skip to main content
10.1145/1073884.1073911acmconferencesArticle/Chapter ViewAbstractPublication PagesissacConference Proceedingsconference-collections
Article

Schur partition for symmetric ternary forms and readable proof to inequalities

Published: 24 July 2005 Publication History

Abstract

In this paper, we give a way to partition the ternary symmetric forms. Based on this method, we get a sufficient condition for ternary form to be positive semi-definite. At the end of the paper, we will show the application of the partition.

References

[1]
Baoqian Liu: BOTTEMA, what we have seen--the new theory, new method and new result of the research on triangle inequalities. Lhasa: Tibet People Press, 2003.(In Chinese)]]
[2]
O. Bottema,et al., Geometric Inequalities, Wolters-Noordhoff Publishing, Groningen, The Neherlands(1969).]]
[3]
Bruce Reznick, Extremal psd forms with few terms Duke Math.J. 45, pp. 363--374(1978).]]
[4]
Bruce Reznick, Some Concrete Aspects of Hilbert's 17th Problem Contemporary Mathematics,2000 253: pp. 251C272.]]
[5]
G. E. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition, In: Automata Theory and Formal Languages (Brakhage,H.,ed.), LNCS 33, pp. 134--165. Springer, Berlin Heidelberg(1975).]]
[6]
D.Hilbert, Über die Darstellung definiter Formen als Summe von Formenquadraten Math. Ann.32 pp.342--350(1888).]]
[7]
E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Hamb. Abh. 5(1927), 100--115.]]
[8]
G. H. Hardy, J. E. Littlewood, and G. Póolya, Inequalities (O.Shisha,Ed.), pp.--224, Academic Press, New York(1967).]]
[9]
http://guestbook.nease.net/read.php?owner=zgbdsyjxz&page=1&commentID=1100526260(in Chinese).]]
[10]
Jichang Kuang: The useful inequationsthe third edtion. Shandong Science and Technology Press (2004.1).(in Chinese)]]
[11]
M. D. Choi, T. Y. Lam and Bruce Reznick, Real zeros of positive semidefinite forms, I Math. Z. 171 pp.1--26(1980).]]
[12]
M. D. Choi, T. Y. Lam and Bruce Reznick, Even Symmetric Sextics, Math.Z. 195, 559--580(1987).]]
[13]
A. Tarski, A decision method for elementary algebra and geometry, The RAND Corporation, Santa Monica(1948)]]
[14]
Vlad Timofte, On the positivity of symmetric polynomial functions. Part I: General results, J. Math. Anal. Apple. 284, 174--190(2003).]]
[15]
William R. Harris, Real Even Symmetric Ternary Forms, Journal of Algebra 222,204--245(1999).]]
[16]
L. Yang, Xia Shihong, Automated proving for a class of constructive geometric inequalities, Chinese J. Computer,26(7), pp.769--778(2003).]]
[17]
L. Yang, Zhang J, A practical program of automated proving for a class of geometric inequalities, Automated Deduction in Geometry, Lecture Notes in Artificial Intelligence 2061, pp.41--57, Springer-Verlag, (2001).]]
[18]
L. Yang, Recent advances in automated theorem proving on inequalities, J. Comput. Sci. & Technol., 14:5, pp.434--446(1999).]]
[19]
L. Yang, A Dimension-Decreasing Algorithm with Generic Program for Automated Inequality Proving. High Technology Letters (Chinese ed.), 8:7, 20--25(1998)]]

Cited By

View all

Index Terms

  1. Schur partition for symmetric ternary forms and readable proof to inequalities

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation
    July 2005
    388 pages
    ISBN:1595930957
    DOI:10.1145/1073884
    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]

    Sponsors

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 24 July 2005

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. Schur partition
    2. positive semi-definite
    3. symmetric inequality
    4. ternary symmetric form

    Qualifiers

    • Article

    Conference

    ISSAC05
    Sponsor:

    Acceptance Rates

    Overall Acceptance Rate 395 of 838 submissions, 47%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)1
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 14 Sep 2024

    Other Metrics

    Citations

    Cited By

    View all

    View Options

    Get Access

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media