Example 37.1 Suppose you are working with matrices a,b,c etc. If an NCProcess command discovers that ab = bc and, at that point, you realize that it is reasonable to assume that no eigenvalue of a is an eigenvalue of c, then b must be zero from an analytic argument.1 Therefore, one can add the polynomial equation b = 0 to the collection of polynomial equations and continue. As research progressed, one would add more and more analytic observations at the points where it became clear what those observations were.
The syllogism corresponding to the above type of argument would go as follow.
Fact 37.2 would be seen by using the algorithms in this paper. Fact 37.3 is an observation from analysis. Fact 37.4 would be seen by using the algorithms in this paper. Conclusion 37.5 is a tautological conclusion of the Facts 37.2, 37.3 and 37.4.