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by Hongbo Li

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Author: Hongbo Li
ISBN: 9812708081
Language: English
Pages: 518 pages
Category: Mathematics
Publisher: World Scientific Pub Co Inc (March 10, 2008)
Rating: 4.7
Formats: lit rtf azw doc
FB2 size: 1232 kb | EPUB size: 1284 kb | DJVU size: 1993 kb
Sub: Math

This book contains the author and his collaborators' most recent, original development of Grassmann Cayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries.

This book contains the author and his collaborators' most recent, original development of Grassmann Cayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras Cayley bracket algebra, conformal geometric algebra, and null bracket algebra for highly efficient geometric computing.

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The first several sections of all chapters can also be used as an undergraduate course on Clifford algebras. Throughout, the book features a host of worked out examples and gives a very unified systematic presentation of a wide variety of material.

Clifford Algebra to Geometric Calculus. Invariant Algebras and Geometric Reasoning Symbolic geometric computing based on invariant algebras can alleviate this difficulty. Invariant Algebras and Geometric Reasoning. Automatic Proving of Geometric Theorems. Hongbo Li. In classical invariant theory, the Gr"obner base of the ideal of syzygies and the normal forms of polynomials of invariants are two core contents. To improve the performance of invariant theory in symbolic computing of classical geometry, advanced invariants are introduced via Clifford product. Symbolic geometric computing based on invariant algebras can alleviate this difficulty.

This book contains the author and his collaborators' most recent, original development of GrassmannOCoCayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras OCo Cayley bracket algebra, conformal geometric algebra, and null bracket algebra OCo for highly efficient geometric computing. The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics OCo among them, GrassmannOCoCayley algebra and Geometric Algebra.

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Hongbo Li. Conference paper. Invariant algebras often perform well in meeting the two expectations for relatively simple geometric problems. First Online: 16 April 2016.

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In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form. Some authors restrict this to the case. The universal geometric algebra. It has a nondegenerate signature.

It includes two of the three advanced invariant algebras - Cayley bracket algebra, conformal geometric algebra, and null bracket algebra - for highly efficient geometric computing

It includes two of the three advanced invariant algebras - Cayley bracket algebra, conformal geometric algebra, and null bracket algebra - for highly efficient geometric computing.

The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics — among them, Grassmann-Cayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries.This book contains the author and his collaborators' most recent, original development of Grassmann-Cayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras — Cayley bracket algebra, conformal geometric algebra, and null bracket algebra — for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide.