James Murdock: "An algorithm to produce normal form modules"
Ames, Iowa State University, USA

When the Lie group SL(2) acts on a vector space, it induces actions on the functions and vector fields on the space. Classical invariant theory studies the ring of functions fixed by the action; it can be expressed as a quotient of a polynomial ring by an ideal, and the structure of this ring can be expressed by Gröbner basis theory. Vector fields fixed by the appropriate action are called equivariants, and form a module over the ring of invariants. An algorithm will be given to convert a Gröbner basis description of the ring of invariants into a Gröbner basis description of the module of equivariants. (The algorithm should be easily implementable using a symbolic processing system.) The problem is equivalent to the problem of normal forms for dynamical systems near a rest point when the linear part is nilpotent.