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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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17 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 ...
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0answers
30 views

Matlab book request for optimal control

My subject is optimal control of PDE and I want to put optimal control problems in Matlab to be solved but I don't know how to do this. I would be grateful if you could give me some references in that ...
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1answer
164 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
208 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 ...
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0answers
46 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 ...
36
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1answer
2k 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 ...
-1
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0answers
73 views

Relational Mathematics by Gunther Schmidt

Anyone that studied the text can tell if they used any software for following along with the book examples? In case it helps in anyway having this bit of context to my question: I'm new to the subject ...
4
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2answers
512 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 ...
69
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18answers
19k 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,...
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2answers
439 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 ...
7
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1answer
174 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
51 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
67 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
589 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
100 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
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5answers
803 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
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1answer
182 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
143 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
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1answer
72 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
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1answer
135 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
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1answer
90 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 $...
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0answers
50 views

Rules of thumb for hardness of integer programming and software for fixed parameter integer programming simulation?

I want to simulate a $20$ constraint $13$ variable ($6$ are free) linear integer programming problem. What is the best algorithm out there? Is there a readily available library anywhere? The notes ...
20
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2answers
904 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 ...
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0answers
109 views

Intersection of two complicated surfaces in 3D

I have two surfaces in parametric form ($r$ and $\psi$ are the parameters). The three entries in each matrix represent $x$, $y$ and $z$ equations in order. I want to find angle at which rotation of $...
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0answers
59 views

references for numerical lookup table interpolation of P/ODE(s) RHS

I'm not sure that this *overflow is right place to ask.... Sorry if it is off top. Does anyone know name for numerical dirty trick when we tabulate a right-hand side of given differential equation(s) ...
1
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1answer
108 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: ...
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0answers
678 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
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4answers
673 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 $x \in \mathbb{Z}^n$ ...
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1answer
181 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 $(2,3)$ ...
84
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5answers
5k 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
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0answers
50 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
2answers
496 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 ...
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0answers
373 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 ...
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0answers
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 $\mathbb{C}[GL_3]$ ...
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1answer
68 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
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2answers
366 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 ...
0
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1answer
212 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
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0answers
106 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 ...
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1answer
511 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 ...
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0answers
110 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
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1answer
331 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 ...
127
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21answers
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 ...
23
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3answers
1k views

What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?

Over the years, advances in machine learning has allowed us to communicate and interact, using the same natural language, more and more semantically with computers, e.g. Google, Siri, Watson, etc. On ...
2
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2answers
313 views

Suggestions for dealing with the “timed” balls-into-bins model

Definitions: Let $T$ (for "time") be a random variable $T \sim \text{Exp}(\lambda)$ and $\Delta t$ is a realization (or called an observed value) of $T$. Let $D$ (for "delay") be a random variable $D \...
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0answers
110 views

Programmatically computing dual Hopf algebras: state of the art

Given a graded Hopf algebra of finite type, we know the (graded) linear dual is also a graded Hopf algebra. For instance the dual Hopf algebra to the polynomial algebra on an even degree generator, $R[...
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1answer
276 views

Samuel multiplicity

Let $X$ be the hyper-surface defined by $$f:=\sum_{i=1}^k x_i^n=0$$ in $\mathbb{C}^k$. Let $Y$ be the non-reduced sub-scheme of $X$ defined by the ideal $$I=(x_1^{n-1},\dots , x_k^{n-1}) $$ What is ...
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0answers
283 views

Intersection Multiplicity

Let $X$ be an hyper-surface in an affine space defined by an equation $F$. We can assume that the ground field is $\mathbb{C}$ and $X$ is normal. Take functions $f_1,\dots, f_n$ on $X$ and let $B$ ...
2
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1answer
246 views

finiteness dimension

$R$ is a local Noetherian ring. $f_I(M)$, the finiteness dimension of a module $M$ relative to $I$, is defined in ...
6
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0answers
194 views

Papers/Programs for computing periodic KL polynomials?

Periodic Kazhdan-Lusztig polynomials (for an affine Weyl group) are polynomials that control Jordan-Holder multiplicities for certain representations ("baby Verma modules") of an algebraic group in ...
1
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1answer
435 views

intuitive interpretation of analytic spread

I am studying analytic spreads from Bruns-Herzog's book. The definition is clear but calculation of the analytic spread of an ideal is hard for me in practice. I wonder if it is hard for you too. ...