Opportunities for undergraduate research ⋅ Student research projects I’ve directed
CV ⋅ Recent research ⋅ Publications ⋅ Preprints ⋅ Posters
Talks ⋅ Software ⋅ Associations ⋅ Service
Illustrations of research

(Some information needs updating. This web page has been moved twice, so some links are likely broken — contact me if so.)

Curriculum Vitæ

Research interests:

combinatorial games	fraction-free computation of determinants	Gröbner basis computation
Ideal Nim (a generalization of Chomp)	methods of Dodgson and Bareiss Double-Crossing Method Extended Dodgson’s Method	dynamic algorithms signature-based algorithms (inspired by Faugère’s F5) extended criteria for skipping S-polynomial reduction

Sample posters:

Posters are unrefereed, and by their nature contain out-of-date information.

• ECCAD 2012: Reducing the size and number of linear programs in a dynamic Gröbner basis algorithm
• LETTERS day 2011: Signature-based algorithms to compute Gröbner bases
• LETTERS day 2008: Determinants in Wonderland (with students Deanna Leggett and Ashley Sanders)
• ECCAD 2007: A sufficient and necessary criterion for Buchberger’s chain condition
  (Note: Theorems 1 and 2 have a typo; should read "implies" not "iff")
• ECCAD 2003: Combinatorial Criteria for S-polynomial reduction

Refereed publications:

2020

A dynamic algorithm to compute Gröbner bases
Applicable Algebra in Engineering, Communication and Computing, vol. 31 (2020) combined issue 5-6 pgs. 411-434
The final publication is available at Springer via 10.1007/s00200-020-00450-y, or click on the title for a view-only version

2017

• Exploring the Dynamic Buchberger Algorithm

  John Perry
  ISSAC '17 Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, 2017
• Corrigendum to “The F5 criterion revised” (joint with Alberto Arri)
  Journal of Symbolic Computation, vol. 82 (2017) pgs. 164--165, DOI 10.1016/j.jsc.2016.12.002

2016

• Androids Armed With Poisoned Chocolate Squares: Ideal Nim and Its Relatives (joint with Haley Dozier)
  Mathematics Magazine, October 2016, vol. 89 no. 4 pgs. 235-250
  (Zoltán Kovács wrote a Web app for one relative; try it out!)

2014

• Reducing the size and number of linear programs in a dynamic Gröbner basis algorithm (joint with Massimo Caboara)
  Applicable Algebra in Engineering, Communication and Computing, vol. 25 (2014) issue 1 pgs. 99--117
  (arxiv draft, somewhat denser than accepted version)
  The final publication is available at Springer via http://dx.doi.org/10.1007/s00200-014-0216-5, or click on the title for a view-only version

2011

• The F5 criterion revised (joint with Alberto Arri)
  Journal of Symbolic Computation, vol. 46 (2011) pgs. 1017-1029, DOI 10.1016/j.jsc.2011.05.004
  (arxiv draft, proofs for at least one theorem different from publication version)
• Modifying Faugère’s F5 algorithm to ensure termination (arxiv draft)
  Christian Eder, Justin Gash, John Perry
  ACM Communications in Computer Algebra, 2011

• Signature-based algorithms to compute Gröbner bases (arxiv corrected draft)
  Christian Eder, John Edward Perry
  ISSAC ’11 Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011
• Generalizing Dodgson’s method: a "double-crossing" approach to computing determinants (joint with Deanna Leggett and Eve Torrence)
  College Mathematics Journal, January 2011, vol. 42 no. 1 pgs. 43-54
  (a typo-filled arxiv draft)

2010

• F5C: a variant of Faugère’s F5 algorithm with reduced Gröbner bases (with Christian Eder)
  Journal of Symbolic Computation, December 2010, vol. 45 issue 12 pgs. 1442-1458, DOI 10.1016/j.jsc.2010.06.019
• An Extension of Buchberger’s Criteria for Gröbner basis decision
  London Mathematical Society Journal of Computation and Mathematics, vol. 13 (2010) pgs. 111-129, DOI 10.1112/S1461157008000193)

2007

• Are Buchberger’s Criteria necessary for the chain criterion?  (joint with Hoon Hong)
  Journal of Symbolic Computation, July 2007, vol. 42 issue 7 pgs. 717-732, DOI 10.1016/j.jsc.2007.02.002 (accepted author’s manuscript: PDF)

2005

• Combinatorial Criteria for Gröbner Bases (PhD dissertation: PDF)

Preprints:

Preprints on arxiv.org have not been refereed, unless otherwise noted. My page on arxiv is here.

