The positive root gives the scaling sequence of the D4-wavelet, see below.

For example the following definition constrains the function to return the positive root.

Every positive real number has two square roots, one positive and one negative.

They always used the positive root because this made sense when solving "real" problems.

We choose the positive root, , as its absolute value is less than 1, which becomes useful later in the proof.

In the latter case has a single positive real root for all .

To obtain an arbitrary positive root we need to assume that .

Let us suppose also that a choice of positive roots Φ has been fixed.

He only considered positive roots and he did not go past the third degree.

Given a root system Φ we can always choose (in many ways) a set of positive roots.