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.
180 questions
2 votes
1 answer
185 views
Where does Concorde spend its time
Concorde is the de facto standard for calculating exact solutions for the Traveling Salesman Problem. Question: what is known about the fractions of computation time that are spent on ensuring that ...
- 14k
2 votes
1 answer
334 views
Software that can squeeze a surface
Let $\Sigma$ be an embedded surface in $\mathbb{R}^3$ subject to certain constraints (for example, its normal curvatures lie between $\pm 1$). Now imagine that the space $\mathbb{R}^3$ is filled with ...
- 47.1k
17 votes
6 answers
2k views
Graphical software tools for quick and easy diagrams
What tools do people use for quickly and easily creating presentable, if not publication quality, diagrams of various kinds? When I need to make a high quality diagram, I'm happy to whip up some TikZ. ...
- 1,821
8 votes
0 answers
650 views
Automating the resolution of IMO 2025 Problem 1
The problem 1 of the 2025 IMO is the following: A line in the plane is called sunny if it is not parallel to any of the x-axis, the y-axis, and the line $x + y = 0$. Let $n ⩾ 3$ be a given integer. ...
- 371
1 vote
0 answers
111 views
Compute DeligneLusztigCharacter in CHEVIE
Let $\mathbf{G}^F={\rm Sp}_{10}(q)$, and assume that |$\mathbf{T}^F|=(q^4-1)(q+1)$. In the manual of CHEVIE, it is said that the function DeligneLusztigCharacter(W,w) returns the Deligne-Lusztig ...
- 305
4 votes
1 answer
218 views
Software for testing validity of propositional formulas in finite Kripke frames (modal SAT)
I have a formula $\varphi$ of propositional modal logic or propositional intuitionistic logic, a finite Kripke frame $W$, and I would like to test whether $\varphi$ is valid in $W$. This is an ...
- 38.3k
0 votes
0 answers
132 views
Is there a symbolic computation program that can deal with differential forms, Stokes theorems, the Hodge * operator, etc
I am looking at a messy series of computations of integrals of differential forms on manifolds with boundary, involving repeated application of Stokes' theorem, and also involving the Hodge * operator....
- 1
2 votes
0 answers
159 views
Free, easy-to-use program for noncommutative algebra over finite fields
I am looking for a computer program that can handle computations in noncommutative algebra over a finite field of prime order $p$. My requirements are: The program should be free, as I do not have ...
- 1,143
1 vote
0 answers
79 views
Is there any software package to find the vertices of convex polytope where the inequality constraints are bounded by variable?
I know of this package lcon2vert that computes vertices from given inequality and equality constraints describing a bounded polyhedron. Here the bounds of constraints only accept numerical values, i.e....
3 votes
0 answers
77 views
Tools or software for calculations in Quantum Affine Algebras
I am curious if there's a tool/math software to help with calculations in Quantum Affine Algebras, specially using the Drinfeld realization, i.e. the realization in Theorem 4.7 of Beck. For example I ...
- 31
10 votes
0 answers
444 views
What axiomatic system does AlphaGeometry use?
In January 2024, researchers from DeepMind announced AlphaGeometry, a software able to solve geometry problems from the International Mathematical Olympiad using a combination of AI techniques and a ...
- 371
0 votes
0 answers
241 views
Software for computing polytopes
As can be inferred from the title, I want to do some computation on the facets representation of the polytopes given the vertices. My advisor recommended me Polymake, which is indeed useful even with ...
- 1
4 votes
1 answer
477 views
Experimental mathematics in Ramanujan's work
The field of experimental mathematics has led to the discovery of numerous remarkable identities and relations, often using computer algebra systems. Somos' work on finding algebraic identities ...
- 51
9 votes
1 answer
486 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,...
- 323
0 votes
0 answers
156 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 $D=-3340$. ...
- 913
0 votes
0 answers
162 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 ...
- 51
2 votes
0 answers
125 views
Gröbner implicitization with relationships between the variables
I have the following parametric equations, where cost$=\cos t$, cos2t$=\cos 2t$, and $A^2+B^2=1$: ...
- 2,590
0 votes
2 answers
428 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-...
- 31
2 votes
1 answer
869 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,...
- 123
11 votes
1 answer
783 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 ...
- 1,959
13 votes
1 answer
5k 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: ...
- 1,088
0 votes
1 answer
175 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 $$M:=\{(q_1,\dots,q_k)\in A^k|\, p_1q_1+\dots+p_kq_k=0\}...
- 23k
2 votes
1 answer
321 views
Software tools to find square root modulo $2^t$
Are there any software tools to find modular square roots of $y$ in $$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$?
- 1
2 votes
3 answers
635 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^...
- 1
4 votes
1 answer
297 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 ...
- 1,068
19 votes
5 answers
9k 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." ...
- 309
3 votes
1 answer
325 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 ...
- 47.1k
2 votes
1 answer
692 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 ...
- 123
2 votes
0 answers
156 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 ...
- 21
7 votes
0 answers
162 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} ...
- 633
9 votes
1 answer
780 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 ...
- 88.2k
13 votes
6 answers
2k 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 vote
0 answers
187 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 ...
- 25.7k
6 votes
1 answer
415 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: ...
- 339
6 votes
1 answer
404 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 ...
- 376
1 vote
0 answers
248 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 ...
- 970
25 votes
1 answer
914 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)^{...
3 votes
1 answer
1k 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 ...
- 1
0 votes
0 answers
134 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
-1 votes
1 answer
268 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 (divergence ...
- 117
2 votes
0 answers
222 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 ...
- 31
5 votes
0 answers
191 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 ...
- 745
3 votes
0 answers
236 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 ...
- 1,553
2 votes
0 answers
97 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 ...
- 778
1 vote
1 answer
300 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 ...
- 6,331
1 vote
1 answer
131 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.
- 6,331
1 vote
0 answers
205 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+...
- 25.7k
4 votes
1 answer
272 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 ...
- 1,068
5 votes
1 answer
266 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 ...
- 515
26 votes
8 answers
4k 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 ...