Rouche theorem is implemented in the following way:

- Rouche theorem is checked with respect to the mid-point of a box
- if Roucche theorem is satisfied, then a limited number of Newton iteration is performed to check if Newton indeed converge. If this is the case a ball that include a single solution has been determined
- if a ball has been determined, then, optionaly an inflation procedure )see section 3.1.6) is used to try to enlarge the ball

int Rouche(int DimensionEq,int DimVar,int order, INTERVAL_VECTOR (* TheIntervalFunction)(int,int,INTERVAL_VECTOR &), INTERVAL_VECTOR (* Jacobian)(int, int, INTERVAL_VECTOR &), INTERVAL_MATRIX (* Gradient)(int, int, INTERVAL_VECTOR &), INTERVAL_VECTOR (* OtherDerivatives)(int, int, INTERVAL_VECTOR &), double Accuracy, int MaxIter, INTERVAL_VECTOR &Input, INTERVAL_VECTOR &UnicityBox)where

`DimensionEq`: number of equations`DimVar`: number of variables`order`: the order for Rouche theorem minus 1`TheIntervalFunction`: a procedure in`MakeF`format for computing an interval evaluation of the equations`Jacobian`: a procedure in`MakeF`format that computes the jacobian row by row`Gradient`: a procedure that compute the jacobian in`MakeJ`format`OtherDerivatives`: a procedure in`MakeF`format that computes the derivative of order larger or equal to 2, row by row. This procedure returns an interval vector of dimension

If a ball with a single solution has been found it will be returned in
`UnicityBox` and the procedure returns 1, otherwise it returns 0.

If the flag
`ALIAS_Always_Use_Inflation`
is set to 1, then an
inflation procedure is used to try to enlarge the box up to the
accuracy `ALIAS_Eps_Inflation`.