Questions tagged [magma]

Questions involving the software MAGMA. (For the algebraic structure called magma, please, use the tag magmas.) This tag should hardly ever be the only tag of a question; typically there should be additional tags to indicate the mathematical content of the question. Please note that questions that are purely support-questions on MAGMA are not a good fit for this site.

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453 views

Solving the field membership problem using Grobner bases

Is there an easy way to determine whether a set of elements in a field generates the whole field or only a subfield? Specifically, I have a subfield of $k(x,y)$ described in terms of a canonical set ...
780 views

BSD conjecture for X_0(17)

I use Magma to calculate the L-value, yields E:=EllipticCurve([1, -1, 1, -1, 0]); E; Evaluate(LSeries(E),1),RealPeriod(E),Evaluate(LSeries(E),1)/RealPeriod(E); Elliptic Curve defined by y^2 + x*y + y =...
1k views

350 views

Does MAGMA use a standard p-modular system?

I'd like to ask the following question: Are the Brauer character values of $kG$-modules (where $k$ and $G$ are finite) in MAGMA computed with respect to the standard $p$-modular system described in ...
228 views

Double coset representatives and Magma

I'm trying to use Magma to do a double coset calculation on the group M10, but the answer does not make sense to me. Your help and comments are most appreciated. First, here's the calculation: (1) ...
111 views

MAGMA-question concerning the transformation of a $kG$ -module $M$ into a right ideal of the group algebra

Let $G$ be a finite group and $k$ be a finite field of characteristic $p>0$ such that $p\mid |G|$. Let $M$ be a $kG$-module which has an embedding $M\hookrightarrow kG^{reg}$ into the regular $kG$-...
188 views

Can MAGMA compute almost projective $kG$-homomorphisms?

Let $G$ be a finite group and $k$ be a finite field (big enough) whith char$(k)=p$ and $p\mid |G|$. Let $M$ be a finitely generated $kG$-module. We denote the first syzygy of $M$ by $\Omega(M)$, i.e....
422 views

Integer points of one Mordell equation

How can I determine all integer points of the following equation $$y^2=x^3+10546$$ I tried Magma with IntegralPoints(EllipticCurve([0,10546])); but got the ...
130 views

Understanding Magma issue with maximal subgroups computation

I am trying to compute the maximal subgroups of the wreath product $(\mathbb Z/10\mathbb Z)\wr S_{99}$ using Magma's algorithm for maximal subgroups, which is an implementation of an algorithm of ...
196 views

Computer algebra system that test zero divisors in a quotient algebra

I have an algebra $A$ over a Noetherian ring and an ideal $I=(x,y)$, where $x,y \in A$. I need to examine whether a polynomial $h \in A$ is a zero divisor in $A/I$ or not. Is there a computer algebra ...
437 views

Working with group cosets in MAGMA

When working with group cosets in MAGMA is there a way of treating the cosets as subsets of the overlying group. Specifically I have a group $G$ and subgroups $H$ and $K$ . I wish ...
213 views

My output of a group and inverse-closed subset in MAGMA is no longer inverse-closed when entered as input to GAP.

In MAGMA, I input the following: G:=SmallGroup(20,3); G; E:=[xx:xx in G]; S:=[E[6],E[7],E[13],E[20]]; S; S[1]^2; S[2]^2; S[3]*S[4]; This gives the output: GrpPC : ...
533 views

Homomorphisms and their restrictions in MAGMA

I am trying to look at a representation (so a homomorphism) of a group G, and see what the restriction of the representation to a subgroup of G will be. Is there an easy way (or any way!) to do this ...
511 views

Checking for invertibility of large matrices in MAGMA

If you have a number of large matrices, and you wish to determine whether each matrix has determinant zero or not, what is the most efficient way to do this in MAGMA (it appears that calculating the ...
115 views

Lattices from quaternion algebras (MAGMA software)

I am studying the paper "Lattice Packing from Quaternion Algebras" from 2012 about the construction of ideal lattices. In Section 3.3 the authors construct very interesting examples of lattices using ...
454 views

magma generators for unit group/ sage totally positive

Does anyone know how to find explicit generators for the unit group of a number field on magma? For example, in sage one could do K. = NumberField(x^3+x^2-2*x-1) UnitGroup(K).gens() and it ...
191 views

construct a Hecke character in MAGMA with given infinity type

I need to do some numerical computation on special values of a Hecke L-function $L(s,\chi)$. To do this, I want to construct a Hecke character in MAGMA, given that I know its infinity type. In other ...
267 views

Differences between GAP and MAGMA [closed]

GAP and MAGMA are computer algebra systems. What are the objective differences between the two? Which capabilities are not shared? How do they compare on facilities for working with character tables?...
59 views

MAGMA-question concerning dual modules of bimodules

Let $G$ be a finite group and let $H_1,H_2\leq G$. Let char$(k)=p>0$, $k$ a field, large enough. Let $T$ be a $(kH_1, kH_2)$-bimodule given in MAGMA. Moreover, let $T$ be finitely generated ...
75 views

magma version of FixedGroup(K, L) over a different base field

I have a sequence of field extensions $F\subseteq L\subseteq K$ and I need to compute the Galois group of K over L. If $F=\mathbb{Q}$ then FixedGroup(K, L) does exactly this, but I was wondering if ...
225 views

How to ask Magma to compute the induced morphisim on divisor group

Suppose Magma has computed homomorphism $h$ between function fields $F1 \to F2$. Then we have an induced homomorphism $h$ on the divisor group. Now my question is that if there's a better way to ...
215 views

Why does MAGMA claim that the automorphism group of a curve is trivial?

I have been trying to compute the Automorphism group of a curve using MAGMA with no success. This is what I have tried: I have tried to compute the Automorphism group of the curve $y^3=x^4-x$ and no ...
234 views

Changing the Type of a Module in MAGMA

I am currently working with irreducible $k[G]$-modules in MAGMA for finite fields $k$ and finite groups $G$. To construct these modules, I am using the commands IrreducibleModules(G,k) This results in ...
147 views

Using Magma to Find a Fixed Points Module [closed]

Let $G$ be a group and $H$ a subgroup. Suppose $M$ is a $kN_G(H)$-module ($k$ a field). Then the $H$-fixed points in $M$ denoted $M^H$ is a $kN_G(H)$-module. Is there a way to access this module in ...
175 views

Is there a way to make MAGMA work with surfaces over weighted projective spaces?

Is there a way to use MAGMA to study surfaces defined over a weighted projective space (by "study" I mean computing e.g. invariants (e.g. $p_a$, $p_g$), singularities, etc)? For example, I was trying, ...
Let's say we have two $n$-dimensional lattices $(V,b)$ and $(W,b_1)$ equipped with integral bilinear forms $b$ and $b_1$ respectively. Is there an implemented function in MAGMA that decides whether $(... 0answers 23 views Points of bounded height in Magma/Sage Suppose I have an irreducible curve$C\subseteq \mathbb P^2_K$, where$K$is a number field, given by some equation$f(x,y)=0$. Is there any Magma command to search for points up to a given height on$...
If $l \equiv 1$ mod 3 then $\mathbb{Q}(\zeta_l)$ has a unique cubic subextension. I've been getting this field with the following magma code F:=CyclotomicField(l); S:=Subfields(F); for ...