TITLE:  Algorithms of Computer Algebra.


SPEAKER:  Alexander Mikhalev


          
ABSTRACT:

In the talk we will discuss algorithms for symbolic computation 
in free and finitely presented algebras. We will focus on 
associative algebras, Lie algebras and superalgebras. The 
following types of algorithms will be considered: algorithms 
for linear computation, algorithms for subalgebras of free 
algebras, elementary transformations of sets of elements, 
algorithms to construct standard bases of ideals of free 
algebras and their applications (the theory of Groebner-Shirshov 
bases of ideals of free algebras); algorithms for computation in 
automorphic orbits of elements of free algebras (using free 
differential calculus). This talk is for a general audience.