scholarly journals Dimension-dependent bounds for Gröbner bases of polynomial ideals

2013 ◽  
Vol 49 ◽  
pp. 78-94 ◽  
Author(s):  
Ernst W. Mayr ◽  
Stephan Ritscher
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Polynomial Ideals

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.

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