摘要
Grobner基是符号计算中的基本工具之一 ,在许多实际问题中需要进行Grobner基的转换 .讨论了经线性映射X -AY后Grobner基的转换问题 .首先证明了Grobner基在线性映射下保持基的性质 .然后证明了当且仅当A为可经过行交换化为非退化上三角阵且线性映射与序相容时 ,Grobner基经线性映射仍保持Grobner基的性质 .
Grobner basis is one of basic tools in symbolic computation, and the transformation of Grobner basis is needed in many questions. The transformation question of Grobner basis by linear map X=AY is considered. First, it is proved that Grobner basis keep characters of base through linear map,then it is proved that Grobner basis keep characters of Grobner basis through linear map if and only if the matrix A is a non degenerative upper triangular matrix by changing its rows and the linear map Ф is compatible with the order.
出处
《江西师范大学学报（自然科学版）》
CAS
2001年第3期195-200,共6页
Journal of Jiangxi Normal University(Natural Science Edition)
