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.
67 questions
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Compute corestriction map on group cohomology in Magma
I am trying to use Magma to compute the corestriction of a second cohomology class, but I’m not sure how to interpret the output. The details and code are given below.
Consider the group $G = \mathrm{...
- 984
1
vote
1
answer
84
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MAGMA (pseudo)basis for maximal order in quaternion algebra
I wanted to compute any maximal order in the non-split quaternion algebra $\left(\frac{21, -7}{\mathbf{Q}(\sqrt{-3})}\right)$, so I did the following in MAGMA:
...
- 241
2
votes
0
answers
82
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Explicit $K$-basis of a Lie subalgebra
$\newcommand{\Kbar}{{\overline K}}
\newcommand{\Q}{{\mathbb Q}}
$I consider Example 5.7 of Sansuc's paper Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres of ...
- 14.1k
7
votes
0
answers
170
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Nondeterminism in Magma software while computing generators of an elliptic curve
Computing generators of a Mordell curve
$$y^2 = x^3 - 44275089430000,$$
can be done in Magma by running the following code:
...
- 34.3k
3
votes
1
answer
106
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Subgroups of a Weyl group fixing some vectors and its cohomology: MAGMA
I am trying to calculate the number of subgroups of the Weyl group $W(E_N)$ that fix certain vectors $L_i (i = 1,2,3)$ using Magma.
However, the output of the following code (especially #nicesubs) ...
- 1,364
0
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0
answers
108
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Isogeny classes for elliptic curves over quadratic field
Question. Is it possible for an elliptic curve $E$ over quadratic field $K$ to have two separate (yet connected) isogeny classes?
There are two $\mathbb{Z}/14\mathbb{Z}$ elliptic curves, $E_1$ and $...
- 913
3
votes
0
answers
115
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Describing the primes with each cyclic decomposition group in a given finite Galois extension of $\mathbb Q$
$\newcommand{\Q}{{\mathbb Q}}
$Let $f\in \Q[x]$ be a polynomial,
and let $L/\Q$ be the finite Galois extension
obtaining by adjoining to $\Q$ all roots of $f$.
Magma knows how to compute $\Gamma:={\...
- 14.1k
2
votes
0
answers
141
views
What is the finite group $(\operatorname {PCO}^{\circ}_{2n})^{+}(q)$
In Table 22.1 on Page 193 of Malle & Testerman's book "Linear algebraic groups and finite groups of Lie type", the fixed point subgroup $G^F$ (where $F$ is a Steinberg endomorphism) of ...
- 217
2
votes
0
answers
136
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Similar to a $d$-twist but over a cubic field
This question could be related to my old and Duality's newer questions.
I am building a $\mathbb{Z}/9\mathbb{Z}$ elliptic curve $E$ over $\mathbb{Q}$:
$$E: y^2+(t^3-3t^2+1)xy + t^3(t-1)^3y=x^2$$
For $...
- 913
0
votes
0
answers
125
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Non-isomorphic cubic fields with a given discriminant
For a cubic field $K$ with defining polynomial $P(x)=x^3 + \frac{39}{25}x^2 + \frac{22}{25}x +\frac{4}{25}$ Magma calculates the discriminant $D=-3340$.
...
- 913
6
votes
0
answers
218
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Ranks of elliptic curves over cubic fields
We are writing a paper on the ranks of elliptic curves over cubic fields. The curves of different torsion subgroups are created by the formulas in Jeon et al. and by our new parametrizations.
D. Jeon,...
- 913
4
votes
1
answer
373
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How to have MAGMA work with subgroup of ATLASGroups?
I'm trying to work with various maximal subgroups of the Thompson sporadic group. The command Group("Th"); which works for some of the sporadic groups, ...
- 143
19
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1
answer
709
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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 ...
- 1,531
3
votes
1
answer
200
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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
7
votes
2
answers
353
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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)?...
- 26.5k
1
vote
1
answer
140
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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 $1$-$9$-$6$, $1$-$35$-$28$, $1$-$135$-$...
- 501
6
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2
answers
572
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
1
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0
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453
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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. ...
- 7,172
3
votes
1
answer
143
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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
326
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, ...
- 913
7
votes
2
answers
605
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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 ...
- 913
3
votes
1
answer
256
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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. ...
- 913
0
votes
1
answer
370
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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 ...
- 913
4
votes
1
answer
314
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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, ...
- 1,277
2
votes
2
answers
312
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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
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1
answer
411
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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....
- 913
2
votes
0
answers
381
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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(...
- 1,364
1
vote
1
answer
154
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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
415
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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 $\...
- 913
4
votes
1
answer
300
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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(...
- 1,364
11
votes
2
answers
679
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 ...
- 913
1
vote
1
answer
228
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
206
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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
195
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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
160
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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 $kG$-...
- 1,755
3
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1
answer
226
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....
- 1,755
3
votes
0
answers
810
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
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votes
1
answer
480
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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
205
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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
573
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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 ...
- 492
1
vote
0
answers
70
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 ...
- 1,755
7
votes
1
answer
2k
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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}...
- 3,539
3
votes
1
answer
435
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 ...
- 1,755
3
votes
2
answers
225
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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 ...
- 1,021
3
votes
1
answer
448
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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
1k
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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 ...
- 2,533
1
vote
0
answers
109
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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
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0
answers
95
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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
126
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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
817
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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 ...