $n$ with MAGMA $$G\langle a,b\rangle := \mathrm{Group}\langle a,b\mid a^{2n}, b^4, b*a*b*a, b^{-1}*a*b^{-1}*a\rangle;$$
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MAGMA Commands for Galois Theory calculations

Perhaps this is walking over old ground (or the wrong place to ask this), but I'm looking to use MAGMA to perform certain calculations in Galois Thoery. The motivation of this question is to create an ...
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Magma error: User error: Imported environment value 'z' cannot be used as a local

Can anyone figure out how to fix this error? I want to define z beginning as 1 and update z to 2z everytime. Basically I was z = 1, 2, 4, 8, 16, .... z := 1; Successive := procedure(x1,y1,d); ...
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212 views

calculate structure automorphism group in MAGMA

Please hint me! Is there any instruction in MAGMA to calculate structure automorphism group by using generators? for example: ...
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634 views

Embedding as a subgroup

Suppose I am given two finite groups $G$ and $H$ (not too large: let's say their orders are around $10000$ and $100$ respectively, and the order of $H$ divides the order of $G$). These may be ...
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Does the Windows version of MAGMA have a memory limit?

Sorry if this isn't the best place to ask support type MAGMA questions, but I haven't found a single forum or anything for MAGMA users to talk. I have access to a copy of MAGMA which is running on a ...
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Computing $-\frac{655}{8}$ modulo 35 efficiently in Magma (CAS)

Modexp$(-81.875,1,35);$ will not work. So what I have to do is the following: Modexp$(-81,1,35); = 24$ $875/1000; = 7/8$ Modexp$(24*7,1,35); = 28$ Modexp$(8,-1,35); = 22$ Modexp$(22*28,1,35); = ...
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Expressing a matrix in terms of subgroup generators using Magma

With Magma, it is possible to define a subgroup $H$ of a finite matrix group $G$ in terms of generators. Given a matrix $M\in G$, Magma can also determine whether $M\in H$. Presumably, if Magma ...
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Adjoint action of a Lie algebra in MAGMA

Let's say I have a Lie algebra $L$ and an element $x$ in $L$. I need to compute $(\mathrm{ad} \ x)^n(y)$ for several values of $y$ and a particular value of $n$. I thought the best way to do this ...
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Computing the analytic $p$-adic $L$-function via modular symbols in MAGMA

I need to compute the analytic $p$-adic $L$-function of an elliptic curve at a prime $p$ via modular symbols using MAGMA. In ...
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Printing long lines in MAGMA without line break

In MAGMA, how do I print a long list of items to a file without automatic line breaks? It seems to me that there is an internal length limit and anything longer than it will result in a automatic ...
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564 views

Galois group command for Magma online calculator?

I need to test if a family of 7th deg and 13 deg equations are solvable. I'm new to Magma, so my apologies, but what would I type in, http://magma.maths.usyd.edu.au/calc/ to determine the Galois ...
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1answer
151 views

Reading a Character Table in Magma

These are the outputs of two character tables from Magma. The first is for $A_5$. The second is for $GL_3(2)$. What is the significance of the '$+$' and '$0$' symbols? I can produce more tables if ...
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1answer
161 views

Representing Points of Jacobian in Magma

Although I understand the Mumford representation of points on the Jacobian (of a genus 2 hyperelliptic curve), I don't understand how Magma represents such points. I would guess the confusion arises ...
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Revealing output slowly in Magma

When working in Magma, is there a command to gradually reveal the output. For example, if you have a finite group $G$ and you want to calculate SubgroupLattice(G), then the output may be thousands of ...
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111 views

MAGMA: Retaining original vertex set

I am trying to work with graphs in MAGMA, but to my surprise I noticed that the vertices of the graph are no longer considered elements of the set I started with. Here is an example: X:={1.. 13}; ...
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201 views

Finding all finite field embeddings

Does there exist an efficient (i.e. sub-exponential) algorithm for finding all possible embeddings of one finite field into an isomorphic field? I'm particularly interested in ways to embed ...
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122 views

Producing a set of matrices in MAGMA

As part of my work I need to define the set of all $n\times n$ matrices with entries in $\{0,1,\ldots,n\}$ (considered as a subset of $\mathbb{Z}$), such that each row and column of the matrix sums to ...
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63 views

How embeding the direct product of permutational groups in $S_n$ using the Magma?

I would like embedding the direct product $Sym(\{1,2,3\} ) \times Sym(\{4,5,6\}) \times Sym(\{7,8\})$ in $Sym(8)$ using the software Magma. Anyone can help me?
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a codeword over $\operatorname{GF}(4)$ -> two codewords over $\operatorname{GF}(2)$ using MAGMA

A codeword $X$ over $\operatorname{GF}(4)$ is given. How can I write it as $X= A+wB$ using MAGMA? where $A$ and $B$ are over $\operatorname{GF}(2)$ and $w^2 + w =1$. Is there an easy way, or do I have ...
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125 views

changing the column order of a matrix using MAGMA (software)

I've just begun to use Magma (software). I have several questions. I am trying to change the columns of a 9x18 matrix according to Random(Sym18). the Random gives me a permutation like ...
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473 views

Programmatically solving a system of nonlinear equations over GF(2)

I have the following relatively large system of nonlinear equations over $GF(2)$: $ 0 = w7x7 + w7x5 + w7x4 + w7x0 + w6x6 + w6x5 + w6x1 + w5x7 + w5x6 + w5x2 + w4x7 + w4x3 + w3x4 + w2x5 + w1x6 + w0x7 ...