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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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 ...
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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 ...
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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,...
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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 ...
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23
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Open source mathematical software
I want some recommendation on which software I should install on my computer. I'm looking for an open source program for general abstract mathematical purposes (as opposed to applied mathematics).
I ...
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11
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Non-computational software useful to mathematicians
The MathOverflow question Open source mathematical software contains a list of programs that are useful to perform various computational tasks, such as computer algebra systems.
However, evaluating ...
37
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Computer calculations in A_infinity categories?
Is there a good computer program for doing calculations in A-infinity categories?
Explicit calculations in A-infinity categories are an important, useful, yet very tedious task. One has to keep track ...
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$\prod_{n=1}^{\infty} n^{\mu(n)}=\frac{1}{4 \pi ^2}$
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-...
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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 ...
32
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0
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Is there software to compute the cohomology of an affine variety?
I have some affine varieties whose cohomology (topological, with $\mathbb{C}$ coefficients) I would like to know. They are very nice, they are all of the form $\mathbb{A}^n \setminus \{ f=0 \}$ for ...
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Software for rational homotopy theory
Does anybody know a software manipulating commutative differential graded algebras, and providing a computation of the minimal model? I tried to use the package DGAlgebras of Macaulay2, but I got ...
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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?
...
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Software for symbolic matrix calculus?
Is it possible to get widely available math software (Maple/Matlab/Mathematica, etc) to symbolically differentiate vector and scalar functions of matrices, returning the result in terms of the ...
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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 ...
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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 (...
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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 ...
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OCR for handwritten mathematics
I am in the process of scanning a large collection of handwritten notes. They consist of diagrams and formulae with a relatively small proportion of actual words. Of course it would be hopeless to ...
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Which tools can identify scholarly papers that use the same types of equations?
Many types of equations are being used in multiple contexts, so a search for specific formulas might be one way to identify scholarly papers that are conceptually related.
Is any website or tool ...
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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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answer
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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 (...
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1
answer
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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)^{...
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What is the state of the art for algorithmic knot simplification?
Question: Given a `hard' diagram of a knot, with over a hundred crossings, what is the best algorithm and software tool to simplify it? Will it also simplify virtual knot diagrams, tangle diagrams, ...
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Computer-aided homology computations
Background
I am currently working on the homology of some moduli space and there exists a much simpler chain complex with the same homology.
It is a quotient of a bisimplicial complex by a subcomplex....
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real algebraic geometry software?
Does anyone have suggestions/experience for any software packages to study real algebraic varieties (for example, counting connected components of hypersurfaces, figuring out the topological type of ...
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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."
...
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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 ...
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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 ...
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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 ...
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Consequences of technically proving anything in Coq (on at least Linux) exploiting a bug? [closed]
Technically, it is possible to prove anything in Coq proof assistant [1] (on at least Linux) due to a programming feature (or bug). This seems tractable when validating large proofs. Human analysis ...
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Graph of dependencies from a Latex file [closed]
This question has been "manually migrated" to TeX-SX: https://tex.stackexchange.com/q/40200/86
Apologies if the question is not very appropiate for Mathoverflow. It seems to me more appropiate here ...
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Software for Computing Baker-Campbell-Hausdorff
Does anyone have a recommendation for software which can efficiently calculate the Baker-Campbell-Hausdorff series in classical Lie algebras?
Right now, I have a problem which boils down to ...
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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 ...
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$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$
I'm trying to solve the integral
$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$,
where $s$, $r$ and $m$>1 are positive integers.
My question is whether a closed form ...
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2
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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 ...
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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: ...
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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 ...
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1
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Program for calculating cohomology
Does it exist a computer program which calculates the cohomology of projective algebraic varieties ? For example, smooth surface in $\mathbb{P}^3$? like $\sum_0^3 X_i^3=0$
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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 ...
10
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2
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Software for Borel-Weil-Bott in positive characteristic?
I am interested in calculating cohomology of line bundles on flag varieties $G/B$ in positive characteristic. But I really just have a bunch of scattered examples. Does there exist some kind of ...
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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 ...
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5
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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 ...
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Why are there so few zero-dimensional polynomial system solvers and is this because there is no real market for them?
My questions involve the quotes below from wikipedia regarding solving polynomial systems, which given the size of the market for Big Data & Predictive Analysis applications I find puzzling:
"...
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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 ...
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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 ...
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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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Visualizing polyhedra from their 1-skeletons
Except for a few simple cases (typically pyramids and prisms) I find it hard to visualize a polyhedron from its 1-skeleton embedded in the plane, e.g. the hexahedral graph 5, as can be seen here.
...
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Solving a System of Quadratic Equations
I have many polynomial equations in many variables which I want to jointly minimize (in a mean square sense, but you could pick a different reasonable measure which favors anything where all ...
8
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1
answer
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Software package to manipulate representations
Hi,
I am looking for a software package that will allow me to experiment with the irreducible representations of lie groups (for example, $SL(2,p)$) over the complex field and over finite fields. ...
8
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1
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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 ...
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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 ...