Skip to main content
SpringerLink
Log in

Normalization of Indexed Differentials Based on Function Distance Invariants

  • Conference paper
  • First Online:
Computer Algebra in Scientific Computing (CASC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10490))

Included in the following conference series:

Abstract

This paper puts forward the method of function distance invariant, and develops an efficient normalization algorithm for indexed differentials. The algorithm allows us to determine the equivalence of indexed differentials in , and is mainly based on two algorithms. One is an index replacement algorithm. The other is a normalization algorithm with respect to monoterm symmetries, whose complexity is lower than known algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Fulling, S.A., King, R.C., Wybourne, B.G., Cummins, C.J.: Normal forms for tensor polynomials: I. The Riemann tensor. Class. Quantum Grav. 9, 1151–1197 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Christensen, S., Parker, L.: MathTensor, A System for Performing Tensor Analysis by Computer. Addison-Wesley, Boston (1994)

    Google Scholar 

  3. Ilyin, V.A., Kryukov, A.P.: ATENSOR-REDUCE program for tensor simplification. Comput. Phys. Commun. 96, 36–52 (1996)

    Article  MATH  Google Scholar 

  4. Jaén, X., Balfagón, A.: TTC: symbolic tensor calculus with indices. Comput. Phys. 12, 286–289 (1998)

    Article  Google Scholar 

  5. Portugal, R.: An algorithm to simplify tensor expressions. Comput. Phys. Commun. 115, 215–230 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Portugal, R.: Algorithmic simplification of tensor expressions. J. Phys. A: Math. Gen. 32, 7779–7789 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Portugal, R.: The Riegeom package: abstract tensor calculation. Comput. Phys. Commun. 126, 261–268 (2000)

    Article  MATH  Google Scholar 

  8. Balfagón, A., Jaén, X.: Review of some classical gravitational superenergy tensors using computational techniques. Class. Quantum Grav. 17, 2491–2497 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Manssur, L.R.U., Portugal, R., Svaiter, B.F.: Group-theoretic approach for symbolic tensor manipulation. Int. J. Mod. Phys. C. 13, 859–880 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Manssur, L.R.U., Portugal, R.: The Canon package: a fast kernel for tensor manipulators. Comput. Phys. Commun. 157, 173–180 (2004)

    Article  MATH  Google Scholar 

  11. Martín-García, J.M., Portugal, R., Manssur, L.R.U.: The Invar tensor package. Comput. Phys. Commun. 177, 640–648 (2007)

    Article  MATH  Google Scholar 

  12. Martín-García, J.M., Yllanes, D., Portugal, R.: The Invar tensor package: differential invariants of Riemann. Comput. Phys. Commun. 179, 586–590 (2008)

    Article  MATH  Google Scholar 

  13. Liu, J., Li, H.B., Zhang, L.X.: A complete classification of canonical forms of a class of Riemann tensor indexed expressions and its applications in differential geometry (in Chinese). Sci. Sin. Math. 43, 399–408 (2013)

    Article  Google Scholar 

  14. Liu, J., Li, H.B., Cao, Y.H.: Simplification and normalization of indexed differentials involving coordinate transformation. Sci. China Ser. A. 52, 2266–2286 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Liu, J.: Simplification and normalization of indexed polynomials. Ph.D. Thesis, Chinese Academy of Sciences, Beijing (2009)

    Google Scholar 

Download references

Acknowledgements

The author is grateful to the reviewers for helpful comments. This work was supported by Natural Science Foundation of Shanghai (15ZR1401600).

Author information

Authors and Affiliations

  1. Department of Systems Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Jiang Liu

Authors
  1. Jiang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiang Liu .

Editor information

Editors and Affiliations

  1. Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Liu, J. (2017). Normalization of Indexed Differentials Based on Function Distance Invariants. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2017. Lecture Notes in Computer Science(), vol 10490. Springer, Cham. https://doi.org/10.1007/978-3-319-66320-3_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66320-3_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66319-7

  • Online ISBN: 978-3-319-66320-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation