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 , thenThere 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 .

Wed Jul 3 10:27:42 PDT 1996