Questions tagged [mathematical-software]

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0answers
228 views

Complexity of computer algebra for systems of trigonometric equations

As discussed in this question, I drafted a spec algorithm that hinges on finding a specific root of a system of trigonometric equations satisfying the following recurrence: $\qquad f_{p_0} = 0\\ \...
5
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3answers
2k views

Constructing a data structure for a computer algebra system

In thinking about how to approach this problem I think several things will be required, some tivial: An expression tree where non-leaf node is an operation (not sure if that part is redundant), but ...
5
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3answers
173 views

Usefulness of Differential Geometry

I recently came across these books: Differential Geometry and Lie Groups: A Computational Perspective Differential Geometry and Lie Groups: A Second Course Their subject matter really intrigues me, ...
4
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1answer
1k views

How do Computer Algebra Systems work? [closed]

In Computer Architecture course, I have learnt how computer performs numerical computations. While using MATLAB, I was introduced to symbolic mathematics toolbox. I was amazed to see it manipulating ...
4
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1answer
302 views

C(++) library for DFAs - free for academic use

(I'm aware that software questions are better suited for stackoverflow, but since DFAs are not something that software developers usually care about, I hope it's alright if I ask here.) I'm currently ...
4
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0answers
45 views

Symbolic Math Systems As Speculative Optimization For Numerical Software?

Has there been published work on hiding symbolic math within numeric software, partitioning parallel processes between speculative symbolic optimization search and numeric evaluations? Real world ...
3
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2answers
118 views

How much can we trust mathematical software when working with large numbers, and how much memory it needs to work with these numbers?

For example, I want to evaluate the expression: $3^{3^{{3}^{3}}}$ so I used wolframalpha.com (it's free, and I don't own any software), which returned the scientific notation of the number above, ...
3
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0answers
28 views

Testing whether polynomial is in algebra of other polynomials

A collection $\Sigma$ of polynomials is an algebra if: (1) $\lambda f + \eta g \in \Sigma$ for any $f,g \in \Sigma, \lambda,\eta \in \mathbb{R}$ and (2) $f,g \in \Sigma$ implies $fg \in \Sigma$. We ...
3
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0answers
153 views

Can cognitive architectures (CLARION, SOAR, ACT-R) be used for creative mathematical reasoning?

Can cognitive architectures (CLARION, SOAR, ACT-R, others) be used for creative mathematical reasoning? As far as I understand, then it is the best to encode formal mathematical knowledge in the ...
2
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2answers
3k views

Function Maximization in Java

I have a bivariate function like $ f(x,y) = \frac{1}{x^3 \sqrt{\pi}}. e^{\frac{2-x}{x^2}} . y^3 . e^{3.y \over 3-y} $ and I want to find its global maximum over a range of $ x \in [0, 200] \text{, ...
2
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1answer
301 views

Imperfection in randomness in VLC shuffle playlist - why?

Whenever I play a playlist of music using VLC (possibly other software too), I notice that some songs never get played while others get played repeatedly (even for a playlist of just 8 songs). I know ...
2
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0answers
118 views

Generate all non-isomorphic bounded-degree rooted graphs of bounded radius

I need to generate/enumerate isomorphism classes of vertex-rooted graphs with the following properties. Let $\Delta$ be the maximal degree (say 3 for subcubic graphs) and $r$ the maximal distance of a ...
1
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2answers
55 views

Implementing piecewise linear functions

I need to implement piecewise linear functions (this is not homework, it is for my own personal project). However, I have been having difficulties to get it right. Below, I describe the ...
1
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1answer
61 views

What is the equation for a spiral path in 3D? [closed]

I am developing games in Unity 3D. Currently, I am trying to place 3D objects in 3D space in a spiral pattern that looks like one of 2 the strands in a pair of the DNA (helix) spiral pattern. Would ...
1
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0answers
87 views

Universal theorem proving algorithms for sequent calculus (e.g. for cut-free logics)?

Some of the logics admit Gentzen-style sequent calculus. Are there universal algorithms that allow to find proof (derivation of the proof) in sequent caculus for every hypthetical theorem? Some of ...
1
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0answers
124 views

Logical formula in DIMACS, SAT, Schaefer's dichotomy theorem and software to test it

I have a very complicated formula logical (CNF) in the file DIMACS. The question is as follows. The formula has hundreds of millions of clauses (assume billion) and a lot of variables. It is a ...
1
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0answers
90 views

Computational approach deciding whether a set of Wang Tile could tile the space up to some size [closed]

As an applied person, I'm facing one practical problem deciding whether a set of Wang tile could tile the plane periodically or aperiodically. Although both problems seem undecidable, but I'm on a ...
0
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0answers
8 views

Good library for Graph Embedding Algorithms

I am working on a project related to virtual network embedding. As the problem is NP-hard, heuristic algorithms are most important for my use case. Looking for good libraries where I can find the ...
0
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0answers
105 views

These sample CNF formulas in DIMACS files are in P? (Schaefer's dichotomy theorem)

Here is my earlier question. But there was no full answer. I've decided to include specific DIMACS files: http://jarvis2.hmcloud.pl/sat/cnf.formula.10 (15.8MB) http://jarvis2.hmcloud.pl/sat/cnf....
-1
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1answer
130 views

Can we find every 216 digit number combination? [closed]

This question popped to my head when I watched Pi where the mathematican told the Jews "Didnt you calculate every 216 digit number allready?" So I want to find every possible 216 digit number ...