**4**

votes

**0**answers

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

**1**answer

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

**1**answer

58 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 ...

**2**

votes

**2**answers

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 ...

**0**

votes

**0**answers

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

**1**answer

127 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 ...

**-1**

votes

**1**answer

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 ...

**4**

votes

**0**answers

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

**1**answer

91 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, ...

**4**

votes

**1**answer

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 ...

**7**

votes

**2**answers

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

**2**answers

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

**2**answers

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 ...

**0**

votes

**1**answer

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 ...

**1**

vote

**2**answers

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 ...

**1**

vote

**3**answers

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 ...

**0**

votes

**1**answer

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 ...

**6**

votes

**3**answers

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

**3**answers

808 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?

**1**

vote

**0**answers

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 ...

**0**

votes

**1**answer

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 $(...