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Cayley factorization and a straightening algorithm

Cayley factorization and a straightening algorithm Acta Applicandae Mathematicae 21: 163-184, 1990. 163 © 1990 Kluwer Academic Publishers. Printed in the Netherlands. CAYLEY FACTORIZATION AND A STRAIGHTENING ALGORITHM Three talks presented to the Computational Algebra Seminar Department of Mathematics, University of Rome "Tor Vergata" May 9-11, 1990 by Neil L. White Department of Mathematics, University of Florida, Gainesville, U.S.A. 1. THE CAYLEY FACTORIZATION PROBLEM AND ITS APPLICATIONS The Cayley Algebra An important problem in computer-aided geometric reasoning is to automatically find geometric interpretations for algebraic expressions. For projective geometry this question caaa be reduced to the Cayley factorization problem. Before describ ing this problem, we give a brief introduction to the Cayley algebra for those readers not already familiar with it. The Cayley algebra is essentially the same as the classical Grassmann algebra. This algebra provides projectively invariant algebraic interpretations of synthetic geometric statements. A more thorough ex- position may be found in Barnabei et al. (1985), Doubilet et al. (1974), ()r Rora & Stein (1976). Let V be a vector space of dimension d over a field F of Chalracteristic z(wo. Let A(V) denote the exterior algebra of V We will write the exterior product in A(V) as V rather than the usual A, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Cayley factorization and a straightening algorithm

White, Neil
Acta Applicandae Mathematicae , Volume 21 (2) – May 7, 2004
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References (19)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00053296
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae Mathematicae 21: 163-184, 1990. 163 © 1990 Kluwer Academic Publishers. Printed in the Netherlands. CAYLEY FACTORIZATION AND A STRAIGHTENING ALGORITHM Three talks presented to the Computational Algebra Seminar Department of Mathematics, University of Rome "Tor Vergata" May 9-11, 1990 by Neil L. White Department of Mathematics, University of Florida, Gainesville, U.S.A. 1. THE CAYLEY FACTORIZATION PROBLEM AND ITS APPLICATIONS The Cayley Algebra An important problem in computer-aided geometric reasoning is to automatically find geometric interpretations for algebraic expressions. For projective geometry this question caaa be reduced to the Cayley factorization problem. Before describ ing this problem, we give a brief introduction to the Cayley algebra for those readers not already familiar with it. The Cayley algebra is essentially the same as the classical Grassmann algebra. This algebra provides projectively invariant algebraic interpretations of synthetic geometric statements. A more thorough ex- position may be found in Barnabei et al. (1985), Doubilet et al. (1974), ()r Rora & Stein (1976). Let V be a vector space of dimension d over a field F of Chalracteristic z(wo. Let A(V) denote the exterior algebra of V We will write the exterior product in A(V) as V rather than the usual A,

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Acta Applicandae Mathematicae – Springer Journals

Published: May 7, 2004

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