2017
DOI: 10.48550/arxiv.1708.09067
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Computing Puiseux series : a fast divide and conquer algorithm

Adrien Poteaux,
Martin Weimann
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Cited by 4 publications
(25 citation statements)
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“…As δ = v i , we have min v i ≤ δ/d and the upper bound for η(F ) follows. If F is quasi-irreducible, then we have also v i ≤ η(F ) = N i by [21,Corollary 4]. As all v i 's are equal in that case, the lower bound follows too.…”
Section: Truncation Boundsmentioning
confidence: 85%
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“…As δ = v i , we have min v i ≤ δ/d and the upper bound for η(F ) follows. If F is quasi-irreducible, then we have also v i ≤ η(F ) = N i by [21,Corollary 4]. As all v i 's are equal in that case, the lower bound follows too.…”
Section: Truncation Boundsmentioning
confidence: 85%
“…m 1 , z 1 are respectively α, 2 and 1. Applying results of [21,Section 3], one can show that an optimal truncation bound to compute G 1 is…”
Section: A Newton-puiseux Type Irreducibility Testmentioning
confidence: 99%
“…Then, we need to compute the Puiseux expansions η i of f at one root of each factor in S f ac , up to precision N = max i i =j v(η i − η j ). Using the algorithm of Poteaux and Weimann [21], the Puiseux expansions are computed up to precision N in O(n(δ + N )) field operations, where δ stands for the valuation of Disc(f ). Indeed, these expansions are computed throughout their factorization algorithm, which runs in O(n(δ + N )) field operations as stated in [21,Theorem 3].…”
Section: Complexity Analysismentioning
confidence: 99%
“…Using the algorithm of Poteaux and Weimann [21], the Puiseux expansions are computed up to precision N in O(n(δ + N )) field operations, where δ stands for the valuation of Disc(f ). Indeed, these expansions are computed throughout their factorization algorithm, which runs in O(n(δ + N )) field operations as stated in [21,Theorem 3]. Therefore, in theory, we will see that computing the Puiseux expansions has a negligible cost compared to other parts of the algorithm since N ≤ n 2 .…”
Section: Complexity Analysismentioning
confidence: 99%
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