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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Why does magma give a cubic as the second coordinate of a Mumford representation for genus 2 curves?

I'm working with Magma to do computations with Jacobians of genus 2 hyperelliptic curves, and I find some behavior for elements that I don't understand. Specifically, let us take the prime $p = 431$ ...
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Alternating Frobenius form in Sage

Given an alternating, non-degenerate matrix $A$ over the integers, I need to compute the matrix "closest" to the standard symplectic form that can be obtained from $A$ by an integer change ...
Oliver Miller's user avatar
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Magma - Differential field extension over a differential field

I want to construct the differential field $\mathbb{Q}(x,\,\log x,\,\log(\log x))$ in Magma. I have tried the following: ...
Mitchell Holt's user avatar
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Iterate through the finite groups in MAGMA

How may I iterate over the finite groups in MAGMA of orders between $1$ and $N$ (where possible), and compute a given property of them?
Robin's user avatar
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How Do I Calculate The Galois Group And Intermediate Fields Of A Certain Extension Using Magma?

here MAGMA Commands for Galois Theory calculations it is discussed how to calculate the galois group when the the field that is fixed is say the rationals. But what if the field that is fixed is $\Bbb{...
Harry Crane's user avatar
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Check if a polynomial is primitive over a galois field using Magma calculator

I want to check if the polynomial $f(x) = 1 + x^{18} + x^{29} + x^{42} + x^{57} + x^{67} + x^{80}$ is primitive over the Galois Field $GF(2^{80})$ using the Magma Calculator (http://magma.maths.usyd....
Divye Kalra's user avatar
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Idempotent polynomials over the finite field $\mathbb F_p$, mod $x^p-x$.

Is there any way of characterizing the idempotent elements of the ring of polynomials in $m$ variables $x,~y,~z, \ldots$ over a finite field $F_p$, modulo $x^p-x$, so that I am really considering ...
user173611's user avatar
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On certain abelian subgroups of $S_{12}$ and $S_{18}$

Let $p$ be a prime, and $\Sigma\le S_{p-1}$ an abelian subgroup of order $p-1$ such that: all the elements of $\Sigma$ have cycle type $\underbrace{\left(\frac{p-1}{k},\dots,\frac{p-1}{k}\right)}_{k\...
citadel's user avatar
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Checking whether two algebras are isomorphic with MAGMA

I want to use MAGMA to check whether to given finite dimensional algebras over a field are isomorphic. Here my attempt: ...
Mare's user avatar
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Is it possible to describe extension of places of a function field in MAGMA?

I would like to describe, for example, the unramified places of an extension $F'/F$ of function field (in one variable) in MAGMA calculator. More specifically, given $F'/F$ an extension of function ...
Adler Marques's user avatar
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Constructing a graph in Magma

I am trying to construct a simple graph in MAGMA and can't figure out how to get the syntax right. My code is below: ...
stillconfused's user avatar
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Automating modular arithmetic in local fields using MAGMA

Let $f(X) = X^4 + a_3X^3 + a_2X^2 + a_1X + a_0$ be an Eisenstein polynomial over the $2$-adic numbers $\mathbb{Q}_2$. Let $\mathbb{Q}_2(\pi)/\mathbb{Q}_2$ be the totally ramified extension defined by $...
Sebastian Monnet's user avatar
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82 views

Constructing maps between cohomology groups in magma

How does one construct maps between cohomology groups in $\texttt{magma}$? Here is a (randomly generated) example: ...
user297024's user avatar
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Aschbacher Class $2$ subgroup structure

In $PGL(12,3)$, there should be an Aschbacher Class $2$ subgroup the image of $GL(2,3)^6 \wr{\rm Sym}(6)$. I am trying to locate the image of $GL(2,3)^6$ in Magma using derived subgroup but it doesn't ...
scsnm's user avatar
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Construction of $SL(2,5)^4$ in a maximal subgroup in Magma

There is a Class $2$ maximal subgroup $SL(2,5)^{4}.4^{3}.S_{4}$ (denoted by $MM_2$ in the following code) in $PGL(8,5)$. I am trying to locate the $SL(2,5)^4$ part in Magma. But after I constructed ...
scsnm's user avatar
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construct the normaliser of a subgroup and then construct the subgroup

There is a maximal nontoral (not contained in a conjugate of a fixed maximal torus) elementary abelian $2$-subgroup of rank 6 in $G = PGL(8,7)$. I denote this group by $A$. Its normaliser $N_{G}(A)$ ...
scsnm's user avatar
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1 vote
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split maximal torus construction

