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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 -- the algebra might be
*n × n*
matrices, bounded linear transformations
on a complex separable Hilbert space or a variety of
other algebras.
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.

*Helton *

Wed Jul 3 10:27:42 PDT 1996