double *lagrange_basis_antideriv ( int npol, int ipol, double *xpol );
double *lagrange_basis_coef ( int npol, int ipol, double *xpol );
double  lagrange_basis_deriv ( int npol, int ipol, double *xpol, double xval );
double  lagrange_basis_deriv2 ( int npol, int ipol, double *xpol, double xval );
double  lagrange_basis_value ( int npol, int ipol, double *xpol, double xval );
double *r8poly_ant_coef ( int n, double *poly_cof );
void    r8poly_print ( int n, double a[], string title );
double  r8poly_value ( int m, double c[], double x );
bool    r8vec_is_distinct ( int n, double x[] );
void    r8vec_print ( int n, double a[], string title );
int     s_len_trim ( string s );