# 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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102 views

### 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 ...
• 129
1 vote
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 ...
• 24.2k
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 ...
1 vote
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 ...
• 6,174
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 ...
• 1,405
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 ...
1 vote
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 ...
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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 ...
• 350
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] &= (...
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### 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 ...
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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 ...
• 241
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, ...
• 83
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} ...
• 24.2k
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 ...
• 139
1 vote
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 ...
• 913
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 ...
• 913
1 vote
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 ...
• 125
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 ...
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: <...
• 1,964
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 ...
• 509
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 ...
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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 ...
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 ...
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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 ...
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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 ...
• 351
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/...
• 815
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 ...
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1k views

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### 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 ...
• 309
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 ...
• 305
1 vote