Let be a polynomial and be maxroot the maximal modulus of
the root of
. From
we may derive a the unitary polynomial
such that the
roots of
have a modulus lower or equal to 1 and if
is a root
of
then maxroot
is a root of
.
Let
which may also be written as
where
is some fixed point.
Let a range for
and let
be the mid point of the
range. We consider the square in the complex plane centered at
and whose edge length is
. Let
be the length of the
half-diagonal of this square.
If