@Carl Love Yes, but I found that there is nothing but (x,y) -> x-y.  At least it works for the cases I have tried. Many thanks.

@Carl Love Many thanks.  Would inner always be available?

@Kitonum Thank you ever so much.   There is another function that I could find in the version.  Here is an example:

(anglebracket(X-Y))(y2, -(-x1*x2+u0)*x2-(x1^2-2*x2)*x1+u1)

Unfortunately I don't have a foggiest idea where this function comes from.

I would rather not use LinearAlgebra right now.  If I do I have changing all the definitions from vector to Vector. Once I get the code working I will definitely change it.  Many thanks.