Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [sagemath]

For questions concerning the mathematical software system SageMath.

SageMath is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

StackOverflow has a fairly heavily used [sage] tag as well for more programming-related question, with more links; see also the [sage] tag on MathOverflow.

Note also that Ask Sage, SageMath's questions-and-answers site, and sage-support, the user support mailing list, are very active and that questions asked there typically get answered faster than on the StackExchange network.

You can also look at the official documentation of SageMath.

434 questions
54
votes
1 answer

Is Sage on the same level as Mathematica or Matlab for graph theory and graph visualization?

The context: I'm going to start working on a project that involves running predefined algorithms (and defining my own) for very big graphs (thousands of nodes). Visualization would also be welcome if possible. This is a research project and the goal…
Alexandre Martins
  • 643
17
votes
1 answer

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

What is the genus of the complete $4-$partite graph $K_{4,2,2,2}$? What i know: Since $K_{4,4,2}$ is a subgraph of $K_{4,2,2,2}$, and genus of $K_{4,4,2}$ is 2, $K_{4,2,2,2}$ has genus greater than or equal to 2. Also $K_{4,2,2,2}$ is a subgraph of…
bor
  • 1,063
16
votes
2 answers

Math-related open source software to contribute to

I'm interested in finding a math-related open source project that I can contribute to. I've studied maths and stats at undergraduate level, but I'm a professional software developer and I'll have some spare time in the next few months at least that…
TooTone
  • 6,443
16
votes
2 answers

Advantages to learning Sage?

I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search algorithms). Currently, I do a lot of my work with…
xxxxxxxxx
  • 13,688
12
votes
2 answers

Plotting graphs of Modular Forms

After watching all the 8 parts of "“Introduction to Modular Forms,” by Keith Conrad" on YouTube, I got "extremely intrigued" by plotting graphs of Modular Forms ( on SL(2,Z) ). So after watching all those videos, I tried the following approach by…
GilesGoat
  • 121
  • 4
11
votes
1 answer

Simplify function in Sage

In Sage, simplify(x/(x^2 + x)) gives x/(x^2 + x) I would instead expect to get 1/(x + 1) Is there a way to achieve that?
Ystar
  • 2,966
  • 4
  • 22
  • 39
10
votes
3 answers

Integer Partition Refinement in Sage

A partition of an integer $n$ is a non-decreasing list of positive integers summing to $n$. For example, $3$ can be partitioned as $1 + 1 + 1$, $1 + 2$ or just $3$, but $2 + 1$ is indistinct from $1 + 2$ (e.g., order does not matter). A refinement…
Austin Mohr
  • 26,272
8
votes
3 answers

Find the rational points on $1 + 18 x + 81 x^2 + 44 x^3 = y^2$ with Sage

I'm trying to use Sage on-line,but I meet some trouble with the code of it. I want to find the rational points on an elliptic curve,such as $$1 + 18 x + 81 x^2 + 44 x^3 = y^2,\tag1$$ I know that $(x,y)=(0,1),(1,\pm12),(-\frac{1}{11},0)$ are on the…
lsr314
  • 16,048
7
votes
2 answers

Calculating the rank of an elliptic curve

In SageMath we may define an elliptic curve $$E : y^{2} = x^{3}+a_{2}x^{2}+a_{4}x+a_{6}$$ by E = mwrank_EllipticCurve([0,a2,a3,a4,a6]). To calculate the rank of $E/\mathbb{Q}$, we can use the SageMath functions rank(E) or E.rank(). Consider the…
Atratrana Suna
  • 571
7
votes
1 answer

What's the proper way to take a Groebner basis with respect to a quotient polynomial ring?

Suppose I have the quotient ring $R=\mathbb{Q}[x,y]/I$ for some ideal $I$, and I want to find a Groebner basis for another ideal $J\subseteq R$. When computing the basis, does it make a difference if I consider $J$ as a subset of $\mathbb{Q}[x,y]$,…
Calvin Godfrey
  • 1,574
7
votes
2 answers

Definition of Modular Forms over finite Fields

I'm still severely lacking in background at the moment, but I'm interested in doing something with congruence properties of modular forms (relations between coefficients of the q-expansions that hold modulo a prime). I'm trying to compute these…
DCT
  • 3,415
7
votes
2 answers

Are results found of an Elliptic Curve by SageMathCell proven (does there exists no more solutions)?

Well, I have for example the following SageMathCell-code: sage: E = EllipticCurve(QQ, [0,63,-2205,-12348,0]) sage: E sage: for P in E.integral_points(): ....: Q = -P ....: print( "P = %8s and -P = %8s" % (P.xy(), Q.xy()) ) This code…
Jan Eerland
  • 29,457
6
votes
1 answer

Investigating subgroups of finitely presented groups in SageMath

Investigating the subgroups of a finitely presented group in SageMath seems to be problematic. Simple questions like is_normal() do not work for them. In this question I am specifically interested in obtaining the elements of such subgroup. They are…
Leen Droogendijk
  • 7,878
6
votes
5 answers

Graphing Compex Functions 3D (x,y,i axes) Instead Of Color-Coded (SAGE).

Following this guide to Sage: and using Sage Online produced the following graphs: Graphing $\frac{1}{1-z}$ that way yeilds: Graphing $\frac{1}{1-z^2}$ that way yields: It would be nice to see it in 3D instead of merely color coded. The y-axis is…
User3910
  • 2,440
6
votes
1 answer

Computing the endomorphism ring of an elliptic curve over a finite field (using SAGE)

$ \newcommand{\End}{\mathrm{End}} \newcommand{\Gal}{\mathrm{Gal}} \newcommand{\kb}{\overline{k}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\F}{\mathbb{F}} \newcommand{\Q}{\mathbb{Q}} $ I would like to have an algorithm (possibly very inefficient)…
Watson
  • 24,404
1
2 3
…
28 29