# 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.

141
questions

**-1**

votes

**1**answer

109 views

### Math software for 3d-visualisation [closed]

What are good and user-friendly math-softwares for 3d-visualization as in
https://www.youtube.com/watch?v=x7d13SgqUXg (sphere-eversion process).
https://www.youtube.com/watch?v=rB83DpBJQsE (...

**2**

votes

**0**answers

37 views

### Representations in Archimedean quadratic modules

Let $\mathbb R [X] = \mathbb R [X_1,\dots,X_n]$ and $\Sigma[X] = \big\{ \, f \in \mathbb R[X] \mid \exists r \in \mathbb N, \ g_i \in \mathbb R[X] \colon f = g_1^2 + \dots + g_r^2 \,\big\}$ denote ...

**4**

votes

**0**answers

97 views

### program to compute hurwitz numbers

Is there a computer program available to compute Hurwitz numbers easily? In fact I only care about counting covers $C\to\mathbb{P}^1$ branched over $0,1,\infty$, and am even willing to restrict to the ...

**3**

votes

**0**answers

85 views

### (Implemented) algorithm for Hodge numbers

Let $X$ be a smooth projective toric variety. Do any of the math computer algebra systems have an algorithm implemented to compute the Hodge numbers of a generic complete intersection in $X$? Say in ...

**2**

votes

**0**answers

63 views

### Software recommendation request: deciding whether a system of polynomial equations is solvable by radicals

The following system of equations comes from a very simple geometric figure I have to deal with a lot at work. Here $r_0,r_1,r_2$ and $L$ are known parameters, and the $x_i$s are the coordinates I'm ...

**0**

votes

**1**answer

131 views

### How to find all minimal dependent sets of a set of vectors effectively?

In my research, I need to find the set of all minimal dependent sets of a given set of vectors. One method is to check every subset of the given set. But this method is very slow when the set of ...

**1**

vote

**1**answer

78 views

### Software for Hilbert series of quotients of exterior algebras

Is there some software which computes Hilbert series of quotients of exterior algebras? In commutative case, Maple can compute Hilbert series. Thank you very much.

**1**

vote

**0**answers

66 views

### pari/gp “bnfisintnorm” as poor man (quadratic) Thue equations solver?

For simplicity explaining only the quadratic case.
Given integers $n,m$, pari/gp "bnfisintnorm" finds $X,Y$
such that $X^2+n Y^2=m$ working in the number field
with defining polynomial $x^2+n$ and ...

**3**

votes

**1**answer

118 views

### Most adequate software for proof checking graph theory proofs

What might be the best software for checking the validity of proofs of graph theoretical statements? Lean, HOL, ... ? One criterion would also be, what would be the easiest for a graph theorist to ...

**5**

votes

**1**answer

137 views

### Asking SnapPy for core curves after surgery

Suppose I give SnapPy a cusped hyperbolic 3-manifold (using, say, the link editor) and specify some filling. SnapPy can then provide a presentation of the fundamental group of the filled manifold. Can ...

**22**

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 ...

**2**

votes

**0**answers

60 views

### Is there a software to solve functional inequalities?

Suppose I have some inequalities that my function (say $\mathbb R\to \mathbb R$) needs to satisfy, like $\forall x,y\; f(x)+f(y)\le f(x+y)$ and $f(1)=0$. Is there some software that can find solutions/...

**1**

vote

**2**answers

146 views

### Openly available software to work with Demazure modules

Does someone know of any sort of software openly available online which can be used to compute various characteristics of Demazure modules for semisimple Lie algebras? Specifically, I'm interested in ...

**3**

votes

**2**answers

115 views

### Program to solve Optimization Problem

I have an optimization problem, this problem has linear constraints and nonlinear constraints. I solved the linear part by MATLAB but the nonlinear constraints I could not solve it. I downloaded ...

**1**

vote

**1**answer

175 views

### Intersection Solutions of four nonlinear equations

I have four nonlinear equations I want to find the points of intersection of these equations, and I used the software Mathematica, unfortunately after many hours of waiting it does not give me any ...

**6**

votes

**0**answers

223 views

### Best software to do big number calculations quickly [closed]

I am trying to do some work on some math conjecture. I am testing the conjecture numbers using very large math numbers (100+ digits ). I am currently using python to test these numbers.
In the ...

**1**

vote

**0**answers

252 views

### Generate all connected non-isomorphic graphs of n vertices modulo local complementation?

I'd like to generate a list of all simple, connected, undirected graphs of $n$ vertices, modulo standard graph isomorphism, and modulo local complementation, which is the following operation: for a ...

**44**

votes

**2**answers

3k 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 ...

**4**

votes

**2**answers

550 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 ...

**75**

votes

**18**answers

21k 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,...

**13**

votes

**2**answers

519 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 ...

**8**

votes

**1**answer

204 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 ...

**2**

votes

**1**answer

57 views

### CAS implementing free algebras with involution

Is there any software that easily allows to make symbolic computations with involutions and homomorphisms? I need to define a product in an associative algebra with an (abstract) involution and ...

**1**

vote

**0**answers

88 views

### Lie Algebra Module Decomposition in GAP

Let $\mathfrak{g}$ be a complex finite-dimensional Lie algebra and let $V$ be a finite-dimensional $\mathfrak{g}$-module. Is there a way for me to check in GAP or some other software package whether $...

**18**

votes

**1**answer

667 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 (...

**2**

votes

**1**answer

142 views

### On software for ILP

In 'Computational Experience with Lenstra's Algorithm' by L Gao, Y Zhang it is claimed that they have an implementation of Lenstra's fixed dimension integer programming algorithm. Is this available ...

**21**

votes

**5**answers

921 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 (...

