psins.r

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if ((r[1]==2) & (r[2]==1) & (r[3]==1) & (r[4]==4))
psi <-
3*(8*a14*(a13*a24 + a12*a34)*a44 + 4*a14^2*(2*a24*a34 + a23*a44) + 
  a44*(4*a11*a24*a34 + 2*a12*a13*a44 + a11*a23*a44))
if ((r[1]==2) & (r[2]==1) & (r[3]==0) & (r[4]==5))
psi <-
15*a44*(4*a14^2*a24 + 2*a12*a14*a44 + a11*a24*a44)
if ((r[1]==2) & (r[2]==0) & (r[3]==6) & (r[4]==0))
psi <-
15*a33^2*(6*a13^2 + a11*a33)
if ((r[1]==2) & (r[2]==0) & (r[3]==5) & (r[4]==1))
psi <-
15*a33*(2*a13*a14*a33 + 4*a13^2*a34 + a11*a33*a34)
if ((r[1]==2) & (r[2]==0) & (r[3]==4) & (r[4]==2))
psi <-
3*(2*a14^2*a33^2 + 16*a13*a14*a33*a34 + 4*a13^2*(2*a34^2 + a33*a44) + 
  a11*a33*(4*a34^2 + a33*a44))
if ((r[1]==2) & (r[2]==0) & (r[3]==3) & (r[4]==3))
psi <-
3*(6*a14^2*a33*a34 + 6*a13*a14*(2*a34^2 + a33*a44) + 
  a34*(2*a11*a34^2 + 6*a13^2*a44 + 3*a11*a33*a44))
if ((r[1]==2) & (r[2]==0) & (r[3]==2) & (r[4]==4))
psi <-
3*(16*a13*a14*a34*a44 + 4*a14^2*(2*a34^2 + a33*a44) + 
  a44*(4*a11*a34^2 + 2*a13^2*a44 + a11*a33*a44))
if ((r[1]==2) & (r[2]==0) & (r[3]==1) & (r[4]==5))
psi <-
15*a44*(4*a14^2*a34 + 2*a13*a14*a44 + a11*a34*a44)
if ((r[1]==2) & (r[2]==0) & (r[3]==0) & (r[4]==6))
psi <-
15*a44^2*(6*a14^2 + a11*a44)
  if ((r[1]==1) & (r[2]==7) & (r[3]==0) & (r[4]==0))
psi <-
105*a12*a22^3
if ((r[1]==1) & (r[2]==6) & (r[3]==1) & (r[4]==0))
psi <-
15*a22^2*(a13*a22 + 6*a12*a23)
if ((r[1]==1) & (r[2]==6) & (r[3]==0) & (r[4]==1))
psi <-
15*a22^2*(a14*a22 + 6*a12*a24)
if ((r[1]==1) & (r[2]==5) & (r[3]==2) & (r[4]==0))
psi <-
15*a22*(2*a13*a22*a23 + 4*a12*a23^2 + a12*a22*a33)
if ((r[1]==1) & (r[2]==5) & (r[3]==1) & (r[4]==1))
psi <-
15*a22*(a14*a22*a23 + a13*a22*a24 + 4*a12*a23*a24 + a12*a22*a34)
if ((r[1]==1) & (r[2]==5) & (r[3]==0) & (r[4]==2))
psi <-
15*a22*(2*a14*a22*a24 + 4*a12*a24^2 + a12*a22*a44)
if ((r[1]==1) & (r[2]==4) & (r[3]==3) & (r[4]==0))
psi <-
9*a13*a22*(4*a23^2 + a22*a33) + 12*a12*a23*(2*a23^2 + 3*a22*a33)
if ((r[1]==1) & (r[2]==4) & (r[3]==2) & (r[4]==1))
psi <-
3*(a14*a22*(4*a23^2 + a22*a33) + 2*a13*a22*(4*a23*a24 + a22*a34) + 
  4*a12*(2*a23^2*a24 + a22*a24*a33 + 2*a22*a23*a34))
if ((r[1]==1) & (r[2]==4) & (r[3]==1) & (r[4]==2))
psi <-
3*(2*a14*a22*(4*a23*a24 + a22*a34) + a13*a22*(4*a24^2 + a22*a44) + 
  4*a12*(2*a23*a24^2 + 2*a22*a24*a34 + a22*a23*a44))
if ((r[1]==1) & (r[2]==4) & (r[3]==0) & (r[4]==3))
psi <-
9*a14*a22*(4*a24^2 + a22*a44) + 12*a12*a24*(2*a24^2 + 3*a22*a44)
if ((r[1]==1) & (r[2]==3) & (r[3]==4) & (r[4]==0))
psi <-
9*a12*a33*(4*a23^2 + a22*a33) + 12*a13*(2*a23^3 + 3*a22*a23*a33)
if ((r[1]==1) & (r[2]==3) & (r[3]==3) & (r[4]==1))
