Main presenter			Co-presenter(s)
Name :	Dr. Jianong Zhou		Name:
E-mail:	jnzhou@hotmail.com		E-mail:
Institution or Company:	University of Ottawa		Name:
Department:	NCCT Laboratory		E-mail:
City:	Ottawa		Name:
State/Province:	ON		E-mail:
Country:	Canada		Name:
Type of presentation:	Lecture :  25 minutes.		E-mail:
Conference strand and number:	Derive & TI-CAS  ,    Number: D08		Schedule:   Room:	Friday, 11h30   1520
Related website:
Title of presentation:	The Combinatorial Matrix Approach on Symbolic Polynomial Systems
Abstract:
A new approach(The Combinatorial Matrix Approach) to eliminate variables on symbolic polynomial systems will be presented. It is proved that in the cases of a polynomial systems with bi-variable two degrees or with bi-variable three degrees it is more efficient than other methods such as the Wu’s Elimination and the Grobner Bases Approach even the Dixon approach. We know that, in computer algebra, to efficiently eliminate the variables in a symbolic polynomial system is very crucial to a computer algorithm and a software to solve the realistic problems. For example, in machine proving and in computer automated reasoning, there are a bunch of symbolic polynomial systems in which the variables needed to be eliminated. Some of the problems are difficult to be solved with the existed eliminating methods such as Wu’s elimination and the Grobner Bases Approach. The Combinatorial Matrix Approach focuses on how to derive a linear symbolic system from a nonlinear polynomial system. Then solve the equivalent linear system instead of the nonlinear system. If an algebraic software is implemented with the Combinatorial Matrix Approach to the variable elimination algorithm, it will significantly improve the performance of the software. It will play an important role in automated reasoning and in math educational software products.