# 13.4 A Demo¶

Before looking at the Implementation part of QuadraticForm, let’s try some examples.

Build a domain QF.

.. spadMathAnswer


Define a matrix to be used to construct a quadratic form.

.. spadMathAnswer


Construct the quadratic form. A package call \$QF is necessary since there are other QuadraticForm domains.

.. spadMathAnswer


Looks like a matrix. Try computing the number of rows. FriCAS won’t let you.

.. spadMathAnswer


Create a direct product element v. A package call is again necessary, but FriCAS understands your list as denoting a vector.

.. spadMathAnswer


Compute the product vTAv.

.. spadMathAnswer


What is 3 times q minus q plus q?

.. spadMathAnswer