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Results tagged with algorithms
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user 28104
Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
4
votes
How to quickly determine whether a given natural number is a power of another natural number?
The computer algebra system GAP performs this test and determines a
smallest root $a$ of a given integer $n$ quite efficiently.
The following is copied directly from its source code (file gap4r6/lib/i …
- 19.6k
2
votes
Accepted
Find root in finite field
Pasting the title of your question into Google gives references like
http://www.math.leidenuniv.nl/~astolk/monday/notes/stolk-roots.pdf and
http://www.ma.utexas.edu/users/voloch/Preprints/roots.pdf
-- …
- 19.6k
14
votes
Is there an algorithm to solve quadratic Diophantine equations?
Let me just add that for solving quadratic diophantine equations in 2 variables, i.e. equations of the form
$$
ax^2 + bxy + cy^2 + dx + ey + f = 0, \ \ a, b, c, d, e, f \in \mathbb{Z},
$$
there is a …
- 19.6k
23
votes
5
answers
1k
views
Securing privacy of "who communicates with whom" under Orwell-like conditions
Assume that there is a big and powerful country with an
information-greedy secret service which has backdoors to all internet nodes
throughout the world which permit him to observe all exchanged data …
- 19.6k
4
votes
Permutation search problems with no known $o(n!)$ algorithms
If you are also interested in problems of that type where $n = \infty$:
Given a mapping $f: \mathbb{N} \rightarrow \mathbb{N}$ from the natural
numbers to themselves, it is often a notoriously hard pr …
- 19.6k
2
votes
Does a classification of simultaneous conjugacy classes in a product of symmetric groups exist?
For the sake of simplicity, consider only the case $d=2$.
In this case, two pairs $(a,b), (a,c) \in {\rm S}_n^2$ lie in
the same orbit if and only if there is a permutation $\pi$
in the centralizer of …
- 19.6k
6
votes
Algorithm for solving systems of linear Diophantine inequalities
GAP provides a function NullspaceIntMat which solves systems
of linear diophantine equations. The documentation says:
25.1-2 SolutionIntMat
* SolutionIntMat( mat, vec ) ───────────────────────────── …
- 19.6k
12
votes
Is there a way of canonically labelling permutation groups?
A quick way to obtain canonical conjugates of permutation groups would of
course be nice, but hoping for that may be a bit too optimistic.
Rather than trying to go that route, in your situation I woul …
- 19.6k
33
votes
3
answers
6k
views
Are surjectivity and injectivity of polynomial functions from $\mathbb{Q}^n$ to $\mathbb{Q}$...
Is there an algorithm which, given a polynomial $f \in \mathbb{Q}[x_1, \dots, x_n]$,
decides whether the mapping $f: \mathbb{Q}^n \rightarrow \mathbb{Q}$ is surjective,
respectively, injective? --
And …
- 19.6k