int i4_max ( int i1, int i2 ); int i4_min ( int i1, int i2 ); double r8_sign ( double x ); void r82poly2_print ( double a, double b, double c, double d, double e, double f ); int r82poly2_type ( double a, double b, double c, double d, double e, double f ); void r82poly2_type_print ( int type ); double *r8mat_inverse_3d ( double a[] ); void r8mat_print ( int m, int n, double a[], string title ); void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, int jhi, string title ); int r8poly_degree ( int na, double a[] ); double *r8poly_deriv ( int n, double c[], int p ); double r8poly_lagrange_0 ( int npol, double xpol[], double xval ); double r8poly_lagrange_1 ( int npol, double xpol[], double xval ); double r8poly_lagrange_2 ( int npol, double xpol[], double xval ); double *r8poly_lagrange_coef ( int npol, int ipol, double xpol[] ); void r8poly_lagrange_factor ( int npol, double xpol[], double xval, double &wval, double &dwdx ); int r8poly_lagrange_val ( int npol, int ipol, double xpol[], double xval, double &pval, double &dpdx ); int r8poly_order ( int na, double a[] ); void r8poly_print ( int n, double a[], string title ); void r8poly_shift ( double scale, double shift, int n, double poly_cof[] ); double r8poly_value ( int n, double a[], double x ); double r8poly_value_horner ( int n, double a[], double x ); double *r8poly_values_horner ( int m, double c[], int n, double x[] ); double *r8poly_value_2d ( int m, double c[], int n, double x[], double y[] ); int r8poly2_ex ( double x1, double y1, double x2, double y2, double x3, double y3, double &x, double &y ); int r8poly2_ex2 ( double x1, double y1, double x2, double y2, double x3, double y3, double &x, double &y, double &a, double &b, double &c ); void r8poly2_root ( double a, double b, double c, complex &r1, complex &r2 ); void r8poly2_rroot ( double a, double b, double c, double &r1, double &r2 ); void r8poly2_val ( double x1, double y1, double x2, double y2, double x3, double y3, double x, double &y, double &yp, double &ypp ); void r8poly2_val2 ( int ndata, double tdata[], double ydata[], int left, double tval, double &yval ); void r8poly3_root ( double a, double b, double c, double d, complex &r1, complex &r2, complex &r3 ); void r8poly4_root ( double a, double b, double c, double d, double e, complex &r1, complex &r2, complex &r3, complex &r4 ); void r8r8_print ( double a1, double a2, string title ); double *r8vec_copy_new ( int n, double a1[] ); double *r8vec_even_new ( int n, double alo, double ahi ); double r8vec_even_select ( int n, double xlo, double xhi, int ival ); double *r8vec_indicator1_new ( int n ); bool r8vec_is_distinct ( int n, double x[] ); double *r8vec_linspace_new ( int n, double a_lo, double a_hi ); void r8vec_print ( int n, double a[], string title ); void r8vec_transpose_print ( int n, double a[], string title ); double *r8vec_uniform_01_new ( int n, int &seed ); double *r8vec_zeros_new ( int n ); void r8vec2_print ( int n, double a1[], double a2[], string title ); double *roots_to_r8poly ( int n, double x[] ); int s_len_trim ( string s ); void timestamp ( );