Luu Ba Thang ( I leave)

PhD at Laboratoire J.A.Dieudonne, University of Nice and INRIA, Sophia Antipolis, France Supervisor: Andre Galligo and Co-Supervisor: Laurent Buse Team of Project Galaad

Research Interests: Commutative Algebra, Computational Algebra and Computational Algebraic Geometry.

Matrix-based implicit representation of algebraic curves and surfaces and applications. July 2011.Click
 

Here are some programs which we make to develop the intersection problem between curve/curve, curve/surface and surface/surface. All programs are based on MAPLE 15. We focus on finding the matrix representation of parameterized curves and parameterized surfaces. And after, we develop some techniques in linear algebra to solve the intersection problems. See my paper [4, 6, 7] for more detail.

1. Maple

• Compute mu-basis MUBASIS
  
• Compute matrix representation of curve and surface MATRIXREP
  
• Extract the part regular of a matrix and compute generalized eigenvalues PENCILREDUCTION
  
• Compute the intersection curve/curve, curve/surface INTERSECTION
  
• W -Decomposition, extract the part regular of polynomial matrix and compute the intersection surface/surface WDecomposition
  
Example

• Compute the intersection of two space parameterized curves IntersectionCurve.mw
  
• Compute the intersection of two parameterized surfaces IntersectionSurface
  
• W -Decomposition, extract the part regular of polynomial matrix WDecomposition
  

We also make some programs which are based on MATHEMAGIX (http://www.mathemagix.org/www/main/index.en.html) to develop all above problems. All these programs are included in the current distribution of Mathemagix, in the shape module (mmx/shape/mmx/matrixrepresentation).
Note that MATHEMAGIX is a free computer algebra system under development by ours project team.

2. Mathemagix

• Compute mu-basis mubase
  
• Extract the part regular of non square matrix and computing generalized eigenvalues Pencilregular
  
• Compute the intersection curve/curve, curve/surface and matrices representationCurveSurface
  
• Compute the singular points of curve SingularPoint
  
• Solve the equation polynomial Solve
  
• Compute Extended Euclidean Algorithm EEA
  
Help to use

• An report for explaining my work in Mathemagix Click
  
 

- Postdoc Fellowship of EU-funded Initial Training Network SAGA, National and Kapodistrian University of Athens, Greece, 10/2011-06/2012.
- Scholarship of INRIA, Sophia Antipolis, France, 1/2009-12/2011.
- Vietnam Government Fellowship 09/2008-09/2011.
- Second Prize in the Vietnam National Mathematical Olympiad for students 2000.
- Second Prize in the Vietnam National Mathematical Olympiad for students 1999.
- First Prize in the Hai Duong Province Mathematical Olympiad for students of high school, 1996.
- First Prize in the Hai Duong Province Mathematical Olympiad for pupils of primary school, 1993.

- The surface/surface intersection problem by means of matrix-based representations (Fall School Shape, Geometry and Algebra, Vilnius, Lithuania, Septembre 27-30, 2011). Click
- Solving the curve/curve and curve/surface intersection problems with Mathemagix (SAGA Fall School, 4-8/10/2010, Kolympari, Crete, Greece).Click
- Solving the curve/curve and curve/surface intersection problems with Mathemagix (Seminar Galaad, 21/09/2010, INRIA, France).
- Matrix-based Implicit Representations of Rational Algebraic Curves and Applications. (SAGA Workshop, March 2010, Auron, France). Click
- Singularities of a rational space curves and matrix representation (Seminar Galaad, 10/03/2010,INRIA, France).
- Matrix representation of rational space curves and the problem intersections (Seminar Galaad, 05/02/2010,INRIA, France).
- Curve/Surface intersection problem by means of matrix representation.(SNC'09, August 2009, Kyoto, Japan). Click
- Extension of a result of Huneke and Miller. Conference in Algebra - Geometry - Topology, Ho Chi Minh, Vietnam 2005.
- Several talks at Seminar Algebra, Hanoi National University of Education, 2003-2007. 

- Fall School Shape, Geometry and Algebra, Vilnius, Lithuania, Septembre 27-30, 2011.
- SAGA Fall School, Kolympari, Crete, Greece, October 4-8, 2010.
- The Fifth RISC/SCIENCE Training School in Symbolic Computation, Johannes Kepler University of Linz,Hagenberg, Austria, June 28-July 9, 2010.
- SAGA Workshop, Auron, France, March 2010.
- International Conference on Symbolic-Numeric Computation, Kyoto, Japan, 2009.
- Summer School on Computational Mathematics, Soria, Spain, 2009.
- International Conference on Tensors and Interpolation, Nice, France, 2009.
- International Conference on Number Theory and Related Topics, Hanoi, Vietnam, 2006.
- International Conference on Commutative Algebra, Hanoi, Vietnam, 2006.
- CIMPA School on Commutative Algebra, Hanoi, Vietnam, 2005.
- Conference on Algebra - Geometry - Topology, Ho Chi Minh city, Vietnam, 2005.
- Summer School on Informatics in Algebra Combinatorics and Geometry, Hanoi, Vietnam, 2004.
- Summer School and Conference on Algebraic K- Theory and its applications, ICTP, Trieste, Italy, 2002.