# Questions tagged [computation]

The computation tag has no usage guidance.

The computation tag has no usage guidance.

32
questions

5
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3
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I am currently trying to get the Groebner basis for 9 equations with 12 variables:
$
a_1^2+b_1^2+c_1^2+d_1^2-48.73=0\\
a_2^2+b_2^2+c_2^2+d_2^2-50.53=0\\
a_3^2+b_3^2+c_3^2+d_3^2-40.69=0\\
a_1a_2+b_1b_2+...

1
vote

1
answer

96
views

Consider the class of simple connected n/2-regular graphs, n even. Are the maximum clique problem and/or maximum independent set problem NP-complete on such graphs? Is there any known result which ...

11
votes

1
answer

275
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I have a formal power series in one variable that I think might be algebraic (or perhaps just D-finite). Is there software that could help me explore this?
By way of comparison, there’s a very simple ...

3
votes

1
answer

326
views

Taking the doctrine of computational trinitarianism ( https://ncatlab.org/nlab/show/computational+trinitarianism ), if one understands the incompleteness theorems as the "logic" version, and ...

1
vote

0
answers

77
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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 ...

4
votes

0
answers

72
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Let $P$ be the class of all polynomial time computable functions from $\{0,1\}^*\rightarrow \{0,1\}$. For any $f\in P$, define function $f^A:\mathbb{N}\rightarrow \{0,1\}^*$ by
$$f^A(n)=(f(x_1),\cdots,...

4
votes

1
answer

122
views

Suppose I have a Kac-Moody algebra (maybe even Borcherds-Kac-Moody) $\mathfrak{g}$ with symmetric cartan matrix $A$. Let the simple roots be $e_{\alpha_i}$ for $i = 1, \ldots n$.
I know there is ...

0
votes

1
answer

796
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what is written below is a conjecture that I posed , and I ask for a proof or a disproof of it .I have checked the conjecture from $n$=$1$ up to $n$=$10$ using Matlab, and all results were in ...

1
vote

1
answer

146
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Recently, a student and I have been working through Waksman's paper ``An Optimum Solution to the Firing Squad Synchronization Problem.'' The paper claims that for any value of $n$, the proposed ...

5
votes

0
answers

73
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I am searching for a big list of papers or researches devoted to limit cycles of planar polynomial vector fields based on a computational and numerical approach.
I would like to ask ...

3
votes

0
answers

161
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Suppose $X$ is a smooth toric Fano $3$-fold, and $D$ is a torus invariant divisor corresponding to a face of the polytope associated to $X$. I would like to search for (smooth) curves $C \subset D$, ...

4
votes

1
answer

678
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The conjecture is as follows:
Let $n\in\mathbb{N}\setminus\{1\}$. Define $a(n)=2^n+1$ and the set:
$$S(n) = \{ (a(n)^m+1)/2\ :\ m\in \mathbb{N}_0\}.$$
Then for all $c\in\mathbb{N}$, the number $(a(n)...

8
votes

1
answer

458
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The conjecture says that for any a, b belong to the the set of non-negative integers ($a$ and $b$ are not necessarily distinct), taking any natural value of $c$; we have always that $$(10^c-1) \cdot \...

1
vote

1
answer

631
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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 ...

7
votes

1
answer

394
views

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 ...

0
votes

0
answers

139
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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 ...

6
votes

1
answer

242
views

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 ...

6
votes

1
answer

464
views

The (generalised) sign-rank of a (generalised) sign pattern $S\in \{+,-,0\}^{n\times m}$
is the minimum rank of all matrices with the same sign pattern, i.e.
$$
\min\left\{\operatorname{rank}(M)\ :\ M\...

8
votes

2
answers

333
views

Given two closed simple(no self-intersection point) curves $C_1,C_2$ in the plane $\mathbb R^2$, is there a good way to judge whether one curve can be embedded inside the other one, here embedding ...

6
votes

2
answers

1k
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If one looks at the code for a Turing Machine (TM) with
$q$ states and, let's say, $2$ symbols, they all look
pretty much the same:
A list of $5$-tuples:
$$
< state, symbol{-}read, symbol{-}to{-}...

19
votes

0
answers

490
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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 ...

5
votes

0
answers

94
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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 ...

1
vote

1
answer

197
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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 $s$ ...

-1
votes

1
answer

87
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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-...

0
votes

0
answers

76
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We have a real rank $r$ matrix $M\in\{0,1\}^{n\times n}$.
Suppose we have diagonalized using $LMR=D$.
I want to recover a real matrix $\widetilde{M}$ such that maximum absolute entry of $\widetilde{...

3
votes

2
answers

448
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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 ...

3
votes

0
answers

115
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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} ...

5
votes

6
answers

446
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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 ...

0
votes

3
answers

459
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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 ...

76
votes

16
answers

5k
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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....

16
votes

3
answers

1k
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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 ...

3
votes

1
answer

586
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Often when computing in category theory, one has to show that some square is cartesian. Depending on the number of maps involved, and their arrangement, it's somewhat difficult to write down exactly ...