Article

Symbolic computation in the homogeneous geometric model with clifford algebra

Author:

Hongbo LiAuthors Info & Claims

ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computation

Pages 221 - 228

https://doi.org/10.1145/1005285.1005318

Published: 04 July 2004 Publication History

Abstract

Clifford algebra provides nice algebraic representations for Euclidean geometry via the homogeneous model, and is suitable for doing geometric reasoning through symbolic computation. In this paper, we propose various symbolic computation techniques in Clifford algebra. The content includes representation, elimination, expansion and simplification. Simplification includes contraction, combination and factorization. We apply the techniques to automated geometric deduction, and derive the conclusion in completely factored form in which every factor is a basic invariant. The efficiency of Clifford algebra in doing geometric reasoning is reflected in the short and readable procedure of deriving it sincere geometric factorization.

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Cited By

Zhang XZhu NHe YZou JQin CLi YLeng T(2024)FGeo-SSS: A Search-Based Symbolic Solver for Human-like Automated Geometric ReasoningSymmetry10.3390/sym1604040416:4(404)Online publication date: 30-Mar-2024
https://doi.org/10.3390/sym16040404
Shao CLi HHuang L(2016)Challenging Theorem Provers with Mathematical Olympiad Problems in Solid GeometryMathematics in Computer Science10.1007/s11786-016-0256-210:1(75-96)Online publication date: 2-Apr-2016
https://doi.org/10.1007/s11786-016-0256-2
Wang RZhang XCao W(2015)Clifford Fuzzy Support Vector Machines for ClassificationAdvances in Applied Clifford Algebras10.1007/s00006-015-0616-z26:2(825-846)Online publication date: 27-Oct-2015
https://doi.org/10.1007/s00006-015-0616-z
Show More Cited By

Index Terms

Symbolic computation in the homogeneous geometric model with clifford algebra
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Representation of mathematical objects

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Published In

cover image ACM Conferences

ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computation

July 2004

334 pages

ISBN:158113827X

DOI:10.1145/1005285

General Chair:
Josef Schicho
RICAM, Austrian Academy of Sciences, Linz, Austria

Copyright © 2004 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 04 July 2004

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ISSAC04: International Symposium on Symbolic and Algebraic Computation

July 4 - 7, 2004

Santander, Spain

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Zhang XZhu NHe YZou JQin CLi YLeng T(2024)FGeo-SSS: A Search-Based Symbolic Solver for Human-like Automated Geometric ReasoningSymmetry10.3390/sym1604040416:4(404)Online publication date: 30-Mar-2024
https://doi.org/10.3390/sym16040404
Shao CLi HHuang L(2016)Challenging Theorem Provers with Mathematical Olympiad Problems in Solid GeometryMathematics in Computer Science10.1007/s11786-016-0256-210:1(75-96)Online publication date: 2-Apr-2016
https://doi.org/10.1007/s11786-016-0256-2
Wang RZhang XCao W(2015)Clifford Fuzzy Support Vector Machines for ClassificationAdvances in Applied Clifford Algebras10.1007/s00006-015-0616-z26:2(825-846)Online publication date: 27-Oct-2015
https://doi.org/10.1007/s00006-015-0616-z
Li HCao Y(2011)On Geometric Theorem Proving with Null Geometric AlgebraGuide to Geometric Algebra in Practice10.1007/978-0-85729-811-9_10(195-215)Online publication date: 2011
https://doi.org/10.1007/978-0-85729-811-9_10
Zou YZhang J(2010)Automated generation of readable proofs for constructive geometry statements with the mass point methodProceedings of the 8th international conference on Automated Deduction in Geometry10.1007/978-3-642-25070-5_13(221-258)Online publication date: 22-Jul-2010
https://dl.acm.org/doi/10.1007/978-3-642-25070-5_13
Li HWang D(2007)A recipe for symbolic geometric computingProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277584(261-268)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277584
Li HXu RZhang N(2004)On miquel's five-circle theoremProceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications10.1007/11499251_18(217-228)Online publication date: 19-May-2004
https://dl.acm.org/doi/10.1007/11499251_18

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