Noether整环上的复合Groebner基

Composed Groebner basis over Noetherian domain

对于Noether整环上n个变元的多项式环中的Groebner基以及m(m≥n)个变元的多项式环中的复合,通过引入S-多项式及合冲条件,证明了当复合与2个不同多项式环上的项序均相容并且是一组由首幂积为幂置换与置换外其余变元幂积的乘积组成的首1多项式时,Groebner基的计算与复合可交换.从而在此条件下,极小Groebner基的计算也与复合可交换.特别地,当m=n时,如果复合是与项序相容的一组首幂积为幂置换的首1多项式,Groebner基的计算与复合可交换.

For Groebner basis in n variables and composition in m （m≥n） variables in a polynomial ring over Noetherian domain, it is proved that Groebner basis computation and composition is commutative if composition is compatible with two term orderings on the different polynomial rings and composition is a lists of monic polynomials with its leading powering products is the products of permuted powering and powering products of other remained variables by using S-polynomial and syzygy condition. Therefore, minimal Groebner basis computation is also commutative with composition under this condition. Especially, Groebner basis computation and composition is commutative if composition is compatible with term orderings and composition is a lists of monic polynomials with its leading powering product is a permuted powering when m = n.