scholarly journals Bezout's theorem and Cohen-Macaulay modules

2001 ◽  
Vol 237 (2) ◽  
pp. 373-394 ◽  
Author(s):  
J. Migliore ◽  
U. Nagel ◽  
C. Peterson
Keyword(s):  
Bézout’S Theorem

Converse to Bezout’s Theorem

1999 ◽  
pp. 171-191
Author(s):  
Hubert Flenner ◽  
Liam O’Carroll ◽  
Wolfgang Vogel
Keyword(s):  
Bézout’S Theorem

Complexity of Bezout’s Theorem IV: Probability of Success; Extensions

1996 ◽  
Vol 33 (1) ◽  
pp. 128-148 ◽  
Author(s):  
Michael Shub ◽  
Steve Smale
Keyword(s):  
Probability Of Success ◽  
Bézout’S Theorem

A short Proof of Bezout's Theorem in P2

2010 ◽  
Vol 38 (7) ◽  
pp. 2585-2587
Author(s):  
R. V. Gurjar ◽  
A. K. Pathak
Keyword(s):  
Short Proof ◽  
Bézout’S Theorem

scholarly journals Constraint Equations for a Planar Parallel Platform

2021 ◽  
Author(s):  
◽  
Amani Ahmed Otaif
Keyword(s):  
Gröbner Basis ◽  
Linear Constraints ◽  
Grobner Basis ◽  
Real Solutions ◽  
Constraint Equations ◽  
Kinematic Mapping ◽  
Univariate Polynomials ◽  
Forward Kinematic Problem ◽  
Bézout’S Theorem ◽  
Forward Kinematic

<p>The aim of this thesis is to apply the Grünwald–Blaschke kinematic mapping to standard types of parallel general planar three-legged platforms in order to obtain the univariate polynomials which provide the solution of the forward kinematic problem. We rely on the method of Gröbner basis to reach these univariate polynomials. The Gröbner basis is determined from the constraint equations of the three legs of the platforms. The degrees of these polynomials are examined geometrically based on Bezout’s Theorem. The principle conclusion is that the univariate polynomials for the symmetric platforms under circular constraints are of degree six, which describe the maximum number of real solutions. The univariate polynomials for the symmetric platforms under linear constraints are of degree two, that describe the maximum number of real solutions.</p>

scholarly journals A note on Bézout's theorem

2005 ◽  
Vol 87 ◽  
pp. 219-227 ◽  
Author(s):  
Sławomir Rams ◽  
Piotr Tworzewski ◽  
Tadeusz Winiarski
Keyword(s):  
Bézout’S Theorem
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