# 13.4 A DemoΒΆ

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
```