Skip to main content
SpringerLink
Log in

Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

This paper discusses two problems: one is some important theories and algorithms of affine bracket algebra; the other is about their applications in mechanical theorem proving. First we give some efficient algorithms including the boundary expanding algorithm which is a key feature in application. We analyze the characteristics of the boundary operator and this is the base for the implementation of the system. We also give some new theories or methods about the exact division, the representations and structure of affine geometry and so on. In practice, we implement the mechanical auto-proving system in Maple 10 based on the above algorithms and theories. Also we test about more than 100 examples and compare the results with the methods before.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wun W T. Mathematical Mechanization (in Chinese). Beijing: Sci Press, 2003)

    Google Scholar 

  2. Sturmfels B. Algorithms in Invariant Theory. New York: Springer, 1993. 77–93

    MATH  Google Scholar 

  3. White N, Mcmillan T. Cayley Factorization. New York: Proc. ISSAC 88, ACM Press, 1988, 4–8

    Google Scholar 

  4. Whiteley W. Invariant computations for analytic projective geometry. J Symbolic Computation, 11: 549–578 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Li H B. Automated geometric theorem proving, clifford bracket algebra and clifford expansions. In: Qian T, et al. eds. Proceedings of Trends in Mathematics: Advances in Analysis and Geometry. Basel: Birkhauser, 2004, 345–363

    Google Scholar 

  6. Li H B, Wu Y H. Automated theorem proving in projective geometry with cayley and bracket algebras I. Incidence Geometry. J Symbolic Computation, 36: 717–762 (2003)

    Article  MATH  Google Scholar 

  7. Li H B, Wu Y H. Automated theorem proving in projective geometry with cayley and bracket algebras II. Conic geometry. J Symbolic Computation, 36: 763–809 (2003)

    Article  MATH  Google Scholar 

  8. Wu Y H. Bracket Algebra, Affine bracket algebra and mechanical theorem proving. Phd Thesis. Beijing: AMSS, 2001, 9–23

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. China Institute for Actuarial Science (CIAS), Central University of Finance and Economics, Beijing, 100081, China

    Ning Zhang

  2. Academy of Mathematics and Systems Science, Chinese Academy Sciences, Beijing, 100080, China

    Hong-bo Li

Authors
  1. Ning Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong-bo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ning Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10471143)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, N., Li, Hb. Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving. SCI CHINA SER A 50, 941–950 (2007). https://doi.org/10.1007/s11425-007-0076-6

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-007-0076-6

Keywords

MSC(2000)

Search

Navigation