Questions tagged [sage]

Sage is a mathematical software system, and this tag is intended for questions involving this software in a substantive way. 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 Sage are not a good fit for this site.

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Re: Vertices of hyperbolic triangle with given angles [closed]

I'm working on visualizing hyperbolic triangles given angles following a previous discussion on MathOverflow. The algorithm, as outlined in this MathOverflow answer, involves computing the side ...
Rowing0914's user avatar
1 vote
1 answer
123 views

Factorial series $j(D)=\sum_{n=1}^\infty \frac{1}{(n^D)!}$ and hypergeometric functions

For positive integer $D$, define $j(D)=\sum_{n=1}^\infty \frac{1}{(n^D)!}$. For $D \le 6$, sage finds closed form in terms of hypergeometric functions at algrebraic arguments and fails to find closed ...
joro's user avatar
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0 votes
0 answers
103 views

Software for Intersection of Ideals in Noncommutative Polynomial algebra

I am looking for software which can compute an intersection of ideals (in particular right ideals) in a noncommutative polynomial algebra and then find its Gröbner Basis. Most software somehow does ...
Mukilraj K's user avatar
1 vote
0 answers
75 views

Hall-Littlewood polynomials with sage

I need to make some computations with Sage involving Hall-Littlewood polynomials. I couldn't find any satisfying information in the Sage manuals/tutorials that I found on the internet. What I found is ...
Paul Broussous's user avatar
18 votes
1 answer
649 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 ...
Duality's user avatar
  • 1,405
3 votes
1 answer
162 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 ...
swati setia's user avatar
1 vote
0 answers
158 views

Units in group rings in SAGE

Is there a recorded/known SAGE code to compute units in integral group rings for finite abelian groups ? I would be happy with a code that only works for cyclic groups. I sort of know how to ...
Maxime Ramzi's user avatar
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3 votes
0 answers
150 views

Disconnected reductive algebraic groups in Sage

All simply connected split simple groups have been implement on Sage and it is possible to find their highest roots, fundamental weights, Dynkin diagrams or compute the tensor of two of their ...
dm82424's user avatar
  • 350
0 votes
1 answer
621 views

How does Sage order the elements of the symmetric group?

In Sage, the symmetric group is a list. For instance if G = SymmetricGroup(3), we have \begin{align*} G[0] & = e \\ G[1] & = (1,3,2)\\ G[2] & = (1,2,3) \\ G[3] &= (2,3)\\ G[4] &= (...
Dan1618's user avatar
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4 votes
0 answers
188 views

Is it possible to compute Lie bialgebra structures with SageMath?

Is it possible to use SageMath (or some Linux open source program) to compute the bialgebra structures on a given finite dimensional Lie algebra? I wonder if such program can compute all the ...
amine's user avatar
  • 503
9 votes
1 answer
305 views

Construction of skew-Hadamard matrix of order 292

I am currently looking into how to construct a skew-Hadamard matrix of order 292. Where can I find such construction? According to multiple papers (e.g. Koukouvinos and Stylianou - On skew-Hadamard ...
Matteo Cati's user avatar
8 votes
2 answers
700 views

How to get the dimension of Atkin-Lehner eigenspace or do you have any data already obtained?

I need the dimensions of the Atkin-Lehner eigenspace for the paper I'm writing. As is well known, the cuspidal space $S_{k}(\Gamma_{0}(N))$ can be decomposed by Atkin Lehner involution. For example, ...
kslhg's user avatar
  • 83
9 votes
3 answers
525 views

Why mpmath computes $\sum_{n=2}^\infty (-1)^n\log(n)=\log\left(\frac1 2 \sqrt{2} \sqrt{\pi}\right)$

Working with precision 500 decimal digits, mpmath in sage computes: $$\sum_{n=2}^\infty (-1)^n\log(n)=\log\left(\frac1 2 \sqrt{2} \sqrt{\pi}\right).\tag{1}\label{1}$$ We believe the LHS of \eqref{1} ...
joro's user avatar
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13 votes
3 answers
4k views

Is there any fast implementation of four color theorem in Python?

I'm now using scipy.spatial.Voronoi to generate a Voronoi graph, as shown here: voronoi graph. I'd like to apply the four color theorem on it, so that no adjcent regions share the same color. I ...
ReZhacai's user avatar
  • 139
1 vote
0 answers
168 views

Calculating multiplication in a finite dimensional algebra over $\mathbb{Q}$

Suppose $ L $ be an extension over $ \mathbb{Q} $ of degree $ n $. Let $\{e_{1},e_{2},\dots,e_{n}\} $ be a basis of this extension. Now I know the product $ e_{i}^{2} $ and $ e_{i}e_{j} $ . So we can ...
Sky's user avatar
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2 votes
0 answers
268 views

Degree $8$ cyclic extension over $\mathbb{Q}$

Actually I am interested in degree $ 8 $ cyclic extension over $ \mathbb{Q} $. Let $ L $ be such extension. At first I was thinking to take basis as normal basis, as we can determine the galois group ...
Sky's user avatar
  • 913
1 vote
0 answers
130 views

Can PARI compute class numbers without factoring the discriminant?

