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.
56
questions
18
votes
1
answer
535
views
Discrepancy in Magma's calculation and Sage's of elliptic curve?
$\DeclareMathOperator\Sha{Sha}$I calculated the Tate–Shafarevich group $\Sha(E/K)[2]$ of the elliptic curve $E:y^2=x^3+17x$ over $K=\Bbb{Q}(\sqrt{-37})$.
I calculated that by hand and I reached the ...
- 1,087
3
votes
1
answer
125
views
Computations of half-integer forms in SAGE/Magma
I am currently going through Shimura's paper on half-integer weight modular forms. I would like to understand given a 𝑞-expansion of half-integral weight modular forms of arbitrary level and ...
- 63
0
votes
0
answers
100
views
2-Selmer group over quadratic field and Magma
In the linked question, Professor Bjorn Poonen states that the $2$-Selmer group over a quadratic field can be computed using MAGMA.
In the link provided (What's the Hilbert class field of an ...
- 1,087
6
votes
2
answers
334
views
Checking for a normal p-complement with a computer
Let $G$ be a finite group.
Question 1: What are the fastest available programs to test whether $G$ has a normal $p$-complement (see https://en.wikipedia.org/wiki/Normal_p-complement for a definition)?...
- 24.9k
1
vote
1
answer
133
views
Orbit sizes of $G=\operatorname{SO}^{+}_{2n}(2)$
Let $G=\operatorname{SO}^{+}_{2n}(2)$. I did some Magma computation and found there were $3$ orbits on the natural $G$-set when $n=2,3,4$. The orbit sizes are $1$-$9$-$6$, $1$-$35$-$28$, $1$-$135$-$...
- 449
6
votes
2
answers
490
views
Is It possible to determine whether the given finitely presented group is residually finite with MAGMA or GAP?
I am working on finitely presented groups with more than 5 generators and relators and I'm so curious: is it possible to determine residually finitness of finitely presented groups with MAGMA or GAP?
- 61
2
votes
0
answers
408
views
What are the integer solutions to $y^3=2x^3+x+1$?
The question is in the title.
Short motivation. Consider Diophantine equations in $2$ variables. Quadratic ones are easy, and can be solved, for example, here https://www.alpertron.com.ar/QUAD.HTM. ...
- 4,603
3
votes
1
answer
119
views
du Val singularities in Magma
Is there any way to decide whether a singularity of a surface embedded in $\mathbb{P}^5(\mathbb{Q})$ is a du Val/rational double point in Magma?
Any help is much appreciated.
- 31
2
votes
1
answer
290
views
$2$-isogenous to a curve in the Tate normal form
It is well-known that an elliptic curve $E$ that has a point of order $2$ and is represented as $E=[0,a,0,b,0]$ has a $2$-isogenous curve $E^\prime=[0,-2a,0,a^2-4b,0]$, see e.g. p. 507 in
A. Dujella, ...
- 833
7
votes
2
answers
541
views
ℤ/18ℤ elliptic curves over cubic fields
I am working on $\mathbb{Z}/18\mathbb{Z}$ elliptic curves over cubic fields. The curves are created using the formulas on p. 584 of
D. Jeon, C. H. Kim, Y. Lee, Families of elliptic curves over cubic ...
- 833
3
votes
1
answer
239
views
Rationalizing and minimizing elliptic curve coefficients
I am working on elliptic curves with torsion group $\mathbb{Z}/14\mathbb{Z}$ over quadratic fields. The curves are constructed using the model $E_1=[0,a,0,b,0]$ following the formulas on p. 13 of
L. ...
- 833
0
votes
1
answer
336
views
Systems of equations for elliptic curves without $3$-torsion
In his YouTube video New rank records for elliptic curves having rational torsion, Noam Elkies uses systems of equations at 6:16 and 8:38 to present $\mathbb{Z}/3\mathbb{Z}$ curves of rank 14 and rank ...
- 833
4
votes
1
answer
228
views
Good algorithmic properties for quotients of braid groups
I'm trying to understand some things about quotients of braid groups, and particularly I'd like to solve the word problem for some elements of these quotients. I'm using MAGMA to try to access this, ...
- 1,055
2
votes
2
answers
286
views
Coefficient field of a newform using Magma
It is well-known that, for a newform $f = \sum c_nq^n \in \Gamma_0(N)$, the coefficient field $K_f := \mathbb{Q}(a_1, a_2, a_3, \cdots )$ is a number field.
I am introducing myself in Magma, and I was ...
- 29
4
votes
1
answer
398
views
Z2xZ6 elliptic curves with missing generators
By implementing the techniques described in and similar to
A. Dujella, J. C. Peral, Elliptic curves with torsion group Z/8Z or Z/2Z x Z/6Z, arXiv, Number Theory [math.NT] (2013), arXiv:1306.0027v1
A....
