-------- 0 order ---------- 2D 
fe.N(1)        =       [[1-y,x]]
fe.N(2)        =       [[y,1-x]]
fe.N(3)        =       [[-y,x]]
-------- 1 order ---------- 2D
fe.N(1)        =       [[-2-8*y*x+2*y+6*x,8*x^2-4*x]]
fe.N(2)        =       [[4+8*y*x+8*y^2-12*y-6*x,-8*y*x-8*x^2+6*x]]
fe.N(3)        =       [[8*y^2-4*y,-2-8*y*x+6*y+2*x]]
fe.N(4)        =       [[-8*y*x-8*y^2+6*y,4+8*y*x+8*x^2-6*y-12*x]]
fe.N(5)        =       [[-8*y^2+4*y,8*y*x-2*x]]
fe.N(6)        =       [[-8*y*x+2*y,8*x^2-4*x]]
fe.N(7)        =       [[-8*y*x-16*y^2+16*y,16*y*x+8*x^2-8*x]]
fe.N(8)        =       [[16*y*x+8*y^2-8*y,-8*y*x-16*x^2+16*x]]
-------- 2 order ---------- 2D
fe.N(1)        =       [[9*y*x+9*x^2-45*y*x^2+3*(1-y-x)*y+3*(1-y-x)^2-18*(1-y-x)*x,9*y*x-36*x^2+45*x^3+9*(1-y-x)*x]]
fe.N(2)        =       [[-168*y*x-18*x^2+180*y*x^2+12*(1-y-x)*y-18*(1-y-x)^2+180*y^2*x+84*(1-y-x)*x,12*y*x+162*x^2-180*x^3-180*y*x^2-48*(1-y-x)*x]]
fe.N(3)        =       [[48*y*x+3*x^2-45*y^3+45*y^2-45*y*x^2-36*(1-y-x)*y+9*(1-y-x)^2-90*y^2*x-18*(1-y-x)*x,-42*y*x-42*x^2+45*x^3+90*y*x^2+45*y^2*x+18*(1-y-x)*x]]
fe.N(4)        =       [[9*y*x+45*y^3-36*y^2+9*(1-y-x)*y,9*y*x+9*y^2-18*(1-y-x)*y+3*(1-y-x)^2-45*y^2*x+3*(1-y-x)*x]]
fe.N(5)        =       [[12*y*x-180*y^3+162*y^2-48*(1-y-x)*y-180*y^2*x,-168*y*x-18*y^2+180*y*x^2+84*(1-y-x)*y-18*(1-y-x)^2+180*y^2*x+12*(1-y-x)*x]]
fe.N(6)        =       [[-42*y*x+45*y^3-42*y^2+45*y*x^2+18*(1-y-x)*y+90*y^2*x,48*y*x+45*x^2-45*x^3+3*y^2-90*y*x^2-18*(1-y-x)*y+9*(1-y-x)^2-45*y^2*x-36*(1-y-x)*x]]
fe.N(7)        =       [[-9*y*x-45*y^3+36*y^2-9*(1-y-x)*y,-27*y*x+3*x^2+45*y^2*x+3*(1-y-x)*x]]
fe.N(8)        =       [[48*y*x+18*y^2-12*(1-y-x)*y-180*y^2*x,-48*y*x-18*x^2+180*y*x^2+12*(1-y-x)*x]]
fe.N(9)        =       [[27*y*x-3*y^2-45*y*x^2-3*(1-y-x)*y,9*y*x-36*x^2+45*x^3+9*(1-y-x)*x]]
fe.N(10)        =       [[-30*y*x-270*y^3+270*y^2-90*(1-y-x)*y-180*y^2*x,-210*y*x+180*y*x^2+270*y^2*x+30*(1-y-x)*x]]
fe.N(11)        =       [[300*y*x-180*y*x^2-60*(1-y-x)*y-360*y^2*x,-60*y*x-180*x^2+180*x^3+360*y*x^2+60*(1-y-x)*x]]
fe.N(12)        =       [[-120*y*x+270*y^3-270*y^2+90*y*x^2+180*(1-y-x)*y+360*y^2*x,240*y*x+90*x^2-90*x^3-360*y*x^2-270*y^2*x-60*(1-y-x)*x]]
fe.N(13)        =       [[-60*y*x+180*y^3-180*y^2+60*(1-y-x)*y+360*y^2*x,300*y*x-360*y*x^2-180*y^2*x-60*(1-y-x)*x]]
