多元幂级数乘法

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI:10.1145/1073884.1073925

É. Schost

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引用次数: 17

摘要

我们研究多元幂级数的乘法。我们证明了在足够大的域上，乘积模单项式理想M的双线性复杂度由M的正则性与M的阶积所限定。在某些特殊情况下，如部分阶截断，这个估计延续到总复杂度。这使得一些基本的代数数算法和一些多项式系统求解算法的复杂度得到了提高。

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Multivariate power series multiplication

We study the multiplication of multivariate power series. We show that over large enough fields, the bilinear complexity of the product modulo a monomial ideal M is bounded by the product of the regularity of M by the degree of M. In some special cases, such as partial degree truncation, this estimate carries over to total complexity. This leads to complexity improvements for some basic algorithms with algebraic numbers, and some polynomial system solving algorithms.

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Proceedings of the 2005 international symposium on Symbolic and algebraic computation

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