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Deflation

The procedure `DeflationUP` will create a simplification procedure
based on a re-writting of the univariate polynomial of degree . Let us assume
that approximate roots
of the polynomial has been
found. Then the polynomial may be written as

where has degree . In the generated simplification
procedure a C++ program will use the `ALIAS_Nb_Solution`
approximate roots
stored in the interval matrix `ALIAS_Solution` to compute safely
and will then use the above form of to compute the interval
evaluation of for the current box. If this evaluation does not
include 0, then the simplification procedure will return -1, allowing
the current box to be discarded.
The syntax of this procedure is:

DeflationUP(Func,Vars,EvalProc,JevalProc,name)

where
`Func`: the polynomial
`Vars`: the name of the polynomial variable
`EvalProc`: the name of a C++ procedure in `MakeF`
format that will be used to
evaluate the polynomial. If `GradientSolve` or `HessianSolve`
are used as solving procedure this name is by default "F". Otherwise
the user may use its own procedure, for example by using `MakeF`.
`JevalProc`: the name of a C++ procedure in `MakeJ`
format that will be used to
evaluate the derivative of the polynomial. If `GradientSolve` or `HessianSolve`
are used as solving procedure this name is by default "J". Otherwise
the user may use its own procedure, for example by using `MakeJ`.This procedure is used to compute accurately the approximate
roots of
by using the Newton scheme with as initial guess the mid-point of the
global C++ variable
`ALIAS_Solution` until the residues are lower than ``ALIAS/fepsilon``.
Alternatively you may specify `"none"` for `JevalProc` in
which case the mid-point of `ALIAS_Solution` will be used as
approximate solution
`name`: the name of the simplification procedure that will
be written in the file `name.C`

To be used the coefficients of must be either real numeric or
intervals.

** Next:** Parametric polynomial
** Up:** Simplification procedures
** Previous:** Simplification procedures
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Jean-Pierre Merlet
2012-12-20