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DEPARTMENT OF MATHEMATICS TECHNICAL REPORT
 

Summary: DEPARTMENT OF MATHEMATICS
TECHNICAL REPORT
SOME APPLICATIONS OF
GRšOBNER BASES
IN ROBOTICS AND ENGINEERING
DR. RAFAL ABLAMOWICZ
DECEMBER 2008
No. 2008-3
TENNESSEE TECHNOLOGICAL UNIVERSITY
Cookeville, TN 38505
Some Applications of Gršobner Bases in Robotics
and Engineering
Rafal Ablamowicz
Abstract Gršobner bases in polynomial rings have numerous applications in geome-
try, applied mathematics, and engineering. We show a few applications of Gršobner
bases in robotics, formulated in the language of Clifford algebras, and in engineer-
ing to the theory of curves, including Fermat and BŽezier cubics, and interpolation
functions used in finite element theory.1
Keywords: BŽezier cubic, Clifford algebra, elimination ideal, envelope, Fermat
curve, Gršobner basis, ideal of relations, interpolation function, left ideal, monomial

  

Source: Ablamowicz, Rafal - Department of Mathematics, Tennessee Technological University

 

Collections: Mathematics