【摘要】 Grbner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Grbner基的转换。讨论了经变元的线性变换φ:k[x₁,…,x_n]→k[x₁,…,x_n]后Grbner基的转换问题。证明了Grbner基在这种变换下保持基的性质。并证明了当变换矩阵为可经过行交换化为非退化上三角阵且变换后k[x₁,…,x_n]的序与原有序相容时,Grbner基经变换后仍保持Grbner基性质。更多还原

【Abstract】 Grobner basis is one of basic tools in symbolic computation, and the transformation of Grobner basis is needed in many practical questions. The transformation question of Grobner basis by linear map: φX→AX is considered. First, it is proved that Grobner basis keep characters of base through linear map. Then it is proved that Grobner basis keeps characters of Grobner basis through linear map if the matrix A is a non-degenerative upper-triangular matrix by changing its rows and the linear map φ is compatible with the order.更多还原