When calculating properties of algebraic number fields, one of the hardest steps is factorizing the discriminant of a defining polynomial. This is necessary in the Pohst-Zassenhaus algorithm for ...
wandersam's user avatar
  • 125
4 votes
1 answer
281 views

How to calculate genus number of number field using sage?

I am looking to find real quadratic fields whose Hilbert class field is abelian over $\Bbb Q$. Then I learned about genus numbers and genus field of the number field. It is enough to find a number ...
SUNIL PASUPULATI's user avatar
3 votes
1 answer
318 views

Understanding the implementation of the $p$-adic(?) sigma function in SageMath

I'm trying to understand the (pretty undocumented) method .sigma() method for formal groups of elliptic curves, as listed here. The source code looks like this: <...
xir's user avatar
  • 1,964
2 votes
1 answer
172 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
4 votes
1 answer
450 views

All rational periodic points

I am trying to find all rational periodic points of a polynomial. To specify: a periodic point is the point that satisfy $f^n(x)=x$. It is related to dynamical systems in fact. So the current codes ...
nomadd's user avatar
  • 41
3 votes
2 answers
349 views

How to find a solution of a large system of linear diophantine inequalities?

I need to find a solution (all solutions, or at least upper and lower bounds) in positive integer numbers to the system $Ax \ge f$, where $A$ is an integer matrix. With SageMath, I solved it with the ...
Mikhail Golubiatnikov's user avatar
4 votes
0 answers
241 views

Indexed character tables for wreath products in Sage and GAP

I am trying to obtain character table for the Hyperoctahedral group $\mathcal{H}_n$ in Sage using GAP. This group arises as the wreath product $\mathcal{C}_2 \wr \mathcal{S}_n$, so of course I can ...
Josh's user avatar
  • 41
0 votes
1 answer
344 views

Mistake in SageMathCell code, finding integral points on elliptic curves [closed]

I've the following number: $$12\left(n-2\right)^2x^3+36\left(n-2\right)x^2-12\left(n-5\right)\left(n-2\right)x+9\left(n-4\right)^2\tag1$$ Now I know that $n\in\mathbb{N}^+$ and $n\ge3$ (and $n$ has ...
Jan Eerland's user avatar
5 votes
1 answer
389 views

Implementing zeta functions of algebraic varieties in SAGE

I am fairly new to sage, I was studying zeta functions of hypersurfaces over finite fields and I don't know how to compute them in Sage. Are there any packages that do most of the work, or maybe some ...
Martin Ortiz's user avatar
4 votes
1 answer
191 views

Branching to Levi subgroups in SAGE and the circle action

In the SAGE computer package, there useful exist tools for branching representations of a simple Lie group to a Levi subgroup: http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/...
Nadia SUSY's user avatar
4 votes
2 answers
372 views

GAP versus SageMath for branching to Lie subgroups

Which computer package is better, GAP or SageMath, for decomposing an irreducible representation of a (simple) Lie group $G$ into representations of a Lie subgroup. I am most interested when ...
Nadia SUSY's user avatar
12 votes
0 answers
1k views

Euler's totient function and Riemann hypothesis

I am looking for an upper-bound of the Euler's totient function $\varphi$ which would be equivalent to the Riemann hypothesis (RH). There is the following Nicolas' criterion about primorial numbers $...
Sebastien Palcoux's user avatar
1 vote
1 answer
240 views

Sage: Evaluation precision for elliptic curves over p-adic fields

Consider the elliptic curve $E: y^2 = x^3 + 23x+11$ over p-adic fields. In Sage I use: k = GF(257) E = EllipticCurve(k,[23,11]) kp = Qp(257,5) # 257-adic Field with capped relative ...
user5507059's user avatar
3 votes
0 answers
696 views

Puzzle in 3D grid with black and white boxes, related to shelling

Consider a $n$ by $n$ by $n$ grid represented by the set of $3$-uples $S=\{1,2,\dots, n\}^3$. A line (resp. slice) of $S$ is a subset of cardinal $n$ (resp. $n^2$) where two components (resp. one ...
Sebastien Palcoux's user avatar
24 votes
6 answers
2k views

Number of collinear ways to fill a grid

A way to fill a finite grid (one box after the other) is called collinear if every newly filled box (the first excepted) is vertically or horizontally collinear with a previously filled box. See the ...
Sebastien Palcoux's user avatar
5 votes
0 answers
179 views

normal form for some finite groups, extending the small groups library

I am in need of a normal (that is, canonical) form for (some) finite groups, computable with - for example - gap or sage or any other freely available package. The goal is to make finite groups ...
Martin Rubey's user avatar
  • 5,563
11 votes
1 answer
547 views

How do computer algebra packages like Sagemath implement rank of a matrix

I am not sure if this is the right place to ask this question, but I believe there will be people here who do computations on computer algebra packages like Sage in their work. I have been using ...
Nikhil's user avatar
  • 263
2 votes
1 answer
259 views

