# 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.

163
questions

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### 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.

9
votes

1
answer

841
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### 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: ...

0
votes

1
answer

98
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### 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
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1
answer

86
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### 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
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3
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413
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### 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
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1
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189
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### 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 ...

0
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0
answers

68
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### State of the art in solving systems of polynomial equations over the rationals?

What is state of the art software in solving systems of polynomial equations over the rationals or over the algebraic closure of the rationals?
We have heard Maple is better than sagemath, is this ...

13
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4
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### 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
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0
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98
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### 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
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173
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### 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
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0
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### 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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0
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### 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
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645
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### 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 ...

9
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6
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### 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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0
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### 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
votes

1
answer

249
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### 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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0
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190
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### 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 ...

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0
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138
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### 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
votes

1
answer

518
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### 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
votes

3
answers

2k
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### 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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1
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### 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
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0
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98
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### 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,...

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1
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### 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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0
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### 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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0
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### 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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0
answers

145
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### (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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0
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68
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### 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 ...

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1
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### 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 ...

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1
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86
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### 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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0
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### 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
votes

1
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139
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### 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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1
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### 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 ...

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8
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### 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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0
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### 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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2
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### 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
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226
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### 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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1
answer

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### 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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0
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244
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### 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 ...

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0
answers

533
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### 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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2
answers

4k
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### 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
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### 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 ...

80
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18
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24k
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### 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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2
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### 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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1
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240
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### 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
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68
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### 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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0
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98
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### 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 $...

19
votes

1
answer

790
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### 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

175
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### 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 ...

25
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5
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1k
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### 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

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### 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 ...