• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文会议>International Symposium on Symbolic and Algebraic Computation Aug 3-6, 2003 Philadelphia, Pennsylvania, USA >Factoring Sparse Resultants of Linearly Combined Polynomials
【24h】

Factoring Sparse Resultants of Linearly Combined Polynomials

机译：分解线性组合多项式的稀疏结果

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This paper is part of the author's work on determining the irreducible factors of sparse (toric) resultants of composed polynomials. The motivation behind this work is to use the factors for efficient elimination of variables, by sparse resultant computation, from composed polynomials. Previous works considered the sparse (toric) resultant of polynomials having arbitrary (mixed) supports composed with (i.e. evaluated at) polynomials having the same (unmixed) supports and of polynomials having the same (unmixed) supports composed with polynomials having arbitrary (mixed) supports, resp. Here, we consider the sparse resultant of linear polynomials having arbitrary (mixed) supports composed with polynomials having arbitrary (mixed) supports, also called "linearly combined polynomials", (under a natural assumption on their exponents). The main contribution of this paper is to determine the irreducible factors, together with their exponents, of the sparse resultant of these linearly combined polynomials. This result essentially generalizes a result by Gelfand, Kapranov and Zelevinsky factoring the sparse resultant of unmixed dense linear polynomials composed with polynomials with unmixed supports. It is expected that this result can be applied to eliminate variables from linearly combined polynomials with improved efficiency.
机译：本文是确定组合多项式的稀疏（toric）结果的不可约因子的工作的一部分。这项工作背后的动机是利用稀疏的结果计算，从合成的多项式中使用这些因子来有效消除变量。先前的工作考虑了具有任意（混合）支撑的多项式的稀疏（复数）结果，该多项式由具有相同（未混合）支撑的多项式组成（即，在其中求值），并且具有相同（未混合）支撑的多项式由任意（混合）多项式构成的多项式支持，分别。在此，我们考虑具有任意（混合）支撑的线性多项式的稀疏结果，该线性多项式由具有任意（混合）支撑的多项式组成，也称为“线性组合多项式”（在其指数的自然假设下）。本文的主要贡献是确定这些线性组合多项式的稀疏结果的不可约因子及其指数。该结果从本质上概括了Gelfand，Kapranov和Zelevinsky的结果，该结果将未混合的稠密线性多项式的稀疏结果分解为包含具有未混合支持项的多项式。预期该结果可用于消除线性组合多项式中的变量，从而提高效率。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号