Syzygies的多项式gcd

2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) Pub Date : 2016-09-01 DOI:10.1109/SYNASC.2016.021

Eliana Duarte, Daniel Lichtblau

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引用次数: 3

摘要

我们提供了一个简单的方法，使用Gröbner基在模块上，计算多元多项式的最大公因数。我们展示的方法是灵活的，适用于有理数或素数域的代数扩展，并且明显比先前使用Gröbner基的方法快。它可以用于稀疏插值可能难以实现的情况，例如，当插值点很少(小素数域)或存在非数值代数关系时。

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Polynomial GCDs by Syzygies

We provide a simple method, using Gröbner bases over modules, to compute multivariate polynomial greatest common divisors. The approach we show is flexible, adaptable to algebraic extensions of the rationals or prime fields, and is notably faster than prior methods that work with Gröbner bases. It can be used in situations where sparse interpolation might be difficult to implement, e.g. when there are few points for interpolation (small prime fields) or in the presence of non-numeric algebraic relations.

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来源期刊

2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

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