Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Magma is a computer algebra system distributed by the Computational Algebra Group at the University of Sydney. It is designed for solving problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma.

204 questions
21
votes
2 answers

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 represented as groups of permutations with known, fairly…
Robert Israel
  • 470,583
16
votes
2 answers

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 algorithms). Currently, I do a lot of my work with…
xxxxxxxxx
  • 13,688
14
votes
3 answers

Learning to use MAGMA

I'm trying to learn to use MAGMA for research in group theory, but it's been slow going. I've been using the MAGMA handbook provided online, but it's rather hard to learn with. I feel like it's hard to find anything in the handbook unless you…
Cardboard Box
  • 5,141
9
votes
3 answers

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 group of $x^5+5x-12=0$ (for example)?
Tito Piezas III
  • 60,745
8
votes
1 answer

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 archive of 'useful' MAGMA commands for anyone…
Mathmo
  • 5,003
8
votes
0 answers

Computing block systems for non-transitive permutation groups.

Atkinson as well as Schönert and Seress describe methods to compute the minimal block system for transitive permutation groups; in particular in Permutation Group Algorithms by Ákos Seress, we find Theorem 5.5.1 Suppose that a set S of generators…
Ingolfur
  • 183
8
votes
1 answer

Schönert & Seress Algorithm - Computing all block systems - blocks of imprimitivity

Atkinson as well as Schönert and Seress describe methods to compute the minimal block system; in particular in Permutation Group Algorithms by Ákos Seress, we find Theorem 5.5.1 Suppose that a set S of generators for some transitive $G \leq…
Ingolfur
  • 183
7
votes
2 answers

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 valuation rings. But the generator is not unique. If,…
Larara
  • 1,490
7
votes
1 answer

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 because Magma represents hyperelliptics in a…
davidbrent
  • 255
7
votes
1 answer

Computing endomorphism ring of finite groups via computer

I'm trying to figure out the structure of endomorphisms of some some rather precise class of finte solvable groups and I'm looking for "the less" expensive way to compute End$(G)$ with some computer system. I've been trying with the GAP function…
Alex Doe
  • 645
7
votes
0 answers

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 left and right almost split sequences of…
Bernhard Boehmler
  • 421
7
votes
1 answer

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 $m=5^7$, $$x\big(x+78124^2\big) \big(x+78124^2\big) = y^2$$ However, Allan…
Tito Piezas III
  • 60,745
7
votes
2 answers

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, $$x(x - 129^2) (x - 4\times2^7) = y^2\tag1$$ I tried the…
Tito Piezas III
  • 60,745
7
votes
0 answers

Finding the $H$-orbit of $W$ using either Magma or Gap.

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 conjugation).
ameer
  • 71
6
votes
2 answers

How to construct amalgamated product of groups in magma or gap

Denote by $A_4$ the alternating group on $4$ letters, and by $\pi: A_4 \rightarrow \mathbb Z/3$ a quotient. What is the best/easiest/proper way to construct the amalgamated product $$ \{ (x,y) \in A_4 \times A_4: \pi(x) = \pi(y) \} \qquad…
mathflow
  • 317
1
2 3
…
13 14