A *parametric polynomial* is a polynomial whose coefficients are
functions of a set of parameters (in other words it is a set of
polynomials). A typical parametric polynomial is obtained when
calculating the characteristic polynomial of a parametric matrix.

In this chapter we propose some algorithms to deal with the real roots of a parametric polynomial and, in some cases, with the real part of these roots. If the considered polynomial is the characteristic polynomial of a matrix we may make use of the components of the matrix.

Some of these algorithms use a primary and secondary algorithms. The
secondary algorithm uses also a list of boxes which is stored in the
interval matrix `BoxUP`.

- Minimal and maximal real roots of a parametric polynomial
- Possible parameters values for a given range on the real roots

- Condition number
- Kharitonov polynomials

- Gerschgorin circles

- Cassini ovals

- Routh
- Weyl filter

- Coefficient of the characteristic polynomial

Jean-Pierre Merlet 2012-12-20