- 833
2
votes
0
answers
229
views
A computation of the rank of the Jacobian of a hyperelliptic curve over a number field using MAGMA
In this paper,
the authors says that, in order to show the rank of a Jacobian over $\mathbb{Q}$ is 0, they use the L function.
In the section 3.3, the authors compute the rank of the Jacobian of $X_1(...
- 1,274
1
vote
1
answer
149
views
The orders of $\mathbb{F}_{p^n}$- rational points of a fixed abelian variety and MAGMA computation
Let $A$ be an abelian variety over $\mathbb{F}_p$.
Then of course for every natural number $i$, we have that $\# A(\mathbb{F}_{p^i})$ divides $\# A(\mathbb{F}_{p^{i+1}})$.
But MAGMA says this is false:...
- 185
4
votes
1
answer
396
views
3-, 6-, 12-descent for Z2xZ6 elliptic curves
We are trying to write a snippet of Magma code to clarify the steps in the simplified procedure of applying $3$-, $6$-, $12$-descent and hopefully resolve the missing generator of the following $\...
- 833
4
votes
1
answer
288
views
An explicit equation for $X_1(13)$ and a computation using MAGMA
By a general theory $X_1(13)$ is smooth over $\mathbb{Z}[1/13]$, and so is its Jacobian $J$.
And the hyperelliptic curve given by an affine model $y^2 = x^6 - 2x^5 + x^4 -2x^3 + 6x^2 -4x + 1$ is $X_1(...
- 1,274
11
votes
2
answers
649
views
Z/8Z elliptic curve with a missing generator
We are searching for the rank $6$ elliptic curves with the torsion subgroup $\mathbb{Z}/8\mathbb{Z}$ using the families similar to Allan MacLeod's as described in
A. J. MacLeod, A Simple Method for ...
- 833
1
vote
1
answer
179
views
How to find an explicit value of a Hecke L-function using Magma?
I'm trying to compute special values of Hecke L-function for the field $K=\mathbb{Q}(\sqrt[5]{1})$ using Magma (more exactly, I need $L(k, \chi^k)$, $k$ - integer, $\chi$ - Hecke character for the ...
- 13
4
votes
1
answer
204
views
Software computing dimension and degree
Assume a projective scheme $X_{k_1,\dots,k_r}\subset\mathbb{P}^n$ is given as the set of common solutions of homogeneous polynomials $F_1(x_0,\dots,x_n),\dots,F_s(x_0,\dots,x_n)$, where the $F_i$ ...
user114666
2
votes
1
answer
145
views
Software for $S$-unit equation
Is there any implementation available of an algorithm which solves in full generality the $S$-unit equation $x+y=1$ in a number field? It seems that Magma solves $ax+by=c$ but only in the algebraic ...
- 509
2
votes
1
answer
143
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 $kG$-...
- 1,655
3
votes
1
answer
216
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....
- 1,655
3
votes
0
answers
610
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?...
- 147
0
votes
1
answer
364
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 ...
- 269
1
vote
1
answer
177
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 ...
- 29
2
votes
1
answer
509
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 ...
- 470
1
vote
0
answers
68
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 ...
- 1,655
7
votes
1
answer
1k
views
Why does MAGMA claim that the automorphism group of an elliptic curve is order 24 when it is order 12?
I am trying to get the hang of the available software for computing automorphism groups of plane curves over finite fields. I am using this Magma code to test it out on $y^2 = x^3 - x$ over $\mathbb{F}...
- 3,499
3
votes
1
answer
400
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 ...
- 1,655
2
votes
2
answers
180
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 ...
- 991
3
votes
1
answer
384
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) ...
- 519
6
votes
1
answer
865
views
Computing kernels of maps of modules over a finitely presented algebra
I have the following problem: I have an associative (noncommutative) algebra $A$ defined over a rational function field $k = \mathbb{Q}(\delta, \lambda)$. $A$ is given by a presentation in terms of ...
- 2,353
1
vote
0
answers
96
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 ...
5
votes
0
answers
94
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, ...
- 25.1k
-2
votes
1
answer
109
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
708
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
335
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 ...
- 21
1
vote
1
answer
273
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 ...
- 443
0
votes
1
answer
184
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 ...
- 119
4
votes
0
answers
185
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}...
- 414
0
votes
1
answer
265
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
2
answers
685
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 ...
- 305
7
votes
2
answers
840
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 =...
- 73
1
vote
2
answers
228
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 : ...
- 13
8
votes
2
answers
516
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 ...
- 841
0
votes
1
answer
267
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 ...
- 295
1
vote
2
answers
553
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 ...
- 295