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28
votes
9answers
4k views

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 ...
25
votes
0answers
647 views

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 ...
24
votes
3answers
3k views

$\prod_{n=1}^{\infty} n^{\mu(n)}=\frac{1}{4 \pi ^2}$

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) ...
24
votes
0answers
1k views

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 ...
21
votes
0answers
488 views

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 ...
19
votes
4answers
2k views

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 ...
17
votes
2answers
5k views

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 ...
15
votes
3answers
570 views

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, ...
13
votes
1answer
279 views

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 ...
12
votes
3answers
838 views

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 ...
11
votes
13answers
3k views

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 ...
11
votes
3answers
806 views

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 ...
10
votes
2answers
2k views

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 ...
10
votes
0answers
165 views

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 ...
9
votes
3answers
603 views

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 ...
9
votes
2answers
478 views

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 ...
8
votes
2answers
993 views

Graph of dependencies from a Latex file [closed]

This question has been "manually migrated" to TeX-SX: http://tex.stackexchange.com/q/40200/86 Apologies if the question is not very appropiate for Mathoverflow. It seems to me more appropiate here ...
8
votes
1answer
1k views

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 ...
7
votes
5answers
739 views

$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$

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 ...
7
votes
2answers
844 views

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: ...
7
votes
1answer
260 views

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. ...
7
votes
1answer
245 views

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 ...
7
votes
1answer
521 views

Non-algebraic curve visualisation

Is there any software which can automatically visualise a non-algebraic complex curve, I mean the structure of it's ramification points and sheet? I think a good test example would be the Lambert ...
6
votes
3answers
684 views

Looking for cubic, bipartite graphs with girth at least six and no cycles of length 8.

Aside from the Desargues graph, are there nice (at least vertex-transitive), small (say, less than 60 vertices), cubic, bipartite graphs with girth at least 6 and no 8-cycles? (or, even better, no ...
5
votes
5answers
511 views

Noncommutative computational package

I am wondering if there is a program which can do simple operations over noncommutative rings, like expand products and substitute one expression for another. To clarify, consider the following ...
5
votes
2answers
1k views

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 ...
5
votes
1answer
467 views

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 $\sum_0^3 X_i^3=0$
5
votes
2answers
668 views

Integral with Dirac delta (me or wolfram mathematica?) [closed]

I asked the question on math.stackexchange but didn't get an answer so I came here. I tried to compute with Wolfram Mathematica the following integral $$I=\int_0^\pi\int_{-\infty}^\infty x e^{-\mathrm ...
5
votes
2answers
794 views

P-adic Arithmetic Software

I would like to automate a huge amount of computation that involve basic arithmetic operations with $p$-adic numbers. I have found a Mathematica packages for it, but it is old and acts quite ...
5
votes
0answers
93 views

How many simultaneous polynomial equations of degree 2 can software solve today?

Consider the following problem: Input: $n$ polynomial equations of degree $2$ in approximately $n$ variables. Each equation contains about $\sqrt{n}$ monomials. We would like to find one ...
5
votes
0answers
121 views

Software for BMW algebra calculations?

Does software exist for computations in the BMW algebra? For example, I'd like to be able to express elements in a basis of "totally descending tangles" as in a paper of Morton–Wassermann. At ...
4
votes
3answers
477 views

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. ...
4
votes
2answers
264 views

Visualizing a graph

I have a finite but huge metric graph with say 1000 vertices. It comes say as 10000x10000 symmetric matrix filled by $0,1,\dots$ and $\infty$; 0's on the diagonal and $\infty$ is for pairs of vertices ...
4
votes
1answer
2k views

Create djvu from jpeg - best practices and tutorial? [closed]

This is definitely not a mathematical question, but a relevant one I believe. There are incomplete versions of some books floating around the web and I want to put in the missing pages. There is a ...
4
votes
1answer
354 views

Mathematica package for supergravity and string theory

I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra ...
3
votes
2answers
326 views

Is there a software to prove or deduce symbolic inequalities?

I have a bunch of inequalities, and I'm trying to see if another inequality can be deduced from the first bunch. For example, assuming that $a \leq b$ and $c \leq d$, we can deduce that $a + c \leq b ...
3
votes
2answers
154 views

Markov Partitions for toral automorphisms

I know that my question is more practical than theoretical. But, I do know where to look for the theoretical sources. I want to find a program in the case that it exists (does it?), or to program it. ...
3
votes
4answers
549 views

Softwares for drawing hyperbolic surfaces , closed, with boundaries or with punctures ?

In a paper I am in the process of writing in LaTeX, I need to draw and incorporate some diagrams of hyperbolic surfaces in my LaTeX document. Is there any software I can use to draw hyperbolic ...
3
votes
1answer
268 views

Formal verification of simple equational proofs (as in Universal Algebra…)?

Is there an software package aimed at verfication of simple equational proofs? I am hoping to avoid the usual overhead involved with First Order Logic or Higher Order Logic verification systems. ...
3
votes
2answers
215 views

Force-directed graph drawing in 1D?

I have a real-world graph that I wish to draw in one dimension. Here's the graph: I'd like to draw it using some kind of force-directed graph drawing method. I'm supposing this is both possible ...
3
votes
1answer
234 views

Use a graphic tablet to write in Latex or MathML [closed]

I have a Graphic Tablet and I am looking for a software which have the following features: Math equation recognition I want to write and solve math equations in Graphic Tablet and auto recognized to ...
3
votes
3answers
523 views

Good Computer Package for Calculating Inverse of a Formal Power Series?

This might be a question people already asked or is obvious to experts, or is not appropriate for this forum, if so, I apologize. I am trying to calculate things like $z/(e^z-1)$, or find the inverse ...
3
votes
1answer
231 views

Software for calculating products and sums of Kronecker deltas

I am looking at a Kahler metric $g$ on a certain manifold $M$, which has the good taste to be invariant under a transitive group of isometries, and I want to say something about its holomorphic ...
3
votes
1answer
169 views

software for numerical constraint satisfaction problems

Let $m$ be an even integer greater than $8$. Is there any software I can use to determine for some small $m$ whether the following constraints on $t_0,\ldots,t_{m-1}$ and $w$ have solutions? ...
3
votes
0answers
330 views

Software for Combinatorial Algebra sought

I am looking for software which helps me do straightforward tasks in combinatorial algebra. Let me give an example of what I mean by a straightforward task: I have two graded (generally ...
2
votes
3answers
433 views

Green polynomials

Hello, Is there any software for calculating Green polynomials (of type A)? Or, at least, where can I find tables of Green polynomials? Also, I would be interested in some formulas for Green ...
2
votes
2answers
129 views

Software producing complex trees

Does anyone know any kind of graph software that could produce graphs like this for publication? Those links and crosses and numbers actually needs to be presented…. Thank you:) One small update, ...
2
votes
2answers
267 views

Software for drawing intervals in Weyl groups

I am looking for an automated way to draw diagrams of intervals in Weyl groups and in their various subsets such as minimal representatives of cosets $W/W_p$ for a parabolic Weyl group $W_p$ or ...
2
votes
2answers
348 views

Software to decide equality between expressions involving powers and trigonometry

Given two expressions A and B involving integers, $\pi$, powers to rational exponents, and cosine, is there a software that determines if A = B? (Previous question asked A > B, but the bottleneck is ...
2
votes
4answers
1k views

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 ...