In PGL(n,q) there is a split maximal torus T of order $(q-1)^{n-1}$. How to construct this in Magma? Let's use the example of $PGL(4,11)$. I took a detour to construct it: ...
scsnm's user avatar
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Isomorphism between two p-groups

I've been looking for an explicit isomorphism between the following two groups (h and g): ...
Mr. J's user avatar
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compute group automorphisms, part 2

This is continuation of my previous question about computing automorphism groups using MAGMA. My new question goes in a different direction so I start a new thread. If this breaks the forum rules, I'...
W Sao's user avatar
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compute group automorphisms using magma

I'm learning how to use MAGMA to compute automorphism groups, and I have difficulty interpreting the output. Concrete (and functional) example: ...
W Sao's user avatar
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Magma error: Could not find a covering group

Let $G = PGL_{4}(5)$. I find an elementary abelian $2$-subgroup of rank $3$ denoted by L1[35] in the following code. Then I have Magma compute the centralizer and normalizer of this subgroup which are ...
scsnm's user avatar
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matrix group construction in Magma [closed]

Can we construct the following matrix groups in Magma? If so, how and is there a uniform method? \begin{pmatrix} SO_7(2) & *_{7 \times 1}\\ 0 & 1\\ \end{pmatrix} and \begin{pmatrix} SL_2(2) &...
scsnm's user avatar
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1 vote
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Semidirect product of Heisenberg group 3 and $SL(2,3)$

I've been trying to build the semidirect of $He_3$ and $SL(2,3)$ in Magma, but haven't had much luck yet. This may be because of a lack of experience with the software, but any help would be amazing. ...
abruhman's user avatar
3 votes
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195 views

Weierstrass form of $x^4+ux^2y^2+y^4=z^2$

I think $x^4+ux^2y^2+y^4=z^2$ is an elliptic curve, so how should I transform it into Weierstrass form? Either by hand or by software like MAGMA is fine. I am new to MAGMA and I tried something ...
fp1's user avatar
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Finding random point of specified order using MAGMA

I would like to use MAGMA to construct a random point of specified order on an elliptic curve over a finite field. I have created the elliptic curve E0, but I'm not ...
stillconfused's user avatar
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207 views

Orbits of a matrix group

How to get the orbits of the action of the following matrix group on the standard basis of a 3-dim vector space? \begin{pmatrix} SL_2(2) & 0\\ * & 1\\ \end{pmatrix} where * denotes a 1$\times$...
scsnm's user avatar
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6 votes
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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 ...
Ingolfur's user avatar
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Magma: an algebraic curve having singularities over an unknown extension

I am working with a plane algebraic curve $C$ defined over the rational numbers $\mathbb{Q}$ that has singularities over an extension of $\mathbb{Q}$. The problem is that the equation defining $C$ is ...
Howard's user avatar
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Limit of time to get an output on MAGMA

I would to ask you if there is a way to put a MAGMA command that stop a function in a script if the occurring time is greater than a certain prefixed time $T\geq 0$ (for example $T=15 $ minutes ). ...
Federico Fallucca's user avatar
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Computing Divisors with MAGMA

I am relatively new to MAGMA, and trying to use it to verify a computation. I would like to find the ramified points of the map $\phi : C \to \mathbb{P}^1$ given by $[X:Y:Z] \mapsto [Y:Z]$, where $C$ ...
stillconfused's user avatar
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1 answer
47 views

coerce matrix into unitary groups

I try to coerce this matrix \begin{pmatrix} -1 & 0\\ 0 & 1\\ \end{pmatrix} into $GU(2,9)$. I used the following command: ...
scsnm's user avatar
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centraliser computation of projective linear group in MAGMA

I wish to computer the centraliser in $PGL(4,5)$ of $$ [\begin{pmatrix} 4 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}] $$ ...
scsnm's user avatar
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7 votes
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128 views

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 ...
Ingolfur's user avatar
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1 vote
0 answers
81 views

Computing rank of finitely-generated but large Z-module

I have a collection of $\mathbb{Z}$-modules, each defined by a set of formal generators $x_1, \ldots, x_n$ module a respective set of relations of the form $\sum_j a_i x_i = 0$. I would like to ...
mpc's user avatar
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2 votes
1 answer
142 views

Magma - Coercing a Function Field element to a Rational Function

Here's an example of what I'm trying to do: I have an elliptic curve $E : y^2 = x^3+x$ over the field $F= GF(43)$. I want to be able to go back and forth between $F(E)$ and $F(x,y)$ in MAGMA. This is ...
Rdrr's user avatar
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1 vote
1 answer
56 views

Symbolic points in an elliptic curve over $\mathbb{Q}$ of the form $(u/e^{2},v/e^{3})$

