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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

then the polynomial has no root in the square.
For a given list of equations we consider in turn each equation and
determine if it may be considered as a parametric polynomial.
For example the equation
will be
considered as a second order polynomial in with coefficients
(but not a polynomial in ). The procedure
WeylFilter(Func,Vars,FullVars,MaxRoot,TypeB,name)

will consider each equation in the list `Func` and examine if it
may considered as a parametric polynomial successively in each
variable in the list `Vars`. If yes the Weyl filter will be used
on the polynomial whose coefficients are functions of the variables in
the list `FullVars` (all variables in `Vars` must be a member of
`FullVars`). `MaxRoot` is a list which indicates for each
variable in `Vars` what is the maximum
modulus of the roots of all parametric polynomials in this
variable. An element of `MaxRoot` may be a numerical value of the
key-word "automatic" which indicates that the C++ program will try to
determine the maximal modulus. The list `TypeB` indicates for each
variable in `Vars` how are computed the i.e. numerically
with the keyword "numeric", or symbolically (which is usually more efficient) with the keyword
"symbolic". The simplification procedure will be named `name` and
be written in the file `name.C`. For the previous example the
procedure will be
WeylFilter([x^2*sin(x)+x*sin(y)+ x*exp(x)],[x],[x,y],["automatic"],["symbolic"],"SIMP");

Another example of the use of this procedure is presented in
section 12.3.

** Next:** Minimal and maximal real
** Up:** Simplification procedures
** Previous:** The KharitonovConsistency procedure
** Contents**
Jean-Pierre Merlet
2012-12-20