K(■)上可解多项式代数中左Grbner基的计算

Computation of Left Grbner Basis in Solvable Polynomial Algebras on K(■)

给定域K的单代数扩域K(■)上可解多项式代数A=K(■)[a1,…,an],设A的子代数A0=K[a1,…,an]是K上可解多项式代数.通过考察A与多项式代数A0[x]之间的结构关系,给出将A中左Grbner基的计算转换为A0[x]中左Grbner基计算的有效方法.

Let A=K （ ）[a 1 ,…,a n ]be a solvable polynomial algebra on a simple algebraic extension K （ ）of the field K ,and the subalgebra A0=K [a 1 ,…,a n ]of A be a solvable polynomial algebra on K .The structural relation between A and the polynomial algebra A0 [x]shows the computation of left Grobner bases in A is effectively converted to the computation of left Grobner bases in A0 [x].