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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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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41 views

MAGMA and groups of order 0 [closed]

Many a time it has happened to me that MAGMA, when given a group with a presentation, concluded it had order 0. The following was obtained just now on a newly started MAGMA: ...
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Coding theory using magma-cas

Blockquote Let F={a_1,..,a_q} a field with q elements and C={(f(a_1),..,f(a_q),f_{k-1}) : f in F[x], deg(f)'<'k}, where f_{k-1} is the coefficient of x^(k-1) in f. Find minimun distance, ...
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1answer
15 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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30 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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1answer
46 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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2answers
147 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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1answer
19 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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1answer
101 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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1answer
38 views

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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1answer
50 views

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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1answer
34 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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62 views

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 ...
3
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1answer
55 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 ...
7
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2answers
234 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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2answers
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
73 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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1answer
94 views

Character Table of Finite Group In Magma

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

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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1answer
56 views

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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141 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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518 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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2answers
190 views

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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82 views

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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1answer
108 views

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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76 views

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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1answer
104 views

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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1answer
88 views

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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2answers
341 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
126 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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125 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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124 views

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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1answer
94 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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161 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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1answer
88 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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1answer
55 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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1answer
46 views

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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1answer
107 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 ...
3
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1answer
392 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 ...
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601 views

Why is this curve nonsingular?

Let $C$ be the projective closure of $Z(f) \subset \mathbf{A}^2$ where $f$ is an irreducible polynomial of degree 4 in $x$ and degree 2 in $y$, so $C = Z(f^*) \subset \mathbf{P}^2$ where $f^*$ is the ...
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1answer
105 views

Getting the multiplication table in Magma

I have described a group in Magma by specifying a presentation: ...
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1answer
78 views

Group representation in MAGMA

I worked with MAGMA online and studied the handbook, but I still do not know how to print the Cayley table. It is possible to print the elements, but the representation is somewhat unuseful. It ...
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85 views

Efficiency of Group-Theoretic Algorithms in MAGMA

Given a finite permutation group $G$ and an element $a\in G$ with conjugacy class $X$, I am interested in determining when for a given element $x\in X$ the subgroup $<a,x>$ generated by $a$ and ...
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1answer
338 views

Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$.

Let $A=\mathbb C[x_0,\dots,x_{m-1}]$ be the polynomial ring on $m$ variables. Define $X(u)=\sum_{i=0}^{m-1} x_i u^{i+1}$ and denote by $(X(u)^r)_n$ the coefficient of $u^n$ in the expansion of the ...
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1answer
190 views

Character table in MAGMA

Below is a character table created using the MAGMA computer algebra system. What is the meaning of the rows starting with $p=2$, $p=3$, etc.? I've tried looking in the documentation, but couldn't ...
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1answer
314 views

MAGMA question: SemidirectProduct using a homomorphism $f:G \rightarrow GL_n(\mathbb{F}_p)$.

Suppose I have a homomorphism $f:G\rightarrow GL_n(\mathbb{F}_p)$ and I wish to form the semidirect product $E\rtimes_f G$ with $E$ being the elementary abelian group of order $p^n$. The Semidirect ...
2
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1answer
419 views

Binary notation in Magma

As a part of programming an Elliptic Curve Method with montgomery coordinates in Magma, I need to have an algorithm to convert a number from decimal notation to binary notation. Since there is no ...
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2answers
122 views

Coercion in MAGMA

In MAGMA, if you are dealing with an element $x\in H$ for some group $H$, and you know that $H<G$ for some group $G$, is there an easy way to coerce $x$ into $G$ (e.g. if $H=\text{Alt}(n)$ and ...
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1answer
146 views

How to iterate over power set in MAGMA?

I want do something for all subsets J of a certain cardinality of {1,2,...,n}, for a (previously declared) number n. It seems magma is not happy with: for J in PowerSet([1..n]) do To which MAGMA ...
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1answer
114 views

Picking out columns from a matrix using MAGMA

How do I form a new matrix from a given one by picking out some of its columns, using MAGMA?