论文标题
猜测序列关系的结构化理想的基础
Guessing Gr{ö}bner Bases of Structured Ideals of Relations of Sequences
论文作者
论文摘要
假设给出了在字段上定义的N维表的足够多术语，我们旨在猜测它们所满足的恒定或多项式系数的线性复发关系。在许多应用中，表术语都带有一个结构：例如，它们在圆锥形之外可能为零，它们可能是根据有限组的作用的理想不变的gr {Ö} bner构建的。因此，我们展示了如何利用这种结构来减少表查询的数量和基础场中的操作数量，以恢复表格关系的理想。在像Combinatorics这样的应用程序中，所有这些零术语都使我们猜测许多假关系，这使我们能够大大减少这些错误的猜测。这些算法已经实施，在实验上，它们让我们处理其他无法管理的示例。此外，我们显示了通过偏斜多项式乘法保留哪种锥体和晶格结构。这使我们能够通过计算稀疏的gr {Ö} bner碱基或gr {Ö} bner碱的猜测与多项式系数的猜测加快猜测，或者在有限群体中在偏斜多项式的环中的有限组的作用下，理想不变的基础。
Assuming sufficiently many terms of a n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In many applications, the table terms come along with a structure: for instance, they may be zero outside of a cone, they may be built from a Gr{ö}bner basis of an ideal invariant under the action of a finite group. Thus, we show how to take advantage of this structure to both reduce the number of table queries and the number of operations in the base field to recover the ideal of relations of the table. In applications like in combinatorics, where all these zero terms make us guess many fake relations, this allows us to drastically reduce these wrong guesses. These algorithms have been implemented and, experimentally, they let us handle examples that we could not manage otherwise. Furthermore, we show which kind of cone and lattice structures are preserved by skew polynomial multiplication. This allows us to speed up the guessing of linear recurrence relations with polynomial coefficients by computing sparse Gr{ö}bner bases or Gr{ö}bner bases of an ideal invariant under the action of a finite group in a ring of skew polynomials.
