(4.2) |

int Degree_Max_Convert_Trigo_Interval(int n,VECTOR &A,INTEGER_VECTOR &SSin,INTEGER_VECTOR &CCos); int Degree_Max_Convert_Trigo_Interval(int n,INTEGER_VECTOR &A, INTEGER_VECTOR &SSin,INTEGER_VECTOR &CCos);with:

`n`: number of terms of the equation`A`: the coefficients of each term which may be either real or integer`Ssin`: the sine power of each term`Ccos`: the cosine power of each term

VOID Convert_Trigo_Interval(int n,VECTOR &A,INTEGER_VECTOR &SSin, INTEGER_VECTOR &CCos,VECTOR &Coeff,int *degree); VOID Convert_Trigo_Interval(int n,INTEGER_VECTOR &A,INTEGER_VECTOR &SSin, INTEGER_VECTOR &CCos,INTEGER_VECTOR &Coeff,int *degree); VOID Convert_Trigo_Interval(int n,INTERVAL_VECTOR &A,INTEGER_VECTOR &SSin, INTEGER_VECTOR &CCos,INTERVAL_VECTOR &Coeff,int *degree);with:

`n`: number of terms of the equation`A`: the coefficients of each term which may be either real or integer`Ssin`: the sine power of each term`Ccos`: the cosine power of each term`Coeff`: the coefficients of the polynomial`degree`: the final degree of the polynomial

VOID Convert_Trigo_Pi_Interval(int n,VECTOR &A,INTEGER_VECTOR &SSin, INTEGER_VECTOR &CCos,INTEGER_VECTOR &Coeff,int *degree); VOID Convert_Trigo_Pi_Interval(int n,INTEGER_VECTOR &A,INTEGER_VECTOR &SSin, INTEGER_VECTOR &CCos,INTEGER_VECTOR &Coeff,int *degree); VOID Convert_Trigo_Pi_Interval(int n,INTERVAL_VECTOR &A,INTEGER_VECTOR &SSin, INTEGER_VECTOR &CCos,INTEGER_VECTOR &Coeff,int *degree);Similar procedures exists for interval trigonometric equations i.e. equations where the coefficients

Having determined the equivalent polynomial you my use the tools described in section 5 for determining the number of roots of the trigonometric equation. But you still have to manage the search interval. The following procedure is able to determine this search interval and to determine the number of roots of the trigonometric equation:

int Nb_Root_Trigo_Interval(int n,VECTOR &A,INTEGER_VECTOR &SSin, INTEGER_VECTOR &CCos,REAL Inf,REAL Sup)with:

`n`: number of terms of the equation`A`: the coefficients of each term which may be either real or integer`Ssin`: the sine power of each term`Ccos`: the cosine power of each term`Inf`: the lower bound of the search interval`Sup`: the upper bound of the search interval