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Background on polynomial equations and Ideals

When doing analysis, there is often an algebraic component to the calculations. This algebraic component involves a collection of polynomial equations in a finite number of variables which are to be evaluated at elements of some algebra tex2html_wrap_inline3966 -- the algebra might be n × n matrices, bounded linear transformations on a complex separable Hilbert space or a variety of other algebrasgif. This paper concerns algorithms which assist in transforming the collection of equations into a more suitable form.

In this paper, we will blur the difference between the polynomial equation p = q and the polynomial p - q. An algebraist would say that p is a relation and an analyst would say that p = 0 is a polynomial equation. The difference in language does not lead to problems.

Wed Jul 3 10:27:42 PDT 1996