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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2
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0answers
126 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 ...
6
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0answers
92 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} ...
8
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1answer
598 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 ...
4
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3answers
319 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 ...
1
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0answers
117 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 ...
5
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1answer
223 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
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0answers
178 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 ...
1
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0answers
120 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 ...
19
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1answer
487 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)^{...
14
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3answers
1k 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
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1answer
191 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 ...
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0answers
93 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,...
-1
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1answer
121 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
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0answers
87 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
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0answers
110 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
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0answers
113 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
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0answers
68 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
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1answer
136 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
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1answer
83 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
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0answers
85 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+...
4
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1answer
124 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
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1answer
152 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 ...
24
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8answers
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
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0answers
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
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2answers
169 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
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2answers
189 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
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1answer
180 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
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0answers
233 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
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0answers
376 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 ...
45
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2answers
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
2answers
579 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 ...
78
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18answers
23k 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,...
15
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2answers
647 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
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1answer
219 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
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1answer
61 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
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0answers
91 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
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1answer
753 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
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1answer
155 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 ...
23
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5answers
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 (...
5
votes
1answer
244 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
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0answers
152 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 ...
4
votes
1answer
98 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 ...
3
votes
1answer
195 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
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1answer
107 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 $...
22
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2answers
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
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1answer
192 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
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0answers
776 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 ...
4
votes
5answers
2k 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
1answer
272 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 $(2,3)$ ...
91
votes
5answers
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 ...