fe.N(14)        =       [[-210*y*x+270*y*x^2+30*(1-y-x)*y+180*y^2*x,-30*y*x+270*x^2-270*x^3-180*y*x^2-90*(1-y-x)*x]]
fe.N(15)        =       [[240*y*x-90*y^3+90*y^2-270*y*x^2-60*(1-y-x)*y-360*y^2*x,-120*y*x-270*x^2+270*x^3+360*y*x^2+90*y^2*x+180*(1-y-x)*x]]
no. variables 12
variables no. equations 12
Equations -------- 0 order ---------- 3D 
fe.N(1)        =       [[1-z-y,x]]
fe.N(2)        =       [[y,1-z-x]]
fe.N(3)        =       [[z,z]]
fe.N(4)        =       [[-1/2*sqrt(2)*y,1/2*sqrt(2)*x]]
fe.N(5)        =       [[-1/2*sqrt(2)*z,0]]
fe.N(6)        =       [[0,-1/2*sqrt(2)*z]]
no. variables 30
variables bernstein_pol {{b11_0,b12_0,b13_0},{{b11_0},{b12_0},{b13_0}},{{1,0,0},{0,1,0},{0,0,1}}}
 normal_vec {1/3*sqrt(3),1/3*sqrt(3),1/3*sqrt(3)}
 pspace_n {-1/3*sqrt(3)*(a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1)+1/3*sqrt(3)*(b2_2*x+b2_1*y+y^2*a2_2+a2_5*x^2+a2_0*z^2+(1-z-y-x)*b2_3+z*a2_3*x+a2_1*z*y+y*a2_4*x+z*b2_0),1/3*sqrt(3)*(a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1)+1/3*(-z^2*a1_0-y*b1_1-b1_2*x-a1_5*x^2-a1_1*z*y-y*a1_4*x-a1_2*y^2-z*x*a1_3-(1-z-y-x)*b1_3-b1_0*z)*sqrt(3),-1/3*sqrt(3)*(b2_2*x+b2_1*y+y^2*a2_2+a2_5*x^2+a2_0*z^2+(1-z-y-x)*b2_3+z*a2_3*x+a2_1*z*y+y*a2_4*x+z*b2_0)+1/3*sqrt(3)*(z^2*a1_0+y*b1_1+b1_2*x+a1_5*x^2+a1_1*z*y+y*a1_4*x+a1_2*y^2+z*x*a1_3+(1-z-y-x)*b1_3+b1_0*z)}
i 1
basis {1,0,0}
integrand -1/3*sqrt(3)*(a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1)+1/3*sqrt(3)*(b2_2*x+b2_1*y+y^2*a2_2+a2_5*x^2+a2_0*z^2+(1-z-y-x)*b2_3+z*a2_3*x+a2_1*z*y+y*a2_4*x+z*b2_0)
 eq -1/6*b3_0+1/24*a2_1-1/12*a3_5+1/6*b2_2-1/12*a3_0+1/6*b2_1+1/12*a2_5+1/12*a2_0-1/24*a3_4-1/24*a3_3+1/6*b2_0+1/24*a2_4-1/6*b3_2+1/24*a2_3-1/6*b3_1-1/12*a3_2-1/24*a3_1+1/12*a2_2==0
basis {0,1,0}
integrand 1/3*sqrt(3)*(a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1)+1/3*(-z^2*a1_0-y*b1_1-b1_2*x-a1_5*x^2-a1_1*z*y-y*a1_4*x-a1_2*y^2-z*x*a1_3-(1-z-y-x)*b1_3-b1_0*z)*sqrt(3)
 eq 1/6*b3_0-1/6*b1_0-1/12*a1_2+1/12*a3_5-1/24*a1_1+1/12*a3_0-1/12*a1_5+1/24*a3_4-1/12*a1_0+1/24*a3_3+1/6*b3_2-1/6*b1_2+1/6*b3_1-1/24*a1_4-1/6*b1_1-1/24*a1_3+1/12*a3_2+1/24*a3_1==0
basis {0,0,1}
integrand -1/3*sqrt(3)*(b2_2*x+b2_1*y+y^2*a2_2+a2_5*x^2+a2_0*z^2+(1-z-y-x)*b2_3+z*a2_3*x+a2_1*z*y+y*a2_4*x+z*b2_0)+1/3*sqrt(3)*(z^2*a1_0+y*b1_1+b1_2*x+a1_5*x^2+a1_1*z*y+y*a1_4*x+a1_2*y^2+z*x*a1_3+(1-z-y-x)*b1_3+b1_0*z)