psi <-
3*(2*a14*a23^3 + 6*a13*a23^2*a24 + 3*a14*a22*a23*a33 + 3*a13*a22*a24*a33 + 
  6*a12*a23*a24*a33 + 6*a13*a22*a23*a34 + 6*a12*a23^2*a34 + 3*a12*a22*a33*a34)
if ((r[1]==1) & (r[2]==3) & (r[3]==2) & (r[4]==2))
psi <-
3*(2*a14*(2*a23^2*a24 + a22*a24*a33 + 2*a22*a23*a34) + 
  2*a13*(2*a23*a24^2 + 2*a22*a24*a34 + a22*a23*a44) + 
  a12*(2*a24^2*a33 + 8*a23*a24*a34 + 2*a22*a34^2 + 2*a23^2*a44 + a22*a33*a44))
if ((r[1]==1) & (r[2]==3) & (r[3]==1) & (r[4]==3))
psi <-
3*(2*a13*a24^3 + 6*a12*a24^2*a34 + 3*a13*a22*a24*a44 + 6*a12*a23*a24*a44 + 
  3*a12*a22*a34*a44 + 3*a14*(2*a23*a24^2 + 2*a22*a24*a34 + a22*a23*a44))
if ((r[1]==1) & (r[2]==3) & (r[3]==0) & (r[4]==4))
psi <-
9*a12*a44*(4*a24^2 + a22*a44) + 12*a14*(2*a24^3 + 3*a22*a24*a44)
if ((r[1]==1) & (r[2]==2) & (r[3]==5) & (r[4]==0))
psi <-
15*a33*(4*a13*a23^2 + a13*a22*a33 + 2*a12*a23*a33)
  if ((r[1]==1) & (r[2]==2) & (r[3]==4) & (r[4]==1))
psi <-
3*(a14*a33*(4*a23^2 + a22*a33) + 2*a12*a33*(a24*a33 + 4*a23*a34) + 
  4*a13*(2*a23*a24*a33 + 2*a23^2*a34 + a22*a33*a34))
if ((r[1]==1) & (r[2]==2) & (r[3]==3) & (r[4]==2))
psi <-
3*(2*a14*(2*a23*a24*a33 + 2*a23^2*a34 + a22*a33*a34) + 
  a13*(2*a24^2*a33 + 8*a23*a24*a34 + 2*a22*a34^2 + 2*a23^2*a44 + 
    a22*a33*a44) + 2*a12*(2*a24*a33*a34 + 2*a23*a34^2 + a23*a33*a44))
if ((r[1]==1) & (r[2]==2) & (r[3]==2) & (r[4]==3))
psi <-
3*(a14*(2*a24^2*a33 + 8*a23*a24*a34 + 2*a22*a34^2 + 2*a23^2*a44 + 
    a22*a33*a44) + 2*(a13*(2*a24^2*a34 + 2*a23*a24*a44 + a22*a34*a44) + 
    a12*(2*a24*a34^2 + a24*a33*a44 + 2*a23*a34*a44)))
if ((r[1]==1) & (r[2]==2) & (r[3]==1) & (r[4]==4))
psi <-
3*(a44*(4*a13*a24^2 + 8*a12*a24*a34 + a13*a22*a44 + 2*a12*a23*a44) + 
  4*a14*(2*a24^2*a34 + 2*a23*a24*a44 + a22*a34*a44))
if ((r[1]==1) & (r[2]==2) & (r[3]==0) & (r[4]==5))
psi <-
15*a44*(4*a14*a24^2 + a14*a22*a44 + 2*a12*a24*a44)
if ((r[1]==1) & (r[2]==1) & (r[3]==6) & (r[4]==0))
psi <-
15*a33^2*(6*a13*a23 + a12*a33)
if ((r[1]==1) & (r[2]==1) & (r[3]==5) & (r[4]==1))
psi <-
15*a33*(a14*a23*a33 + a13*a24*a33 + 4*a13*a23*a34 + a12*a33*a34)
if ((r[1]==1) & (r[2]==1) & (r[3]==4) & (r[4]==2))
psi <-
3*(2*a14*a33*(a24*a33 + 4*a23*a34) + a12*a33*(4*a34^2 + a33*a44) + 
  4*a13*(2*a24*a33*a34 + 2*a23*a34^2 + a23*a33*a44))
if ((r[1]==1) & (r[2]==1) & (r[3]==3) & (r[4]==3))
psi <-
3*(6*a13*a24*a34^2 + 2*a12*a34^3 + 3*a13*a24*a33*a44 + 6*a13*a23*a34*a44 + 
  3*a12*a33*a34*a44 + 3*a14*(2*a24*a33*a34 + 2*a23*a34^2 + a23*a33*a44))
if ((r[1]==1) & (r[2]==1) & (r[3]==2) & (r[4]==4))
psi <-
3*(a44*(8*a13*a24*a34 + 4*a12*a34^2 + 2*a13*a23*a44 + a12*a33*a44) + 
  4*a14*(2*a24*a34^2 + a24*a33*a44 + 2*a23*a34*a44))
