Next: Example of discovering Up: Theory and more details Previous: NCProcess2 command

In §, we used the notation in conjunction with problems involving an algebra which possessed an involution, . We now make this notion precise.

We start by assuming that there is an involution on the coefficients, say .

By relabelling the knowns and unknowns if necessary, let us suppose that

(1)The polynomial q depends upon the knowns and upon the unknowns where and .
(2) The polynomial q does not depend on the knowns and does not depend on the unknowns .

Let us also suppose that there is an injective map from to and an injective map from to where and .

We now make the assumption which corresponds to the problem involving the algebra with involution:

If the mathematical problem we are trying to investigate involves elements of an algebra with involution, say , and we substitute for and for for and for , then

There is a unique operation from to such that the following four conditions hold:
(1) is additive (i.e., if , then ).
(2) if , then .
(3) for .
(4) for .

Helton
Wed Jul 3 10:27:42 PDT 1996