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Riemann Tensor Polynomial Canonicalization by Graph Algebra Extension

Authors:

Yang LiAuthors Info & Claims

ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

Pages 269 - 276

https://doi.org/10.1145/3087604.3087625

Published: 23 July 2017 Publication History

Abstract

Tensor expression simplification is an "ancient" topic in computer algebra, a representative of which is the canonicalization of Riemann tensor polynomials. Practically fast algorithms exist for monoterm canonicalization, but not for multiterm canonicalization. Targeting the multiterm difficulty, in this paper we establish the extension theory of graph algebra, and propose a canonicalization algorithm for Riemann tensor polynomials based on this theory.

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Cited By

Liu JYang SLiu WNi FZhu C(2024)Practical Canonical Labeling of Multi-Digraphs via Computer AlgebraSymmetry10.3390/sym1612163816:12(1638)Online publication date: 11-Dec-2024
https://doi.org/10.3390/sym16121638
Gates SHilsenrath IHilsenrath S(2024)Modern tensor–spinor symbolic algebra algorithms and computing non-closure geometry and holoraumy in 11D, 𝒩=1 supergravityInternational Journal of Modern Physics A10.1142/S0217751X2450118539:31Online publication date: 23-Nov-2024
https://doi.org/10.1142/S0217751X24501185
Shpiz GKryukov A(2021)The Method of Colored Graphs for Simplifying Expressions with IndicesProgramming and Computing Software10.1134/S036176882101010247:1(25-28)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1134/S0361768821010102
Show More Cited By

Index Terms

Riemann Tensor Polynomial Canonicalization by Graph Algebra Extension
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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Published In

cover image ACM Other conferences

ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

July 2017

466 pages

ISBN:9781450350648

DOI:10.1145/3087604

Editor:
Michael Burr
Clemson University, USA
,
General Chair:
Chee K. Yap
New York University, USA
,
Program Chair:
Mohab Safey El Din
University Pierre et Marie Curie, France

Copyright © 2017 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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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 23 July 2017

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ISSAC '17

ISSAC '17: International Symposium on Symbolic and Algebraic Computation

July 23 - 28, 2017

Kaiserslautern, Germany

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Liu JYang SLiu WNi FZhu C(2024)Practical Canonical Labeling of Multi-Digraphs via Computer AlgebraSymmetry10.3390/sym1612163816:12(1638)Online publication date: 11-Dec-2024
https://doi.org/10.3390/sym16121638
Gates SHilsenrath IHilsenrath S(2024)Modern tensor–spinor symbolic algebra algorithms and computing non-closure geometry and holoraumy in 11D, 𝒩=1 supergravityInternational Journal of Modern Physics A10.1142/S0217751X2450118539:31Online publication date: 23-Nov-2024
https://doi.org/10.1142/S0217751X24501185
Shpiz GKryukov A(2021)The Method of Colored Graphs for Simplifying Expressions with IndicesProgramming and Computing Software10.1134/S036176882101010247:1(25-28)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1134/S0361768821010102
Liu J(2019)Block distance invariant method for monoterm canonicalization of Riemann tensor polynomialsACM Communications in Computer Algebra10.1145/3377006.337701953:3(134-137)Online publication date: 17-Dec-2019
https://dl.acm.org/doi/10.1145/3377006.3377019
Shpiz GKryukov A(2019)Canonical Representation of Polynomial Expressions with IndicesProgramming and Computing Software10.1134/S036176881902010545:2(81-87)Online publication date: 1-Mar-2019
https://dl.acm.org/doi/10.1134/S0361768819020105
Niehoff B(2018)Faster tensor canonicalizationComputer Physics Communications10.1016/j.cpc.2018.02.014228(123-145)Online publication date: Jul-2018
https://doi.org/10.1016/j.cpc.2018.02.014
MacCallum M(2018)Computer algebra in gravity researchLiving Reviews in Relativity10.1007/s41114-018-0015-621:1Online publication date: 20-Aug-2018
https://doi.org/10.1007/s41114-018-0015-6

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