In this paper we mainly discuss that SAGBI basis under composition of polynomials.Poly-nomial composition is the operation of replacing the variables of a polynomial with otherpolynomials.The main question of this pap...In this paper we mainly discuss that SAGBI basis under composition of polynomials.Poly-nomial composition is the operation of replacing the variables of a polynomial with otherpolynomials.The main question of this paper is:Does there exists a decision procedurethat will determine whetber a given composition commutes with SAGBI basis computationunder a given term ordering?We will give a better answer(using elementary rational rowtransformations of matrice).展开更多
The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were...The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were got. These relations solve a natural question: how to determine the generating set of G(B) and B from any given generating set of B. Based on these some equivalent conditions for the existence of finite SAGBI bases can be got.展开更多
文摘In this paper we mainly discuss that SAGBI basis under composition of polynomials.Poly-nomial composition is the operation of replacing the variables of a polynomial with otherpolynomials.The main question of this paper is:Does there exists a decision procedurethat will determine whetber a given composition commutes with SAGBI basis computationunder a given term ordering?We will give a better answer(using elementary rational rowtransformations of matrice).
文摘The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were got. These relations solve a natural question: how to determine the generating set of G(B) and B from any given generating set of B. Based on these some equivalent conditions for the existence of finite SAGBI bases can be got.