• F4/5 (joint with Martin Albrecht)

More on the way...

Students:

• Undergraduate students
• Haley Dozier, Ideal Nim (2013-2014)
• Matthew Dixon, Tropical Mathematics (2010)
• Lorrin Debenport, Triangularizing matrices without swapping columns, Honors Thesis (2011)
• Elisabeth Palchak, A criterion for identifying stressors in non-linear equations using  Gröbner bases, Honors Thesis (2010)
  (Lisa also participated in an REU at the University of Georgia)
• Ashley Sanders, College Math Journal Problems 866 and 871, an implementation of a double-crossing method of computing determinants (2008-2009)
• Deanna Leggett, Dodgson’s method of computing determinants (2007-2008), see also this preprint
• Courtney Bright, Factors impacting the poor performance of mathematics students in the United States, Honors Thesis (2008)
• Lenton McLendon, Introduction to Gröbner bases (2007)
• Jonathan O’Rourke, Universal Algebra, with Dr. Lee (2006)
• Graduate students
• Shannon Ryle, PhD student (2014, changed adviser)
• Deanna Leggett, Fraction-free computation of determinants, Master’s Thesis (2011)
  (Deanna’s paper won first prize at the 2011 meeting of the LA/MS Section of the MAA)
• Miao Yu, An F4-style Involutive Basis algorithm, Master’s Thesis (2010)
  (Miao’s paper won first prize at the 2010 meeting of the LA/MS Section of the MAA)

Samples of talks:

• A dynamic F4 algorithm (a much longer version is available as Dynamic Gröbner basis algorithms)
• The skeletons you find in your ideal’s closet (updated for ACA 2014)
• Border vectors in a dynamic Gröbner basis algorithm
• Nim^∞
• From Gauss to Gröbner Bases
  (an introduction to Gröbner Bases, given at the University of Southern Mississippi’s Colloquium on Pure and Applied Mathematics as well as several other institutions)
• Criteria on Leading Terms for S-polynomial Representations
  (a more detailed view of my research, originally given to the symbolic computation research group at Universität Passau)
• Understanding and Implementing F5
  (given at Universität Kaiserslautern, March 2008)
• Conference talks:
• LA/MS Section of the MAA, Oxford, MS: Geometry of Hilbert polynomials and Gröbner bases
• Western Florida MAA meeting, Pensacola, FL: Determinants in Wonderland
  (joint research with two undergraduate students, Deanna Leggett and Ashley Sanders; see poster above)
• ACA 2004, Beaumont, TX: Gröbner Basis for Two Polynomials
• ACA 2005, Nara, Japan: Combinatorial Criteria for Gröbner Bases (Young Researchers’ Session)
• NCSU Symbolic Computation Seminar:
• When can we skip S-polynomial Reduction?
  
• NCSU Graduate Student Algebra Seminar
• Combinatorial Criteria for Groebner Bases
• Other talks given:
  • LA/MS Sectional Meeting (2007, 2009)
  • Louisiana State University Algebra Seminar (2007)
  • Mississippi State University Undergraduate Mathematics Seminar (2007)
  • Seton Hall University Mathematics Department (2007)
  • Symbolic Computation Research Group, Moscow State University, Russia (2005)

Software:

All software is open source, unless otherwise noted. I contribute to other projects when I can, and have in the past contributed material to LyX (at least one document format), jEdit (format for the Maple language), and Sage (see here, but mostly I contributed to the MILP and Singular modules).

