Algebra and Algorithms for Invariants and Differential Systems
Evelyne Hubert, INRIA Sophia, France
Thursday, February 9, 2006, at U. of Western Ontario.
Abstract:
Group actions are ubiquitous in science and engineering. Their invariants
provide elegant solutions to classification and equivalence problems. From
a computational point of view invariants are used to take into account the
symmetry of a problem, mainly in order to reduce its size.
The requirements for the above approach include:
1. to compute a generating set of invariants and the relations among them
2. to rewrite a problem in terms of those invariants
3. to work in the algebra of invariants.
In this talk I present an ongoing project for finding efficient
differential elimination schemes for symmetric differential systems. I
introduce a class of algebraic invariants that are particularly well suited
for this problem and for which we clarify the above requirements. I shall
focus on a new algorithm to compute rational invariants, a promising side
result of the project.
Part of this talk is based on joint work with I. Kogan and E. Mansfield.
http://www-sop.inria.fr/cafe/Evelyne.Hubert
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