eq=-x1^2-x2+x3 eq=x1^2-x2+x3 eq=round(x3)All equations in a system of equations may be evaluated by using the procedure

int Evaluate_Interval_With_Parser( char *texte,INTERVAL_VECTOR &P,int Unknowns,int NbEq,INTERVAL_VECTOR &Value)The parameters are:

`texte`: the name of the file describing the analytical form of the equation`P`: the ranges for the unknowns`Unknowns`: the number of unknowns`NbEq`: the number of equations`Value`: the interval evaluation of the equations

Thus for evaluating the formula described by the formula file `toto`:

eq=-x1^2-x2+x3 eq=x1^2-x2+x3 eq=round(x3)for the ranges

INTERVAL_VECTOR P(3); INTERVAL_VECTOR F(3); strcpy(variable_name_IS[0],"x1"); strcpy(variable_name_IS[1],"x2"); strcpy(variable_name_IS[1],"x3"); Unknowns_Number_IS=3; P(1)=INTERVAL(-1,1);//range for x1 P(2)=INTERVAL(0,2);//range for x2 P(3)=INTERVAL(1.1,2.3);//range for x3 Evaluate_Interval_With_Parser("toto",P,3,3,F); cout<<F<<endl;//interval evaluation of the 3 equationsInstead of evaluating the whole system of equations we may have to evaluate one or more particular equation(s) of the system. The following procedures enable to evaluate efficiently particular equations in a system but before using them we need to do some initialization. This is done by calling once the procedure

int Init_Evaluate_Equations_With_Parser(char *texte,int *EqStart)The parameters are:

`texte`: the name of the formula file`EqStart`: an array of integer with size equal to the number of equations in the formula file

After this initialization the following procedure may be used to evaluate one particular equation in a system:

int Evaluate_Equations_With_Parser(char *texte,INTERVAL_VECTOR &P,int Unknowns, int NbEq,int EqToRead,int *EqStart,INTERVAL &Value)The parameters are:

`texte`: the name of the file describing the analytical form of the equation`P`: the ranges for the unknowns`Unknowns`: the number of unknowns`NbEq`: the number of equations`EqToRead`: the number of the equation that has to be evaluated (the equation number start at 1)`EqStart`: the array of integer produced by the initialization procedure for the formula file`Value`: the interval evaluation of the equation`EqToRead`

int Evaluate_Equations_With_Parser(char *texte,INTERVAL_VECTOR &P,int Unknowns, int NbEq,int EqToRead1,int EqToRead2,int *EqStart,INTERVAL &Value)The parameters are:

`texte`: the name of the file describing the analytical form of the equation`P`: the ranges for the unknowns`Unknowns`: the number of unknowns`NbEq`: the number of equations`EqToRead1`: the number of the first equation that has to be evaluated (the equation number start at 1)`EqToRead2`: the number of the last equation that has to be evaluated`EqStart`: the array of integer produced by the initialization procedure for the formula file`Value`: the interval evaluation of the equation`EqToRead`

int Evaluate_Equations_With_Parser_Gradient(int Unknowns,int NbEq,char *texte, char *gradient,INTERVAL_VECTOR &P, INTERVAL_VECTOR &Value,int Exact)The parameters are:

`Unknowns`: the number of unknowns`NbEq`: the number of equations`texte`: the name of the file describing the analytical form of the equation`gradient`: the name of the parser file giving the gradient matrix of the equations. The order in this file is to define successively the derivative of the first equation with respect to each variable, then the derivative of the second equation and so on`P`: the ranges for the unknowns`Value`: the interval evaluation of the`NbEq`equations`Exact`: if 0 stop processing the equations as soon as the interval evaluation of the n-th equation does not include 0 (the interval evaluation of the remaining n,..,`NbEq`equations will be set to 1. If 1 the procedure computes the interval evaluation of all the equations