Integer Relation Among Integers: Difference between revisions

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(Created page with "{{DISPLAYTITLE:Integer Relation Among Integers (Integer Relation)}} == Description == Given a vector $x \in \mathbb{Z}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$ == Related Problems == Generalizations: Integer Relation Among Reals == Parameters == <pre>n: dimensionality of vectors</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Ti...")
 
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== Parameters ==  
== Parameters ==  


<pre>n: dimensionality of vectors</pre>
$n$: dimensionality of vectors


== Table of Algorithms ==  
== Table of Algorithms ==  
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| [[HJLS algorithm ( Integer Relation)|HJLS algorithm]] || 1986 || $O(n^{3}(n+k)$) || $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable || Exact || Deterministic || [https://epubs.siam.org/doi/pdf/10.1137/0218059 Time]
| [[HJLS algorithm ( Integer Relation)|HJLS algorithm]] || 1986 || $O(n^{3}(n+k))$ || $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable || Exact || Deterministic || [https://epubs.siam.org/doi/pdf/10.1137/0218059 Time]
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Latest revision as of 08:24, 10 April 2023

Description

Given a vector $x \in \mathbb{Z}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$

Related Problems

Generalizations: Integer Relation Among Reals

Parameters

$n$: dimensionality of vectors

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
HJLS algorithm 1986 $O(n^{3}(n+k))$ $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable Exact Deterministic Time