Questions tagged [mathematical-software]

Mathematical questions related to mathematical software systems such as Sage, Mathematica, Maple, Pari/GP, and GAP. Note that troubleshooting questions are generally considered off-topic.

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146 votes
21 answers
28k views

Mathematical software wish list

Like many other mathematicians I use mathematical software like SAGE, GAP, Polymake, and of course $\LaTeX$ extensively. When I chat with colleagues about such software tools, very often someone has ...
95 votes
5 answers
8k views

Is there a database for tracking the dependencies of mathematical theorems?

Given a proof for a result, one could denote the proof as a node on a graph, and then draw arrows to the node from axioms and previous results that the proof uses, and then draw arrows from the node ...
Chill2Macht's user avatar
  • 2,622
81 votes
18 answers
25k views

What programming language should a professional mathematician know? [closed]

More and more I am becoming convinced that one should know at least one programming language very well as a mathematician of this century. Is my conviction justified, or not applicable? If I am right,...
45 votes
2 answers
4k views

On proof-verification using Coq

So i recently learnt that there is now a certain software called ''Coq'' by which one can check the validity of mathematical proofs. My questions are: Are there limitations on the kinds of proofs ...
Software enthusiast's user avatar
40 votes
23 answers
16k views

Open source mathematical software

I want some recommendation on which software I should install on my computer. I'm looking for an open source program for general abstract mathematical purposes (as opposed to applied mathematics). I ...
38 votes
11 answers
7k views

Non-computational software useful to mathematicians

The MathOverflow question Open source mathematical software contains a list of programs that are useful to perform various computational tasks, such as computer algebra systems. However, evaluating ...
37 votes
0 answers
1k views

Computer calculations in A_infinity categories?

Is there a good computer program for doing calculations in A-infinity categories? Explicit calculations in A-infinity categories are an important, useful, yet very tedious task. One has to keep track ...
Heinrich Hartmann's user avatar
36 votes
3 answers
5k views

$\prod_{n=1}^{\infty} n^{\mu(n)}=\frac{1}{4 \pi ^2}$

When I tested this in Mathematica, I had expected it to say it did not converge. However, I got this: $$\prod_{n=1}^\infty n^{\mu(n)}=\frac{1}{4 \pi ^2}$$ Note: this is the reciprocal of (3) zeta-...
Fred Daniel Kline's user avatar
32 votes
4 answers
7k views

Computational software in Algebraic Topology?

I was wondering if there is any good software out there that allows you to do specific computations in algebraic topology. For example: Create a simplicial complex/set and ask questions about its ...
Joris Weimar's user avatar
32 votes
0 answers
2k views

Is there software to compute the cohomology of an affine variety?

I have some affine varieties whose cohomology (topological, with $\mathbb{C}$ coefficients) I would like to know. They are very nice, they are all of the form $\mathbb{A}^n \setminus \{ f=0 \}$ for ...
David E Speyer's user avatar
29 votes
1 answer
1k views

Software for rational homotopy theory

Does anybody know a software manipulating commutative differential graded algebras, and providing a computation of the minimal model? I tried to use the package DGAlgebras of Macaulay2, but I got ...
Paolo Salvatore's user avatar
28 votes
12 answers
3k views

Creating high quality figures of surfaces

I am not sure if this question is suitable for mo, it is more about visualization than math. Anyway, here it is: What is the best way to visualize a 2-surface in Euclidean space with high quality? ...
26 votes
2 answers
8k views

Software for symbolic matrix calculus?

Is it possible to get widely available math software (Maple/Matlab/Mathematica, etc) to symbolically differentiate vector and scalar functions of matrices, returning the result in terms of the ...
R Hahn's user avatar
  • 2,721
25 votes
8 answers
3k views

How do we explain the use of a software on a math paper?

Suppose one has written a math/computer science paper that is more focused in the math part of it. I had a very complicated function and needed to find its maximum, so I used Mathematica (Wolfram) to ...
25 votes
5 answers
1k views

Illustrating mathematics with wysiwyg tools

What tools are out there for creating mathematical illustrations in a what-you-see-is-what-you-get mode? Having struggled with tikz for several years, I've found creating figures in Omnigraffle (...
24 votes
3 answers
2k views

What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?

Over the years, advances in machine learning has allowed us to communicate and interact, using the same natural language, more and more semantically with computers, e.g. Google, Siri, Watson, etc. On ...
24 votes
2 answers
15k views

OCR for handwritten mathematics

I am in the process of scanning a large collection of handwritten notes. They consist of diagrams and formulae with a relatively small proportion of actual words. Of course it would be hopeless to ...
23 votes
3 answers
1k views

Which tools can identify scholarly papers that use the same types of equations?