Suppose I have an elliptic curve $E : y^{2} = x^{3} + D$ over $\mathbb{Q}$ , where $D$ is a symbolic constant (an integer). I want to define two points in the curve of the type $P = (u_{1}/e_{1}^{2}, ...
Atratrana Suna's user avatar
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Magma Isogeny Polynomials Coercion

This is bordering the wrong stack exchange but I have the following problem: I have the code; ...
Rdrr's user avatar
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145 views

Elliptic Curve Automorphisms In Magma

I have the elliptic curve $E: y^2 = x^3+x$ over the field $\mathbb{F}_{43^2}$. I am trying to instantiate the automorphism $[i](x,y) = (-x,i*y)$, where $i^2=-1$ and the Frobenius Map $\pi(x,y) = (x^{...
Rdrr's user avatar
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0 votes
1 answer
257 views

Substituting variables in MAGMA

If I have a polynomial $x_1+x_2+x_2x_3+x_2x_4$ and I want to rewrite it as $x_1+x_2+z_{2,3}+z_{2,4}$. Is there a function in MAGMA to substitute $x_2x_3$ as $z_{2,3}$? I know Maple has a subs function ...
tkw4063's user avatar
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Factorize with unknown in MAGMA

Say I have a polynomial $f(x)$ over a finite field $\mathbb{F}_p$ such as $$f(x) = x^2 + \alpha x + \alpha^2$$ for some $\alpha \in \mathbb{F}_p$. Then we can express the zeroes $x_0, x_1$ in terms of ...
Krijn's user avatar
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2 votes
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Finding a K-algebra of centralisers via GAP

Let $X$ be a finite set of $n \times n$-matrices over a field $K$. Let $A_X$ be the $K$-algebra of $n \times n$-matrices $Y$ with $YS=SY$ for all $S \in X$. Question: Is there a quick way to obtain ...
Mare's user avatar
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2 votes
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72 views

centralizer in Magma

Sorry that I am new to Magma. I have a question: I can construct the group of Lie type $3E_6(C)$ and an element $a$ in it. However I cannot have Magma compute the centralizer of $a$ as it gives ...
scsnm's user avatar
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exceptional group via form preserving in magma

let $K$ be the 27-dimensional complex vector space consisting of triples $m$ = ($m_1, m_2, m_3$) of complex 3 x 3-matrices $m_i$, $1 < i < 3$, where addition and scalar multiplication are ...
scsnm's user avatar
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7 votes
1 answer
210 views

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 ...
Alex Doe's user avatar
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4 votes
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The semidirect product of $G$ with ${\rm Aut}(G)$ in the canonical way: its name and its implementation in GAP and/or Magma

Let $G$ be a finite group with automorphism group ${\rm Aut}(G)$. Let $A_G$ denote the semidirect product of $G$ with ${\rm Aut}(G)$ in the canonical way. Question 1: Is there are name for $A_G$ in ...
Mare's user avatar
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5 votes
1 answer
289 views

Writing a group as a product of its generators in MAGMA

Let $G \subseteq S_8$ be generated by the elements $s=\begin{pmatrix} 1 & 2 \end{pmatrix}\begin{pmatrix} 3 & 5 \end{pmatrix}\begin{pmatrix} 4 & 6 \end{pmatrix}\begin{pmatrix} 7 & 8 \...
Rotdat's user avatar
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196 views

Wrong use of minimal polynomial function in MAGMA?

I wrote the following MAGMA code ...
Rotdat's user avatar
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-1 votes
1 answer
158 views

Difference between exclamation mark (!) and point (.) in MAGMA [closed]

In this MAGMA handbook, I found the following code: K := FiniteField(2, 160); // finite field of size 2^160 E := EllipticCurve([K!1, 0, 0, 0, K.1]); There, I noted ...
Rotdat's user avatar
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1 vote
1 answer
111 views

Splitting up a conjugacy class with respect to a subgroup

Suppose we have a conjugacy class $\mathcal{K}$ of elements of a group $G$, and a subgroup $H \leq G$. How can we efficiently (computationally) partition the elements of $\mathcal{K}$ according to ...
xxxxxxxxx's user avatar
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0 votes
1 answer
359 views

Implementation in MAGMA: Field extension over the p-adics with a polynomial which is neither inertial nor Eisenstein

Let $K = Q_3$ and $L = K(a)$ be the extension of $K$ defined by the polynomial $f = x^6+3x^5-2$ (i.e. this is the minimal polynomial of $a$ over $K$). Now I would like to obtain this field $L$ in ...
Rotdat's user avatar
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