# Questions tagged [computation]

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### Quick ways to compute transition matrices for classical symmetric function bases

I am trying to implement quick algorithms for computing the transition matrices involving the monomial, power-sum, elementary, complete homogeneous and Schur polynomials. There are several relations ...
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### Conjecture that relates matrix systems with some polynomials of integer coefficients as solution sets

Assume $x$ is a variable belongs to $\mathbb R \setminus \{ 0,-1,+1 \}$ and consider for all $i, j \in \mathbb N$, $$a(i,j) = \frac{(x^{i+1} + 1)^{j-1} + (x-1)}{x}$$ then for all $n \in \mathbb N$ the ...
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### What Turing degree would allow you to “compute” the axioms of ZFC in some countable model of ZFC?

It is established in this post that you there is no computable model of ZFC, yet it can be computed in by a PA-degree oracle machine. Note that when we see "compute a model", we just mean that ...
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### Computer algebra programs for dummies

In the way of my investigations I have encounter the following computational problem: I have a system of 5 algebraic equations and I want to eliminate 4 of them. I also need to do a functional ...
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### Problem on triangles

Let $T\subset \mathbb{R}^2$ be any triangle and $T^t$ a deformation of $T$. Call $l_1,l_2,l_3$ the squares of the lengths of the sides of $T$ and $l_1^t,l_2^t,l_3^t$ the squares of the lengths of the ...
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### Checking Mertens and the like in less than linear time or less than $\sqrt{x}$ space

Say you want to check that $|\sum_{n\leq x} \mu(n)|\leq \sqrt{x}$ for all $x\leq X$. (I am actually interested in checking that $\sum_{n\leq x} \mu(n)/n|\leq c/\sqrt{x}$, where $c$ is a constant, and ...
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### Efficiently computing all equivariant maps between two $GL_n$-representations

This is sort of a strange question; if it's not appropriate for MathOverflow I apologize in advance. I'm in a situation where I'd like to be able to give a computer two $GL_n$ representations $V$ and ...
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### Polygonal Mersenne numbers [closed]

I posted the same question on Math SE since this one got put on hold. Link to Math SE question:Polygonal Mersenne numbers Polygonal numbers are of the form $\cfrac {n^2(s-2)-n(s-4)}{2}$, where $s$ ...
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### How to generate computational data in graph theory?

For a given number of nodes how many non-isomorphic graphs are available? Might be this is an open problem. For less number of vertices some computational statistics available. I want to get all non-...
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### procedure-based (as opposed to definition-based) concepts

Euler's work on divergent series was guided by computational procedures, rather than any definition of the "value" of such a series. E.g., he was happy to have half a dozen procedures that indicated ...
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### System of quadratic equations with 18 unknown

So I want to solve for a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r which satisfy the following system of equations: ( I only need positive integer (or 0) solution) a g + c h + b i + g j + i ...
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### Important open problems that have already been reduced to a finite but infeasible amount of computation

Most open problems, when formalized, naturally involve quantification over infinite sets, thereby obviating the possibility, even in principle, of "just putting it on a computer." Some questions (e.g....