# Questions tagged [computation]

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### Is there a "natural" interpretation of the power function for octonions and for sedenions?

This question is a sequel to Is there a definition of $\log(x)$ for quaternion/octonion $x$? Since $\log(x)$ is multivalued even for complex $x \in \mathbb{C}$, it is impossible to define $\log(x)$ ...
• 2,010
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### Is there a fast way to check if a matrix has any small eigenvalues?

I have hundreds of millions of symmetric 0/1-matrices of moderate size (say 20x20 to 30x30) which (obviously) have real eigenvalues. I wish to extract from this list the tiny number of matrices that ...
• 12.3k
285 views

### How to recover integer part from known fractional root part?

Suppose you have $r=n+f$ where $n\in\mathbb{N}$ and $f\in (0,1)$. I know that $r^2$ is an integer and I can also get as many digits of $f$ as I like, is there a way to recover the value of $n$? Thank ...
84 views

### Quantum groups as bialgebra cohomology classes

My question below is about how to view the quantum group $U_q(\mathfrak{g})$ as a bialgebra cohomology class. Background: If $A$ is a bialgebra, Gerstenhaber and Schack in Bialgebra cohomology, ...
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56 views

### NC0 randomness vs. non-uniformity

In Ajtai and Ben-Or. A theorem on probabilistic constant depth Computations. STOC '84, 1984 Ajtai and Ben-Or show a non-uniform derandomization of BPAC0. Is there a similar relation known for ...
1k views

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### efficiently checking that a field extension is Galois

Let $K \subset L$ be an algebraic extension of fields finitely presented over a prime field or over an algebraically closed field. Is there an efficient procedure to check that $L/K$ is Galois? To ...
• 4,040
122 views

### Weak randomness relative to finite-state machines

Is there a nice example of a sequence that looks random to any predictor whose predictions use a finite-state machine? More precisely, consider a finite-state machine $M$ with input alphabet {0,1} ...
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452 views

### 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 ...
475 views

### 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 ...
6k views

### 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....
1k views

### What to do when your research runs into a computationally challenging problem?

Occasionally, but more frequently lately, I would like to perform some hard computations. As an example, yesterday the following question came up: What is the projective dimension of the edge ideal ...
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