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 ...

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2
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2answers
113 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 ...
4
votes
0answers
59 views

Is there an interval of finite groups, at index n, with strictly more elements than the subgroup lattice of any group, of order n?

Let $G$ be a finite group and $\mathcal{L}(G)$ its subgroup lattice. Let $s(n):= max\{|\mathcal{L}(G)| \text{ for } |G|=n \}$. There is an OEIS page for the sequence $s(n)$: A018216 1, 2, 2, 5, 2, ...
-2
votes
1answer
63 views

fast way to get subextensions in magma? [closed]

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 ...
1
vote
1answer
59 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 ...
0
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0answers
79 views

representation theory in Magma

I have a submodule named sub of a representation named rep in Magma defined in the following way : sub:= Submodules(rep)[4]. I search for its generators using: Generators(sub), but I am not getting ...
1
vote
1answer
128 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 ...
0
votes
1answer
524 views

Does MAGMA have a function to decide if two indefinite, integral quadratic forms are isometric?

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 $(...
-1
votes
1answer
95 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 ...
1
vote
2answers
338 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 ...
0
votes
1answer
183 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 ...
4
votes
1answer
223 views

Finding relations between invariant polynomials

Suppose I have an action of a linear reductive group ($GL(2,\mathbb{C})^2$ in this case) on a complex vector space (of dimension $16$) and I want to compute explicitly the ring of invariants of this ...
4
votes
0answers
123 views

Computing Tamagawa numbers for jacobians of hyperelliptic curves

Do exist some computational approach to calculation of Tamagawa number for the jacobian of hyperelliptic curve at prime $p$? As followed from this question one can compute $\Phi(\overline{\mathbb F}...
0
votes
1answer
92 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, ...
7
votes
2answers
657 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 + ...
1
vote
2answers
203 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 : ...
7
votes
2answers
286 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 ...
1
vote
3answers
394 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 ...
6
votes
3answers
2k views

Using MAGMA for Group Theory

I've just started a PhD in Group Theory and need to use the computer programme MAGMA. I wonder if anyone could help me with a couple of (probably very basic things). I need to produce a Hasse ...
6
votes
3answers
811 views

Is there a MAGMA function to calculate the absolutely irreducible components of an algebraic curve defined over the rationals?

Given a curve defined over the rationals, is it computationaly possible to find all its absolutely irreducible components? Is there an implementation of this in the MAGMA program?
0
votes
1answer
382 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 ...
1
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0answers
214 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 ...