论文信息 - SAGBI and SAGBI-Gröbner Bases over Principal Ideal Domains

SAGBI and SAGBI-Gröbner Bases over Principal Ideal Domains

Abstract Our aim in this paper is to improve on the algorithms for the computation of SAGBI and SAGBI-Grobner for subalgebras of polynomial rings in the special case where the base ring is a principal ideal domain. In addition we will show the existence in general of strong SAGBI bases (the natural analogue of strong Grobner bases) over a PID.

Philippe Loustaunau | Serkan Hosten | William W. Adams | J. Lyn Miller

[1] B. Sturmfels. Gröbner bases and convex polytopes , 1995 .

[2] Rekha R. Thomas,et al. Variation of cost functions in integer programming , 1997, Math. Program..

[3] David K. Smith. Theory of Linear and Integer Programming , 1987 .

[4] DepartmentGeorge Mason UniversityFairfax. Standard Pairs and Group Relaxations in Integer Programming , 1998 .

[5] Rekha R. Thomas. A Geometric Buchberger Algorithm for Integer Programming , 1995, Math. Oper. Res..

[6] David Mumford,et al. What Can Be Computed in Algebraic Geometry , 1993, alg-geom/9304003.

[7] Lyn J. Miller. Analogs of Gröbner Bases in Polynomial Rings over a Ring , 1996, J. Symb. Comput..