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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Computing the different of an order $\mathcal{O} \subset \mathbb{Z}[\zeta_9]$
Consider the cyclotomic field $K = \mathbb{Q}(\zeta_9)$. There is a totally real subfield $K_0 = \mathbb{Q}(\alpha)$ of $K$ where $\alpha = \zeta_9 + \zeta_9^{-1}$. Let $\mathcal{O}_{K_0}$ be the ring ...
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Ramification locus of a projection
I'm trying to write a code in magma (or sage) that given a smooth cubic surface in $\mathbb{P}^3$ and a point on the surface, it give me the ramifiaction locus (so a quartic).
For writing the map I ...
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Constructing an explicit isomorphism between extension of a finite field and quotient of ring of integers by a prime ideal
Consider the number field $K := \mathbb{Q}[x]/(x^3 - 3x + 1)$ with ring of integers $\mathcal{O}_K = \mathbb{Z}[\alpha]$ where $\alpha$ satisfies the equation $\alpha^3 - 3\alpha + 1 = 0$. A short ...
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$B(3,3), C(2,3)$ Magma notation
When one asks for composition factors of groups, Magma sometimes gives notations like $B(3,3), C(2,3), 2A(3,3)$. What are these? Are they groups of Lie type? I did some searching but just couldn't get ...
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Accessing CharacterTable information in MAGMA
In MAGMA
CharacterTable(G)[2][1]
will list the degree of the second character in the character table. The character table has other information included, such as ...
- 169
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MAGMA: How to efficiently do coercion of element of HomGrp to element of GrpAuto? [closed]
Suppose I have a finite $p$-group $G$ as GrpPC in MAGMA. The computation of the automorphism group $\mathrm{Aut}(G)$ takes a very long time.
Suppose that I also ...
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Homomorphism between vector spaces in MAGMA
I've recently started to use Magma, and I'm stuck with the following problem.
Let $\mathbb{F}_q$ be a quadratic extension of $\mathbb{F}_p$, $p$ prime and let $t$ be the generator of the extension. ...
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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 ...
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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:
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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?
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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{...
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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....
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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 ...
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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:
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