Before looking at the Implementation part of QuadraticForm, let's try some examples.
Build a domain .
Define a matrix to be used to construct a quadratic form.
Construct the quadratic form. A package call $QF is necessary since there are other QuadraticForm domains.
Looks like a matrix. Try computing the number of rows. Axiom won't let you.
Create a direct product element . A package call is again necessary, but Axiom understands your list as denoting a vector.
Compute the product .
What is 3 times minus plus ?