Many types of equations are being used in multiple contexts, so a search for specific formulas might be one way to identify scholarly papers that are conceptually related. Is any website or tool ...
Daniel Mietchen's user avatar
22 votes
2 answers
1k views

A closed form for an integral expressed as a finite series of $\zeta(2k+1)$, $\pi^m$ and a rational?

In this paper the following beautiful integral expression for $\zeta(3)$ is derived: $$\zeta(3)=\frac{1}{7}\,\int_0^{\pi} x\,(\pi-x)\csc(x)\, dx$$ In a comment at the end of this question, I ...
Agno's user avatar
  • 4,179
19 votes
1 answer
883 views

What computer program for automorphic forms

This question has its origins in this entertaining discussion on MO. There are many programs (CAS) and libraries that are able to handle algebraic expressions. These are both a verification tool for (...
Desiderius Severus's user avatar
19 votes
1 answer
646 views

How can we be sure that results that rely heavily on extensive computations are correct?

Recently a ''bug'' was discovered in one of the most popular mathematics software, Wolfram Mathematica (see links here and here). It concerns the evaluation of the sum $$ \sum_{k=1}^{n-1} \frac{(-1)^{...
17 votes
3 answers
1k views

What is the state of the art for algorithmic knot simplification?

Question: Given a `hard' diagram of a knot, with over a hundred crossings, what is the best algorithm and software tool to simplify it? Will it also simplify virtual knot diagrams, tangle diagrams, ...
Daniel Moskovich's user avatar
16 votes
3 answers
2k views

Computer-aided homology computations

Background I am currently working on the homology of some moduli space and there exists a much simpler chain complex with the same homology. It is a quotient of a bisimplicial complex by a subcomplex....
Felix Boes's user avatar
16 votes
0 answers
645 views

real algebraic geometry software?

Does anyone have suggestions/experience for any software packages to study real algebraic varieties (for example, counting connected components of hypersurfaces, figuring out the topological type of ...
Igor Rivin's user avatar
  • 95.6k
15 votes
4 answers
5k views

How do you generate math figures for academic papers?

Good day! I am looking for any tool that would allow me to generate a figure similar to the figures embedded in the paper by King et al. (2020) titled "Trigonometry: a brief conversation." ...
Aidre Cabrera's user avatar
15 votes
3 answers
2k views

PDF readers for presenting Math online

In the current situation it seems especially important to be able to present your mathematical results online in a way that your audience does not fall asleep in front of their screens. But I am ...
15 votes
2 answers
1k views

What kind of computer tools topologists/geometrists use to visualize the objects they deal with?

I have recently started to read a bit about geometry and topology. Hopf fibration, Lense spaces, CW complexes, stuff that are discussed in Hatcher's Algebraic Topology and other things that require ...
stressed out's user avatar
14 votes
14 answers
5k views

Basic software libraries for numerical analysis using modern programming languages?

I'm looking for a software library with a scope similar to "numerical recipes", but implemented in a modern programming language. "Modern" in this context means to me: object oriented (not C or ...
14 votes
2 answers
3k views

Consequences of technically proving anything in Coq (on at least Linux) exploiting a bug? [closed]

Technically, it is possible to prove anything in Coq proof assistant [1] (on at least Linux) due to a programming feature (or bug). This seems tractable when validating large proofs. Human analysis ...
joro's user avatar
  • 24.2k
13 votes
2 answers
2k views

Graph of dependencies from a Latex file [closed]

This question has been "manually migrated" to TeX-SX: https://tex.stackexchange.com/q/40200/86 Apologies if the question is not very appropiate for Mathoverflow. It seems to me more appropiate here ...
Jesus Martinez Garcia's user avatar
13 votes
3 answers
2k views

Software for Computing Baker-Campbell-Hausdorff

Does anyone have a recommendation for software which can efficiently calculate the Baker-Campbell-Hausdorff series in classical Lie algebras? Right now, I have a problem which boils down to ...
Jesse Wolfson's user avatar
12 votes
3 answers
886 views

What CASes say about the analytic rank of rank 8 elliptic curve '457532830151317a1'

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 ...
joro's user avatar
  • 24.2k
11 votes
5 answers
1k views

$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$

I'm trying to solve the integral $\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$, where $s$, $r$ and $m$>1 are positive integers. My question is whether a closed form ...
Mark's user avatar
  • 111
11 votes
2 answers
678 views

Software for computing Thurston's unit ball

Is there any software which can be used for computing Thurston's unit ball (for second homology of 3-manifolds) of link complements? In particular can I do that with SnapPy? PS: even a table for ...
Mehdi Yazdi's user avatar
11 votes
1 answer
3k views

Is there a reasonable "text-to-speech" solution for math papers?

