scholarly journals The Extension of the GVW Algorithm to Valuation Domains

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Dongmei Li ◽  
Licui Zheng
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Effective Algorithm ◽  
Polynomial Ideals ◽  
Valuation Domains

The GVW algorithm is an effective algorithm to compute Gröbner bases for polynomial ideals over a field. Combined with properties of valuation domains and the idea of the GVW algorithm, we propose a new algorithm to compute Gröbner bases for polynomial ideals over valuation domains in this study. Furthermore, we use an example to demonstrate the improvement of our algorithm.

On generating sets and gröbner bases for polynomial ideals

1992 ◽  
Vol 20 (8) ◽  
pp. 2271-2287 ◽  
Author(s):  
Henrik Bresinsky ◽  
Frank Curtis
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Generating Sets ◽  
Polynomial Ideals

Gröbner Bases for Polynomial Ideals

1992 ◽  
pp. 429-471
Author(s):  
K. O. Geddes ◽  
S. R. Czapor ◽  
G. Labahn
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Polynomial Ideals

scholarly journals Gröbner bases and primary decomposition of polynomial ideals

1988 ◽  
Vol 6 (2-3) ◽  
pp. 149-167 ◽  
Author(s):  
Patrizia Gianni ◽  
Barry Trager ◽  
Gail Zacharias
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Primary Decomposition ◽  
Polynomial Ideals

scholarly journals SHARPER COMPLEXITY BOUNDS FOR ZERO-DIMENSIONAL GRÖBNER BASES AND POLYNOMIAL SYSTEM SOLVING

2011 ◽  
Vol 21 (05) ◽  
pp. 703-713 ◽  
Author(s):  
AMIR HASHEMI ◽  
DANIEL LAZARD
Keyword(s):  
Polynomial System ◽  
Gröbner Bases ◽  
Mean Value ◽  
Arithmetic Mean ◽  
Grobner Bases ◽  
Maximal Degree ◽  
Complexity Bounds ◽  
Polynomial System Solving ◽  
Polynomial Ideals ◽  
Dense Representation

The main purpose of this paper is to improve the bound of complexity of the well-known algorithms on polynomial ideals having complexities polynomial in dn, where d is the maximal degree of input polynomials and n is the number of variables. Instead of this bound, we present the more accurate bound max {S, Dn} where S is the size of the input polynomials in dense representation, and D is the arithmetic mean value of the degrees of input polynomials.

Sign in / Sign up

Export Citation Format

Share Document