Nzmath 1.0

Tanaka, Satoru; Ogura, Naoki; Nakamula, Ken; Matsui, Tetsushi; Uchiyama, Shigenori

doi:10.1007/978-3-642-15582-6_45

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2017

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“…The described algorithms were implemented in Python by the author, using the NZMATH library [9]. Several improvements were made, making the implemented version slightly different from the pseudocode of the previous sections, in order to achieve a higher efficiency.…”

Section: Discussionmentioning

confidence: 99%

An Algorithm for Canonical Forms of Finite Subsets of $$\mathbb {Z}^d$$ Z d up to Affinities

Paolini¹

2017

Discrete Comput Geom

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Abstract. In this paper we describe an algorithm for the computation of canonical forms of finite subsets of Z d , up to affinities over Z. For fixed dimension d, this algorithm has worst-case asymptotic complexity O(n log 2 n s µ(s)), where n is the number of points in the given subset, s is an upper bound to the size of the binary representation of any of the n points, and µ(s) is an upper bound to the number of operations required to multiply two s-bit numbers.This problem arises e.g. in the context of computation of invariants of finitely presented groups with abelianized group isomorphic to Z d . In that context one needs to decide whether two Laurent polynomials in d indeterminates, considered as elements of the group ring over the abelianized group, are equivalent with respect to a change of base.

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Section: Discussionmentioning

confidence: 99%

An Algorithm for Canonical Forms of Finite Subsets of $$\mathbb {Z}^d$$ Z d up to Affinities

Paolini¹

2017

Discrete Comput Geom

View full text Add to dashboard Cite

show abstract

Nzmath 1.0

Cited by 1 publication

References 3 publications

An Algorithm for Canonical Forms of Finite Subsets of $$\mathbb {Z}^d$$ Z d up to Affinities

An Algorithm for Canonical Forms of Finite Subsets of $$\mathbb {Z}^d$$ Z d up to Affinities

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