/* test_4d.h  just the test function and derivatives     */
/*            fourth order and through fourth derivative */
/* u(x,y,z,t) and ux(x,y,z,t) etc.  many of them         */

/* every possible term with a unique constant coefficient */

double u(double x, double y, double z, double t);

/* now, for testing, the 69 possible non zero derivatives */

double Uxxxx(double x, double y, double z, double t);
double Uxxxy(double x, double y, double z, double t);
double Uxxxz(double x, double y, double z, double t);
double Uxxxt(double x, double y, double z, double t);
double Uxxyy(double x, double y, double z, double t);
double Uxxyz(double x, double y, double z, double t);
double Uxxyt(double x, double y, double z, double t);
double Uxxzz(double x, double y, double z, double t);
double Uxxzt(double x, double y, double z, double t);
double Uxxtt(double x, double y, double z, double t);
double Uxyyy(double x, double y, double z, double t);
double Uxyyz(double x, double y, double z, double t);
double Uxyyt(double x, double y, double z, double t);
double Uxyzz(double x, double y, double z, double t);
double Uxyzt(double x, double y, double z, double t);
double Uxytt(double x, double y, double z, double t);
double Uxzzz(double x, double y, double z, double t);
double Uxzzt(double x, double y, double z, double t);
double Uxztt(double x, double y, double z, double t);
double Uxttt(double x, double y, double z, double t);
double Uyyyy(double x, double y, double z, double t);
double Uyyyz(double x, double y, double z, double t);
double Uyyyt(double x, double y, double z, double t);
double Uyyzz(double x, double y, double z, double t);
double Uyyzt(double x, double y, double z, double t);
double Uyytt(double x, double y, double z, double t);
double Uyzzz(double x, double y, double z, double t);
double Uyzzt(double x, double y, double z, double t);
double Uyztt(double x, double y, double z, double t);
double Uyttt(double x, double y, double z, double t);
double Uzzzz(double x, double y, double z, double t);
double Uzzzt(double x, double y, double z, double t);
double Uzztt(double x, double y, double z, double t);
double Uzttt(double x, double y, double z, double t);
double Utttt(double x, double y, double z, double t);
double Uxxx(double x, double y, double z, double t);
double Uxxy(double x, double y, double z, double t);
double Uxxz(double x, double y, double z, double t);
double Uxxt(double x, double y, double z, double t);
double Uxyy(double x, double y, double z, double t);
double Uxyz(double x, double y, double z, double t);
double Uxyt(double x, double y, double z, double t);
double Uxzz(double x, double y, double z, double t);
double Uxzt(double x, double y, double z, double t);
double Uxtt(double x, double y, double z, double t);
double Uyyy(double x, double y, double z, double t);
double Uyyz(double x, double y, double z, double t);
double Uyyt(double x, double y, double z, double t);
double Uyzz(double x, double y, double z, double t);
double Uyzt(double x, double y, double z, double t);
double Uytt(double x, double y, double z, double t);
double Uzzz(double x, double y, double z, double t);
double Uzzt(double x, double y, double z, double t);
double Uztt(double x, double y, double z, double t);
double Uttt(double x, double y, double z, double t);
double Uxx(double x, double y, double z, double t);
double Uxy(double x, double y, double z, double t);
double Uxz(double x, double y, double z, double t);
double Uxt(double x, double y, double z, double t);
double Uyy(double x, double y, double z, double t);
double Uyz(double x, double y, double z, double t);
double Uyt(double x, double y, double z, double t);
double Uzz(double x, double y, double z, double t);
double Uzt(double x, double y, double z, double t);
double Utt(double x, double y, double z, double t);
double Ux(double x, double y, double z, double t);
double Uy(double x, double y, double z, double t);
double Uz(double x, double y, double z, double t);
double Ut(double x, double y, double z, double t);