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##

Condition number

The condition number of a polynomial may be defined either
as the ratio lowest root over largest root or as the ratio
over
where are the roots of the
polynomial. In the later case the condition number has a value between
0 and 1.
The minimal and maximal values of the condition number of a parametric
polynomial in both form may be calculated using the procedure:

MinMax_Condition_Number_Gradient(Func,Vars,Init,Type,Absolute,Rand,Min,Pm,Max,PM)

where `Absolute` has to be set to 0 if looking for the ratio
minimal root over maximal root or 1 if looking for the ratio in
absolute value.
The parametric polynomial should appear as last argument of `Func`. Note that is this last element is a matrix then the considered
polynomial will be the characteristic polynomial of the matrix.
This procedure may hence be used to compute the minimal and maximal
value of the condition number of a
matrix. Note here that the derivatives of the polynomial and of its
coefficients must be available.

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Jean-Pierre Merlet
2012-12-20