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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7 votes
2 answers
720 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 ...
11 votes
1 answer
2k 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: ...
6 votes
1 answer
229 views

Software for working with fusion categories

One way to describe fusion categories is via a fusion system: several lists of numbers that define the fusion ring, associator, braiding (if it exists), etc. Often, these sets of numbers are quite big,...
1 vote
1 answer
199 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
0 answers
102 views

Non-isomorphic cubic fields with a given discriminant

For a cubic field $K$ with defining polynomial $P(x)=x^3 + \frac{39}{25}x^2 + \frac{22}{25}x +\frac{4}{25}$ Magma calculates the discriminant $D=-3340$. ...
0 votes
0 answers
98 views

Software for Intersection of Ideals in Noncommutative Polynomial algebra

I am looking for software which can compute an intersection of ideals (in particular right ideals) in a noncommutative polynomial algebra and then find its Gröbner Basis. Most software somehow does ...
0 votes
2 answers
260 views

Simplification of hypergeometric Function

First of all I am not at all a math expert, but I have some working knowledge. That said, please excuse "dumb" questions. I am looking at the following process: Assume you are on the 2-...
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 ...
2 votes
0 answers
74 views

Gröbner implicitization with relationships between the variables

I have the following parametric equations, where cost$=\cos t$, cos2t$=\cos 2t$, and $A^2+B^2=1$: ...
2 votes
1 answer
293 views

Does there exist a Python package that samples random special unitary matrices such that the matrices are parameterized

For reference, the linked paper is Composite parameterization and Haar measure for all unitary and special unitary groups by Christoph Spengler, Marcus Huber and Beatrix C. Hiesmayr (J. Math. Phys. 53,...
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? ...
10 votes
1 answer
605 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 ...
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 ...
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,...
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 ...
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 ...
1 vote
0 answers
226 views

Are there any alternatives to LaTeX that feel more like HTML? [closed]

so I’ll preface this with I’m pretty familiar with HTML and enjoy using it quite a bit. I’m looking for a way to write maths and essays with a language similar to HTML if that’s even possible.
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 ...
0 votes
1 answer
115 views

Software to compute generators of a module over polynomial ring

Let $A=\mathbb{R}[x_1,\dots,x_n]$ be the algebra of real polynomials in $n$ variables. Fix polynomials $p_1,\dots,p_k\in A$. Consider the subset $$M:=\{(q_1,\dots,q_k)\in A^k|\, p_1q_1+\dots+p_kq_k=0\}...
1 vote
1 answer
192 views

Software tools to find square root modulo $2^t$

Are there any software tools to find modular square roots of $y$ in $$x^2\equiv y\bmod p^t$$ where $p$ is a prime $\geq2$? Are there any special techniques which can speed up at $p=2$?
2 votes
3 answers
518 views

Useful software for variable elimination

I have three non-homogeneous trivariate polynomials in $\mathbb Z[x,y,z]$ and I want to eliminate the variables $y$ and $z$ to get a polynomial in $x$. The monomials of the polynomials are $\{1,x^4,x^...
4 votes
1 answer
217 views

About colossally abundant numbers - reference request

This post contains three related questions: In the OEIS sequence 073751 ( https://oeis.org/A073751/ ) there is a short Mathematica program that is said to produce the prime factors of successive ...
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." ...
3 votes
0 answers
124 views

Geometric construction exercises

Many of you know dynamic geometry exercises in Euclidea; if not, here is one example. It lets you do a geometric construction and sends a message once you achieve the result. I am looking for a way to ...
2 votes
1 answer
354 views

Software to prove statements in the way of natural deduction (tabular form introduced by Lemmon)

I'm searching for some software or open source project which is able to prove propositions of predicate logic of first order in the way of natural deduction introduced for example in the book of ...
2 votes
0 answers
148 views

Ultra math search engine [duplicate]

Does anyone know searching engine for arxiv.org math formulas? Like https://www.searchonmath.com and https://approach0.xyz/search/ In my opinion, we should have a search engine that can find formulas ...
7 votes
0 answers
118 views

Softwares to determine semi-simple types of Lie algebras generated over $\mathbb{R}$ or $\mathbb{C}$ by a set of matrices

I wish to determine the type of a Lie algebra generated over $\mathbb{R}$ or $\mathbb{C}$ by a set of square matrices with irrational elements. For example, \begin{align} n^+ = \begin{pmatrix} ...
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 ...
5 votes
5 answers
3k 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
0 answers
138 views

Properties of pointless projective curves over finite fields?

Probably not research level, feel free to downvote. We got construction of bounded degree projective curves with no points over finite fields. This construction generalizes to higher dimension. One of ...
6 votes
1 answer
320 views

Get the commands history from GAP system

I am not sure whether this was asked before, but I didn't find a reference in GAP system documentation on how to print the history of the command line (Ubuntu installation). For instance: ...
4 votes
0 answers
219 views

Referring to computer software in a paper

I'm performing a calculation of the Smith normal form of an integral matrix based on the SageMath worksheet. Is it sufficient in the paper to say something like ``Using a software package like ...
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 ...
19 votes
1 answer
645 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)^{...
1 vote
0 answers
176 views

Using Bertini software to determine whether or not a variety is empty

I have a system of polynomials $f_1,\dots, f_n \in \mathbb{C}[x_1,\dots, x_m]$, and I would like to determine whether the set of solutions to the system $f_1(x)=\dots=f_n(x)=0$ is empty or not. Since ...
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 ...
3 votes
1 answer
870 views

Coppersmith bivariate polynomial roots implementation

Given $f(x,y)\in\mathbb Z[x,y]$ Coppersmith in https://link.springer.com/chapter/10.1007%2F3-540-68339-9_16 provides a provable method to find integer roots in polynomial time and this method was also ...
0 votes
0 answers
108 views

Common integer roots of polynomials

I have two polynomials of form $$f_1(w,x)=M_1$$ $$f_2(y,z)=M_2$$ and I have two polynomials of form $$g_1(w,x,y,z)=M_3$$ $$g_2(w,x,y,z)=M_4$$ where $f_1,f_2,g_1,g_2\in\mathbb Z[w,x,y,z]$ and $M_1,M_2,...
6 votes
2 answers
729 views

Force-directed graph drawing in 1D?

I have a real-world graph that I wish to draw in one dimension. Here's the graph: I'd like to draw it using some kind of force-directed graph drawing method. I'm supposing this is both possible and ...
11 votes
2 answers
677 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 ...
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 ...
-1 votes
1 answer
178 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
158 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 ...
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-...
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 ...
4 votes
0 answers
129 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 ...
5 votes
2 answers
481 views

Computer platforms for combinatorial search problems/mathematical music theory?

I'm finding programming various combinatorial searches (connected to mathematical music theory) in a general purpose computer language tedious, so I'd like pointers to computer platforms/environment ...
3 votes
0 answers
169 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
71 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 ...
1 vote
1 answer
193 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 ...