Is there a software which can read loudly an arXiv paper for me with a decent quality? I googled a little bit. And there are some research/software for reading texts with formulas. So the question is: ...
Vladimir Zolotov's user avatar
10 votes
6 answers
1k views

Homology software

What software is there to efficiently compute homology? Specifically: What software can take a simplicial complex (provided by a file listing maximal simplices, for example) and quickly compute its ...
10 votes
1 answer
1k views

Program for calculating cohomology

Does it exist a computer program which calculates the cohomology of projective algebraic varieties ? For example, smooth surface in $\mathbb{P}^3$? like $\sum_0^3 X_i^3=0$
user avatar
10 votes
1 answer
615 views

Is there a program implementation for generating all non-isomorphic graphs with a given degree sequence?

I know the following problem is famous: For a given degree sequence $L$ that is graphic, find an (efficient) algorithm to generate all of the nonisomorphic realizations of $L$. This algorithm is ...
L.C. Zhang's user avatar
  • 1,605
10 votes
2 answers
753 views

Software for Borel-Weil-Bott in positive characteristic?

I am interested in calculating cohomology of line bundles on flag varieties $G/B$ in positive characteristic. But I really just have a bunch of scattered examples. Does there exist some kind of ...
Steven Sam's user avatar
9 votes
2 answers
2k views

On $p$-adic arithmetic softwares

I would like to automate a huge amount of computation that involves basic arithmetic operations with $p$-adic numbers. I have found a Mathematica package for it, but it is old and acts quite ...
Keivan Karai's user avatar
  • 6,064
9 votes
5 answers
610 views

Software for rigorous optimization of real polynomials

I am looking for software that can find a global minimum of a polynomial function over a polyhedral domain (given by, say, some linear inequalities) in $\mathbb R^n$. The number of variables, $n$, is ...
Boris Bukh's user avatar
  • 7,746
9 votes
2 answers
1k views

Why are there so few zero-dimensional polynomial system solvers and is this because there is no real market for them?

My questions involve the quotes below from wikipedia regarding solving polynomial systems, which given the size of the market for Big Data & Predictive Analysis applications I find puzzling: "...
user2908444's user avatar
9 votes
2 answers
3k views

What is / are the softwares to use to draw surfaces of the form of a two or three-holed torus , or torus, or torus with cusps attached to it?

I am trying to draw surfaces with complete hyperbolic structures and surfaces which are topologically tori. The hyperbolic surfaces I need to draw are torus with one or two holes on it, or torus with ...
Analysis Now's user avatar
  • 1,451
9 votes
1 answer
672 views

Software for detecting Brauer-Manin obstructions?

In the context of another MO question, the following question arose: Does there exist any software for detecting Brauer–Manin obstructions to the existence of integer solutions to a single polynomial ...
Timothy Chow's user avatar
  • 78.1k
9 votes
0 answers
654 views

Software for explicit computations in representations of classical Lie algebras

I'm pretty sure many a mathematician has longed for such a tool but I wasn't able to find such a question here, so here we go. Is there, by any chance, an existing package or program that allows one ...
Igor Makhlin's user avatar
  • 3,493
8 votes
7 answers
2k views

Visualizing polyhedra from their 1-skeletons

Except for a few simple cases (typically pyramids and prisms) I find it hard to visualize a polyhedron from its 1-skeleton embedded in the plane, e.g. the hexahedral graph 5, as can be seen here. ...
Hans-Peter Stricker's user avatar
8 votes
4 answers
6k views

Solving a System of Quadratic Equations

I have many polynomial equations in many variables which I want to jointly minimize (in a mean square sense, but you could pick a different reasonable measure which favors anything where all ...
bobuhito's user avatar
  • 1,537
8 votes
1 answer
522 views

Software package to manipulate representations

Hi, I am looking for a software package that will allow me to experiment with the irreducible representations of lie groups (for example, $SL(2,p)$) over the complex field and over finite fields. ...
Shachar's user avatar
  • 410
8 votes
1 answer
281 views

Creativity and the mechanization of elementary geometry

In plane geometry, it is customary to say that checking proofs is a mechanical process but that finding new theorems is a creative activity. Citing J. Hadamard, "logic only sanctions the conquests of ...
coudy's user avatar
  • 18.5k
7 votes
2 answers
721 views

What happened to TituRel?

TituRel is a language developed in conjunction with the book Relational Mathematics by Gunther Schmidt from Universität der Bundeswehr München. My problem is that I can't find any info related to ...
auxi's user avatar
  • 91