/* phi_tril.h    Phi and derivatives for order 1 through 4 for Galerkin FEM
 *               and dimension 2(x,y) on triangles
 *  phi22l(T,x,y) is second order FEM phi function in 2 dimensions
 *         =sum i=1:3 j=mod i+1 ((x -xi)^2+(y -yi)^2)/((xj-xi)^2+(yj-yi)^2)
 *  phi22lx(T,x,y) is partial derivative of phi22l(c,x,y) with respect to x
 *  phi22ly(T,x,y) is partial derivative of phi22l(c,x,y) with respect to y
 *  phi22lxx(T,x,y) is second partial of phi22l(c,x,y) with respect to x
 *  phi22lxy(T,x,y) is second partial of phi22l(c,x,y) wrt x and wrt y
 *  phi22lyy(T,x,y) is second partial of phi22l(c,x,y) with respect to y
 *
 *  ...  up to fourth derivative of fourth order phi in two dimensions
 *  phi24l(T,x,y) is fourth order four dimensional FEM phi function
 *  ...
 *  phi24lyyyy(T,x,y) is fourth partial of phi24l(T,x,y) wrt y
 *
 *  T man be any of x1,y1,x2,y2,x3,y3  x2,y2,x3,y3,x1,y1  x3,y3,x1,y1,x2,y2
 */

double phi22l(double T[], double x, double y);
double phi22lx(double T[], double x, double y);
double phi22ly(double T[], double x, double y);
double phi22lxx(double T[], double x, double y);
double phi22lxy(double T[], double x, double y);
double phi22lyy(double T[], double x, double y);

/* end phi_tril.h */