Memory usage of Gröbner basis computation

I've been calculating some Gröbner bases in preparation for finding non-commutative Hilbert series (and, once I recreate that, characters of group actions). Specifically, I've been using the ...
W. Cadegan-Schlieper's user avatar
4 votes
1 answer
372 views

Existence of a non-Eulerian atomistic lattice with this property on the Möbius function

Let $L$ be a finite lattice with least element $\hat{0}$, greatest element $\hat{1}$, and Möbius function $\mu$. Question 1: What class of lattices the following property characterizes? $$\mu(\hat{0},...
Sebastien Palcoux's user avatar
8 votes
6 answers
3k views

Computation of a minimal polynomial

It is relatively easy (but sometimes quite cumbersome) to compute the minimal polynomial of an algebraic number $\alpha$ when $\alpha$ is expressible in radicals. For example, the simple query "...
Anton's user avatar
  • 1,573
5 votes
2 answers
376 views

Symmetry-finding with SAGE?

On pp. 152-3 of Hydon's Symmetry Methods for Differential Equations (2000 ed.), he lists some computer packages for symmetry-finding. This related Mathematica StackExchange question mentions the SYM ...
Geremia's user avatar
  • 185
1 vote
1 answer
286 views

How to return elements of a given length in a symmetric group using Sage?

Let $S_n$ be the symmetric group over $\{1,2,\ldots,n\}$. How to return elements of length $m$ in $S_n$ using Sage? I try to find such function in Sage but didn't find one. Thank you very much. Edit: ...
Jianrong Li's user avatar
  • 6,121
2 votes
0 answers
96 views

Is the bounded coset poset of a boolean interval of finite groups, Cohen-Macaulay?

Let $[H,G]$ be a boolean interval of finite groups and let $\hat{C}(H,G)$ be its bounded coset poset (i.e. the poset of cosets $Kg$ with $K \in [H,G]$, bounded below by $\emptyset$ and bounded above ...
Sebastien Palcoux's user avatar
3 votes
0 answers
245 views

Is there an integral simple fusion ring of multiplicity one and Frobenius type? (obvious excepted)

To avoid any confusion, we rewrite the basic definitions for a fusion ring (already written in this post). A fusion ring is a finite dimensional complex space $\mathbb{C}\mathcal{B}$ together ...
Sebastien Palcoux's user avatar
6 votes
0 answers
259 views

Is there an integral simple fusion ring rank<6, FPdim>60 and Frobenius type?

A fusion ring is a finite dimensional $\mathbb{Z}$-module $\mathbb{Z}\mathcal{B}$ together with a distinguished basis $\mathcal{B} = \{ h_1,...,h_r\}$ and fusion rules $ h_i \cdot h_j = \sum_k n_{ij}^...
Sebastien Palcoux's user avatar
2 votes
0 answers
317 views

Basis for a set of polynomials in Sage? [closed]

I have a large set of polynomials in the coordinates $x,y,z$ in Sage, (e.g. $x^5y-3x^2y^2+2xy^3+x^2yz-y^2z$). I want to know, for example, if $x^5y$ is in the span of my set. Is there a Sage command ...
Lauren's user avatar
  • 131
1 vote
1 answer
757 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
364 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
5 votes
2 answers
605 views

Matroids relaxations of a given matroid

Let $\mathcal{M}$ be a rank-$d$ matroid on $[n]$. Say a matroid $\mathcal{N}$ is a relaxation of $\mathcal{M}$ if $\mathrm{rank}(\mathcal{N})=d$, $\mathrm{groundset}(\mathcal{N})=[n]$, and every ...
Camilo Sarmiento's user avatar
9 votes
3 answers
857 views

Multiprecision numerical evaluation of integral: Sage vs. PARI/GP vs. mpmath

I am trying to compute thousands of integrals of the below type, that comes up in a conformal mapping problem, to as many accurate digits as possible (preferably 50+): $$ \int_{-1}^1\textrm{d}t \frac{...
MaviPranav's user avatar
6 votes
3 answers
789 views

Torsion group of the following elliptic curve

Let $p_1=2, p_2 = 3,\ldots,$ be the prime numbers, and define $n_i = \prod_{j=1}^i p_j$. Moreover, let $E_i $ be the elliptic curve defined by $y^2 = x^3 + n_i$. Can one compute the torsion group $...
user1234's user avatar
10 votes
1 answer
492 views

Genus of the graph $K_{4,2,2,2}$

I have ask this question in math.stackexchange, here. Since, there is no answer and apart from that i feel that the problem is difficult, i would like to ask it here. The problem is to find the genus ...
bor's user avatar
  • 309
4 votes
2 answers
719 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
1 vote
2 answers
357 views

Ihara zeta function (graph theory) coefficients using a line graph [closed]

I'VE COMPLETELY REVISED MY QUESTION I wish to take a simple undirected graph (i.e. the complete graph K_4) Arbitrarily direct said graph, and then create a line graph from the directed version of ...
jtaa's user avatar
  • 21