void legendre_2d_exactness ( double a[], double b[], int n, double x[], 
  double y[], double w[], int t );
double legendre_2d_monomial_integral ( double a[], double b[], int p[] );
double r8vec_dot_product ( int n, double a1[], double a2[] );
void r8vec_print ( int n, double a[], string title );
void r8vec2_print ( int n, double a1[], double a2[], string title );
void timestamp ( );