Research-oriented

• Dynamic Gröbner basis computation with new criteria
• DynGB
  • (latest) upload of 14 March 2017 corrects errors in Makefile; provides a few enhancements hither, thither, and yon; and corrects an error in geobucket construction that I thought I fixed with the 11 Feb update, though in fact I merely made it worse without noticing
  • upload of 11 February 2017 corrects errors in examples that sometimes caused a hang
• dynamic_algorithm.pyx
  uploaded 2 November 2012
• Embedded Vector Analysis
• Sage class and documentation
• online documentation (opens in new window)
• "Toy/demonstration" implementations of F5 based on this pseudocode and this variant (last updated January 2009)
• in Singular (joint work with Christian Eder)
• f5ex.lib
  uploaded November 2008; revised January 2009; latest version June 2009
  (example systems; you need this or the other libraries will complain)
• f5_library.lib
  uploaded May 2008; revised January 2009; latest version June 2009
  (F5, F5R, and F5C: use commands basis, basis_r, and basis_c)
• f5r_library.lib
  uploaded November 2008; obsolete (incorporated into f5_library.lib)
• f5c_library.lib
  uploaded November 2008; obsolete (incorporated into f5_library.lib)
• Changes to Till Steger’s Magma implementation,
  which when implemented cause it to terminate on the non-terminating example in that implementation
  uploaded 13 June 2009
  
• in Sage
• f5_arri.py
  uploaded December 2010
• staggered_linear_basis.py
  uploaded December 2010
• f5.py
  uploaded November 2008; latest version June 2009 (there was a bug in the January 2009 version)
  (primarily Martin Albrecht’s code)
• f5.pyx
  uploaded November 2008
  (entirely Simon King’s code)
• f5_sugar.py
  uploaded November 2008
  (an experimental version based on Albrecht’s code to see whether F5 and Sugar would play together; unfortunately this will remain slow unless I find a way to make Sage and/or Singular report the quotients from polynomial division, not just the remainder)
• in Maple: F5_module.mw
  uploaded July 2007; latest version 26 September 2007
  (this version is quite slow and unmaintained)
• Maple:
  • plotacceptableregions3d.mpl
    A Maplet to plot regions that satisfy the criterion described in the joint paper with Hoon Hong, above. Public domain.
    last update/big fix: 14 September 2004
    
  • GBDetection.mw
    A Maple worksheet and module implementing a criterion for detection of a Gröbner basis of two polynomials, using an algorithm from the dissertation above.
    last update/bug fix: 19 November 2007
    
  • efc_buchberger_module.mw
    An implementation of Buchberger’s algorithm, using a new criterion for skipping S-polynomial reductions from a paper I have submitted for publication. The most recent version includes a comparison with the Gebauer-Möller algorithm. GPL.
    uploaded 10 July 2007; latest version 23 November 2007
    
• SmartEiffel:
(requires the 1.1 version of the SmartEiffel compiler)
• SPolys.tar.gz
  Public domain.
  last update/bug fix: 12 August 2004
  (This has seen some work and upgrading since then, but I haven’t checked the new version for release. I’ll do that if someone asks.)
• html_css scripts for SmartEiffel’s short tool 

Teaching-oriented

Apps for Android devices

• Chinese Remainder Clock (based on an idea of Antonella Perucca)
• Droid Nim
• Ideal Nim

Associations:

• American Mathematical Society (in the past)
• Mathematical Association of America
• Assocation for Computing Machinery
  (not the whole thing, actually, but SIGSAM: Special Interest Group for Symbolic and Algebraic Manipulation)
• Symbolic Solutions Group (in the past)

Past Service:

• coordinator, NCSU Graduate Algebra Seminar, Fall 2001
  

Illustrations of research:

• Animated GIFs
  • Two-dimensional computation of a Gröbner basis
  • Three-dimensional illustration of monomials that can satisfy Extended Buchberger criterionn
  • Two-dimensional illustration of signature-redundant criterion

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If you have questions or suggestions or bug reports, please do contact me.