# 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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### 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: <...
73 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 ...
241 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 ...
29 views

184 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 ...
687 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 ...
1k 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 ...
162 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 ...
386 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 ...
186 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 ...
327 views