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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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 ...
BrauerManinobstruction's user avatar
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 đť‘ž-expansion of half-integral weight modular forms of arbitrary level and ...
swati setia's user avatar
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 ...
BrauerManinobstruction's user avatar
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)?...
Mare's user avatar
  • 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 $1$-$9$-$6$, $1$-$35$-$28$, $1$-$135$-$...
user488802's user avatar
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?
ALan Kay's user avatar
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. ...
Bogdan Grechuk's user avatar
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.
user476753's user avatar
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, ...
Maksym Voznyy's user avatar
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 ...
Maksym Voznyy's user avatar
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. ...
Maksym Voznyy's user avatar
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 ...
Maksym Voznyy's user avatar
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, ...
Ethan Dlugie's user avatar
  • 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 ...
Tomás Seguel's user avatar
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....
Maksym Voznyy's user avatar
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(...
k.j.'s user avatar
  • 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:...
zom's user avatar
  • 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 $\...
Maksym Voznyy's user avatar
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(...
k.j.'s user avatar
  • 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 ...
Maksym Voznyy's user avatar
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 ...
tyazko's user avatar
  • 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 $F_i$ ...
user avatar
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 ...
Ferra's user avatar
  • 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 $kG$-...
Bernhard Boehmler's user avatar
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....
Bernhard Boehmler's user avatar
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?...
Philip's user avatar
  • 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 ...
Gregory Eritsyan's user avatar
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 ...
N Brasilis's user avatar
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 ...
yarchik's user avatar
  • 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 ...
Bernhard Boehmler's user avatar
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}...
Catherine Ray's user avatar
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 ...
Bernhard Boehmler's user avatar
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 ...
352506's user avatar
  • 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) ...
W Sao's user avatar
  • 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 ...
Calvin McPhail-Snyder's user avatar
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 ...
Christine McMeekin's user avatar
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, ...
Sebastien Palcoux's user avatar
-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 ...
Christine McMeekin's user avatar
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 ...
Christine McMeekin's user avatar
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 ...
user279941's user avatar
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 ...
Ted Mao's user avatar
  • 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 ...
mv3's user avatar
  • 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}...
Maxim's user avatar
  • 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, ...
user47224's user avatar
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 ...
mathdonk's user avatar
  • 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 =...
Carl's user avatar
  • 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 : ...
tealPajamas's user avatar
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 ...
eithil's user avatar
  • 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 ...
dward1996's user avatar
  • 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 ...
dward1996's user avatar
  • 295