**5**

votes

**1**answer

211 views

### Instructions for using Coxeter 3.0 software

I am trying to use Coxeter 3.0 (http://www.liegroups.org/coxeter/coxeter3/english/coxeter3_e.html) to perform some computations for affine Weyl groups. I managed to install the program and get it ...

**4**

votes

**0**answers

149 views

### Math software / language for analytic / multiplicative number theory

What software/languages are the most used to do computations in analytic / multiplicative number theory?
I use Python, Maple, etc., but each time I want to compute expressions like, for $n$ with an ...

**3**

votes

**1**answer

88 views

### Any visualization software for the intrinsic metric of a convex polyhedron?

I'd like to find a visual simulation of what it would be like to 'live' in a polyhedron with the intrinsic, piecewise-Euclidean length metric. Of course, to make it easier to visualize, I'd prefer to ...

**2**

votes

**1**answer

172 views

### Computation of Hall basis

I am looking for a program that for a given word in a free Lie algebra calculate the coefficients of the word with respect to the Hall basis. Can you suggest me a program?
Thanks

**1**

vote

**1**answer

95 views

### How do I find solutions of a quadratic Diophantine equation mod a large composite?

I'd like to find integral solutions to the equation
$2x^2 -3xy + y^2 \equiv 0 \mod n $
where $n$ is a given composite, for example, $n = 16807708473783470801$ (I prefer solutions that work for any $...

**21**

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 ...

**1**

vote

**1**answer

152 views

### How to return elements of a given length in a symmetric group using Sage?

Let $S_n$ be the symmetric group over $\{1,2,\ldots,n\}$. How to return elements of length $m$ in $S_n$ using Sage? I try to find such function in Sage but didn't find one. Thank you very much.
Edit: ...

**1**

vote

**0**answers

746 views

### Proof of the ABC conjecture - how feasible would it be to automate some of the deciphering of Shinichi Mochizuki’s proof?

This is a question I will come back to. I am very interested in Shinichi Mochizuki’s proof, and in particular, the idiosyncrasies of his notation, which I understand to be at the root of why it is ...

**3**

votes

**4**answers

1k views

### Package for the Closest Vector Problem (CVP)?

Let $A$ be a positive definite, real $n \times n$ matrix. This defines a norm on $\mathbb{R}^n$. Now I have a given point $p \in \mathbb{R}^n$ and I want to find the lattice point $x \in \mathbb{Z}^n$ ...

**1**

vote

**1**answer

222 views

### Is there any algorithm to find the minimal generating set for $A_{n}$

I know that finite simple groups can be generated by two elements.(See this question on MO)
So as a specific example, Take Alternating group $A_{n}$, $n>4$.
We also know that $A_{n}$ is $(2,3)$ ...

**88**

votes

**5**answers

6k 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 ...

**1**

vote

**0**answers

52 views

### Software for matching theorems to inputted conditions/hypotheses

Many times I find myself going through analysis books, wikipedia and papers, looking for what is known for my functions/objects at hand.
So is there any software that at least tries to move in that ...

**1**

vote

**2**answers

586 views

### Which is better for creating tables of group theory info, GAP or MAGMA?

Specifically, I want to compute the set of values of $|G:\text{ker}(\chi)|/\chi(1)$ for all the characters of a p-group, for a lot of p-groups. I don't know how to use either program, so before I ...

**7**

votes

**0**answers

513 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 ...

**1**

vote

**0**answers

215 views

### How to check that an ideal of $\mathbb{C}[GL_n]$ is a coideal or not?

Let $I$ be an ideal of $\mathbb{C}[GL_n]$. Are there effective methods or software to check whether $I$ is a coideal or not? Thank you very much.
For example, let I be the ideal of $\mathbb{C}[GL_3]$ ...

**-2**

votes

**1**answer

70 views

### Behavior of “integer complex number” on computer [closed]

I want to provide software to compute with "integer complex numbers", that live in $\mathbb{Z}\times i \mathbb{Z}$, rather than the $\mathbb{C}$. Some operations are going to give results that are ...

**1**

vote

**2**answers

515 views

### computation of high order bessel function at large variable value [closed]

My work involves computation of high order bessel function at large variable value. Within MATLAB, this has been done without any problems. However, in order to scale up the problem, I have tuned to ...

**1**

vote

**1**answer

232 views

### How to solve this system of equations? [closed]

I am trying to find a Poisson bracket on an algebra, and need to find a solution to a system of equations. The system of equations is very complicated, with more than 10000 equations and 60 variables.
...

**2**

votes

**0**answers

107 views

### Finding generators of symmetric cones

I have a bunch of vectors $\mathbf v_i$ in $\mathbb R^n$. I would like to consider the cone $C$ spanned by these vectors, together with all the other vectors that can be obtained by permuting the ...

**0**

votes

**1**answer

538 views

### A three variable linear diophantine promise problem

Given $a,b,c,s\in\Bbb N$ such that $(a,b,c)=1$ with promise that we have at most one triple $x,y,z\in\Bbb N$ such that $ax+by+cz=s$, what is a good algorithm that runs in $O(\log(abcs))$ time to find ...

**1**

vote

**0**answers

116 views

### How to check with a CAS if a surface is of general type?

The main question is:
How to check with a CAS if a surface is of general type?
Magma's function KodairaEnriquesType is close to this,
but doesn't always work.
...

**4**

votes

**1**answer

358 views

### Faithful linear representation of a nilpotent Lie algebra

Let
\begin{align}
\mathfrak{g} = Span_{\mathbb{C}}\{ e_1, e_2, e_3, e_4, e_5: \text{ non-zero brackets are } [e_1, e_i]=e_{i+1}, i=2,3,4, [e_2, e_3]=e_5 \}
\end{align}
be a $5$-dimensional Lie ...

**133**

votes

**21**answers

26k 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 ...