Rafal Ablamowicz, Professor rablamowicz@tntech.edu ,
Personal page: Sailing Education
Research Interests
Application of Groebner bases to solving engineering problems
Groebner bases for noncommutative algebras like Grassmann
algebras and Clifford algebras (see package GfG )
Hopf algebra of symmetric functions (see package SchurFkt
Applications of category theory to automata theory
Mathematical structure of classical and
generalized
Clifford
algebras for an arbitrary bilinear form and applications in physics Computer algebra (CLIFFORD, Bigebra) and
Clifford
algebra
computations with Maple (see package CLIFFORD/Bigebra )
Application of quaternions and dual quaternions
in robotics: single and double RPR chains, singularity spaces,
workspaces, screw
theory
Hecke algebras (q-Young tableaux,
representations, q-spinors)
Multilinear algebras (Quantum Clifford
algebras, Rota-Stein Cliffordization)
Software
CLIFFORD - A Maple Package for Clifford Algebra
Computations
with Bigebra, SchurFkt, GfG - Groebner for Grassmann, Cliplus, Define,
GTP, Octonion, and code_support
(Copyrights by Rafal Ablamowicz and Bertfried
Fauser) :
Additional packages that use CLIFFORD/Bigebra :
SchurFkt - A Maple
Package for the Hopf Algebra
of Symmetric FunctionsSchurFkt for Maple
10)
GfG - A
Maple package for Computing
Groebner Bases for Ideals in Grassmann Algebras for Maple 11(see GfG for Maple
10)TNB
- A Maple package written by Troy Brachey for computing Groebner GLB
and GLIB bases in Grassmann algebras [a zip file with Maple 11 library
archive containing the TNB package]
Additional packages
SP
- A Maple Package for Symmetric Polynomials for Maple 11 (see SP for
Maple 10 - built into CLIFFORD/Bigebra)RJgrobner
- A Maple Package for Commutative Groebner Bases
for Maple 11 (see RJgrobner
for Maple 10 - built into CLIFFORD/Bigebra)
code_support
- A Maple Package for Maintaining and Manipulating
Help Pages for Maple 11 (see code_support
for Maple 10 - built into CLIFFORD/Bigebra)
How to cite this software and publications citing it:
Publications
Theses Directed
Troy Brachey, Groebner
Basis Algorithms for Grassmann Algebras in a Maple
Package , May
2008
Bennie Hodges: Application of
Category
Theory to Basic Principles of Automata Theory, May 2007
Sean Tunney: On the
Continuous Families of Idempotents in the
Clifford Algebra of the Euclidian Plane, May 2003 Michael Baswell: Clifford Algebra Space
Singularities of a Redundant
Variable Geometry Truss Manipulator , May 2000 (co-directed
with Joe Anderson)
Conferences
45th Annual
Technical
Meeting of the Society of Engineering Science, University of Illinois
at Urbana-Champaign, October 12-15, 2008
Advanced Mathematical Tools: A Frontier Between Mathematics and
Engineering (coming soon)
International Conference of
Numerical Analysis and Applied Mathematics 2008, ICNAAM 2008, Kos,
Greece, 16-20 September 2008 The Third International Conference on Applications of
Geometric Algebra in Computer Science and Engineering, AGACSE'2008
Leipzig, August 24-26, 2008 (coming soon)
ISSAC 2008 -
International Symposium on Symbolic and Algebraic Computation,
Hagenberg, Austria, July 20-23, 2008 ICCA
8:
The 8th Conference on Clifford Algebras and their Applications, 26-30
May 2008, Brazil 44th Annual Technical Meeting
Society of Engineering Science October 21- 24, 2007 ISSAC 2007 - The International
Symposium on Symbolic and Algebraic Computation, Waterloo,
Ontario, Canada, July 29-August 1, 2007 RISC
Summer 2007 at Hegenberg, Linz, Austria Multivariate
Approximation: Theory and Applications MATA 2007, Cancun, Mexico April
26 - May 1, 2007 6th Annual Hawaii
International Conference on Statistics, Mathematics and Related Fields ,
January 17 - 19, 2007, Honolulu Hawaii43rd Annual Technical
Meeting,
Society of Engineering Science , August 13-16th, 2006, PennState,
University ParkISSAC 2006 -
International Symposium on Symbolic and Algebraic Computation , July
9-12, 2006, Genova, ItalySpecial
Semester on Groebner Bases and Related Methods, February - July 2006,
Linz, Austria ICCA 7: The
7th Conference on Clifford Algebras and their Applications in
Mathematical Physics (ICAA 7), Toulouse, May 19-29, 2005 ICCA
6: The
6th Conference on Clifford Algebras and their Applications in
Mathematical Physics, Tennessee Technological University, Cookeville,
May
20-25,
2002
Resources
Institutes:
Encyclopedias, libraries and databases:
Societies and agencies:
Mathematics software:
AXIOM , Maple , Mathematica CLUCalc ,
CoCoA , Macaulay 2 , Maxima FELIX ,
Bergman , FGb , SALSA , SINGULAR Schur Group Theory
Software , MAGMA
Computational Algebra System The Geometer's
Sketchpad , Cinderella
Clifford (geometric) algebra resources:
Other Scientific Resources:
LaTeX resources:
Advanced Courses Taught
MATH 6991 Noncommutative Groebner Bases for Grassmann and
Clifford Algebras (fall 2007)
MATH 6910 Special Topics: Computational Algebraic
Geometry II (fall 2006)
MATH 6910 Special Topics: Computational Algebraic
Geometry I (summer 2006)
MATH 4750/5750 Category Theory of Sets (spring 2006)
MATH 6910 Special Topics: Geometric Algebra and Robotics (fall
2005)
MATH 6910 Special Topics: Clifford Algebras (fall 2004)
MATH 6910 Special Topics: Theory of Quadratic Forms and Clifford
Algebras (summer 2004)
Top of this Page Go to Department
Home Page Last updated: April 14, 2008/ra
