论文标题
关于泰特代数的多项式理想和过度融合
On Polynomial Ideals And Overconvergence In Tate Algebras
论文作者
论文摘要
在本文中，我们研究了泰特代数中多项式或过度会议序列跨越的理想。使用用于计算TATE gr {Ö} bner碱基的最新算法，即使输入是多项式，输出的大小也会以所需的精度增长，无论是在系数的大小和系列支持的大小方面。我们证明，由多项式跨越的理想承认由多项式制成的泰特gr {Ö} bner基础，我们提出了一种算法，利用Mora的弱正常形式算法来计算它。结果，该算法的输出的大小以精度线性增长。遵循相同的想法，我们提出了一种算法，该算法计算了过度融合系列的理想基础。最后，我们证明了泰特代数中多项式理想的通用分析gr {Ö} Bner的存在，与所有收敛半径兼容。
In this paper, we study ideals spanned by polynomials or overconvergent series in a Tate algebra. With state-of-the-art algorithms for computing Tate Gr{ö}bner bases, even if the input is polynomials, the size of the output grows with the required precision, both in terms of the size of the coefficients and the size of the support of the series. We prove that ideals which are spanned by polynomials admit a Tate Gr{ö}bner basis made of polynomials, and we propose an algorithm, leveraging Mora's weak normal form algorithm, for computing it. As a result, the size of the output of this algorithm grows linearly with the precision. Following the same ideas, we propose an algorithm which computes an overconvergent basis for an ideal spanned by overconvergent series. Finally, we prove the existence of a universal analytic Gr{ö}bner basis for polynomial ideals in Tate algebras, compatible with all convergence radii.