 eq -1/24*a2_1+1/6*b1_0+1/12*a1_2-1/6*b2_2+1/24*a1_1-1/6*b2_1-1/12*a2_5-1/12*a2_0+1/12*a1_5+1/12*a1_0-1/6*b2_0-1/24*a2_4-1/24*a2_3+1/6*b1_2+1/24*a1_4+1/6*b1_1+1/24*a1_3-1/12*a2_2==0
bernstein_pol {{b21_0,b22_0,b23_0},{{b21_0},{b22_0},{b23_0}},{{1,0,0},{0,1,0},{0,0,1}}}
 normal_vec {1,0,0}
 pspace_n {0,a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1,-b2_2*x-b2_1*y-y^2*a2_2-a2_5*x^2-a2_0*z^2-(1-z-y-x)*b2_3-z*a2_3*x-a2_1*z*y-y*a2_4*x-z*b2_0}
i 2
basis {1,0,0}
basis {0,1,0}
integrand a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1
 eq 1/6*b3_0+1/12*a3_0+1/6*b3_3+1/6*b3_1+1/12*a3_2+1/24*a3_1==0
basis {0,0,1}
integrand -b2_2*x-b2_1*y-y^2*a2_2-a2_5*x^2-a2_0*z^2-(1-z-y-x)*b2_3-z*a2_3*x-a2_1*z*y-y*a2_4*x-z*b2_0
 eq -1/24*a2_1-1/6*b2_1-1/12*a2_0-1/6*b2_0-1/6*b2_3-1/12*a2_2==0
bernstein_pol {{b31_0,b32_0,b33_0},{{b31_0},{b32_0},{b33_0}},{{1,0,0},{0,1,0},{0,0,1}}}
 normal_vec {0,-1,0}
 pspace_n {a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1,0,-z^2*a1_0-y*b1_1-b1_2*x-a1_5*x^2-a1_1*z*y-y*a1_4*x-a1_2*y^2-z*x*a1_3-(1-z-y-x)*b1_3-b1_0*z}
i 3
basis {1,0,0}
integrand a3_5*x^2+a3_0*z^2+a3_4*y*x+b3_2*x+z*a3_3*x+b3_0*z+(1-z-y-x)*b3_3+z*y*a3_1+y^2*a3_2+y*b3_1
 eq 1/6*b3_0+1/12*a3_5+1/12*a3_0+1/6*b3_3+1/24*a3_3+1/6*b3_2==0
basis {0,1,0}
basis {0,0,1}
integrand -z^2*a1_0-y*b1_1-b1_2*x-a1_5*x^2-a1_1*z*y-y*a1_4*x-a1_2*y^2-z*x*a1_3-(1-z-y-x)*b1_3-b1_0*z
 eq -1/6*b1_0-1/6*b1_3-1/12*a1_5-1/12*a1_0-1/6*b1_2-1/24*a1_3==0
bernstein_pol {{b41_0,b42_0,b43_0},{{b41_0},{b42_0},{b43_0}},{{1,0,0},{0,1,0},{0,0,1}}}
 normal_vec {0,0,1}
 pspace_n {b2_2*x+b2_1*y+y^2*a2_2+a2_5*x^2+a2_0*z^2+(1-z-y-x)*b2_3+z*a2_3*x+a2_1*z*y+y*a2_4*x+z*b2_0,-z^2*a1_0-y*b1_1-b1_2*x-a1_5*x^2-a1_1*z*y-y*a1_4*x-a1_2*y^2-z*x*a1_3-(1-z-y-x)*b1_3-b1_0*z,0}
i 4
basis {1,0,0}
integrand b2_2*x+b2_1*y+y^2*a2_2+a2_5*x^2+a2_0*z^2+(1-z-y-x)*b2_3+z*a2_3*x+a2_1*z*y+y*a2_4*x+z*b2_0
 eq 1/6*b2_2+1/6*b2_1+1/12*a2_5+1/24*a2_4+1/6*b2_3+1/12*a2_2==0
basis {0,1,0}
integrand -z^2*a1_0-y*b1_1-b1_2*x-a1_5*x^2-a1_1*z*y-y*a1_4*x-a1_2*y^2-z*x*a1_3-(1-z-y-x)*b1_3-b1_0*z
 eq -1/12*a1_2-1/6*b1_3-1/12*a1_5-1/6*b1_2-1/24*a1_4-1/6*b1_1==0
basis {0,0,1}
no. equations 31
Equations 