# 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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### Weierstrass equation of smooth projective model of $ay^2=x^4-b$

Let $a,b$ be a rational number. Let $C$ be an smooth projective model of $ay^2=x^4-b$. $C$ is elliptic curve. I want to know the Weierstrass equation of $C$ in $\Bbb{P}^2$. For example $a=2,b=17$, ...
1 vote
116 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 ...
150 views

### Character tables of semidirect products on Sage

I am trying to find the character table of a semidirect product of two group with Sage. If I try the following I get an error. ...
132 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 ...
520 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 & = e \\ G & = (1,3,2)\\ G & = (1,2,3) \\ G &= (2,3)\\ G &= (...
178 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 ...
268 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 ...
631 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, ...
493 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} ...
3k 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 ...
1 vote
160 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 ...
220 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 ...
1 vote
116 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 ...
239 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 ...
253 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: <...
135 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 ...
369 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 ...
275 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 ...
210 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 ...
332 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 ...
348 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 ...
171 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/...
324 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 ...
1k views

474 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 ...
677 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 ...
1 vote
For the rank $8$ elliptic curve with a-invariants $(0, 0, 1, -23737, 960366)$ sage 5.3 reports analytic rank $4$ in about 2.4 hours. Almost sure this a bug, so I am interested what other CAS say on ...