if ((r[1]==1) & (r[2]==1) & (r[3]==1) & (r[4]==5))
psi <-
15*a44*(4*a14*a24*a34 + a14*a23*a44 + a13*a24*a44 + a12*a34*a44)
if ((r[1]==1) & (r[2]==1) & (r[3]==0) & (r[4]==6))
psi <-
15*a44^2*(6*a14*a24 + a12*a44)
if ((r[1]==1) & (r[2]==0) & (r[3]==7) & (r[4]==0))
psi <-
105*a13*a33^3
if ((r[1]==1) & (r[2]==0) & (r[3]==6) & (r[4]==1))
psi <-
15*a33^2*(a14*a33 + 6*a13*a34)
if ((r[1]==1) & (r[2]==0) & (r[3]==5) & (r[4]==2))
psi <-
15*a33*(2*a14*a33*a34 + 4*a13*a34^2 + a13*a33*a44)
if ((r[1]==1) & (r[2]==0) & (r[3]==4) & (r[4]==3))
psi <-
9*a14*a33*(4*a34^2 + a33*a44) + 12*a13*a34*(2*a34^2 + 3*a33*a44)
  if ((r[1]==1) & (r[2]==0) & (r[3]==3) & (r[4]==4))
psi <-
9*a13*a44*(4*a34^2 + a33*a44) + 12*a14*(2*a34^3 + 3*a33*a34*a44)
if ((r[1]==1) & (r[2]==0) & (r[3]==2) & (r[4]==5))
psi <-
15*a44*(4*a14*a34^2 + a14*a33*a44 + 2*a13*a34*a44)
if ((r[1]==1) & (r[2]==0) & (r[3]==1) & (r[4]==6))
psi <-
15*a44^2*(6*a14*a34 + a13*a44)
if ((r[1]==1) & (r[2]==0) & (r[3]==0) & (r[4]==7))
psi <-
105*a14*a44^3
if ((r[1]==0) & (r[2]==8) & (r[3]==0) & (r[4]==0))
psi <-
105*a22^4
if ((r[1]==0) & (r[2]==7) & (r[3]==1) & (r[4]==0))
psi <-
105*a22^3*a23
if ((r[1]==0) & (r[2]==7) & (r[3]==0) & (r[4]==1))
psi <-
105*a22^3*a24
if ((r[1]==0) & (r[2]==6) & (r[3]==2) & (r[4]==0))
psi <-
15*a22^2*(6*a23^2 + a22*a33)
if ((r[1]==0) & (r[2]==6) & (r[3]==1) & (r[4]==1))
psi <-
15*a22^2*(6*a23*a24 + a22*a34)
if ((r[1]==0) & (r[2]==6) & (r[3]==0) & (r[4]==2))
psi <-
15*a22^2*(6*a24^2 + a22*a44)
if ((r[1]==0) & (r[2]==5) & (r[3]==3) & (r[4]==0))
psi <-
15*a22*a23*(4*a23^2 + 3*a22*a33)
if ((r[1]==0) & (r[2]==5) & (r[3]==2) & (r[4]==1))
psi <-
15*a22*(4*a23^2*a24 + a22*a24*a33 + 2*a22*a23*a34)
if ((r[1]==0) & (r[2]==5) & (r[3]==1) & (r[4]==2))
psi <-
15*a22*(4*a23*a24^2 + 2*a22*a24*a34 + a22*a23*a44)
if ((r[1]==0) & (r[2]==5) & (r[3]==0) & (r[4]==3))
psi <-
15*a22*a24*(4*a24^2 + 3*a22*a44)
if ((r[1]==0) & (r[2]==4) & (r[3]==4) & (r[4]==0))
psi <-
24*a23^4 + 72*a22*a23^2*a33 + 9*a22^2*a33^2
if ((r[1]==0) & (r[2]==4) & (r[3]==3) & (r[4]==1))
psi <-
24*a23^3*a24 + 36*a22*a23*a24*a33 + 36*a22*a23^2*a34 + 9*a22^2*a33*a34
if ((r[1]==0) & (r[2]==4) & (r[3]==2) & (r[4]==2))
psi <-
3*(16*a22*a23*a24*a34 + 4*a23^2*(2*a24^2 + a22*a44) + 
  a22*(4*a24^2*a33 + 2*a22*a34^2 + a22*a33*a44))
if ((r[1]==0) & (r[2]==4) & (r[3]==1) & (r[4]==3))
psi <-
9*a22*a34*(4*a24^2 + a22*a44) + 12*a23*(2*a24^3 + 3*a22*a24*a44)
if ((r[1]==0) & (r[2]==4) & (r[3]==0) & (r[4]==4))
psi <-
24*a24^4 + 72*a22*a24^2*a44 + 9*a22^2*a44^2
if ((r[1]==0) & (r[2]==3) & (r[3]==5) & (r[4]==0))
psi <-
15*a23*a33*(4*a23^2 + 3*a22*a33)
if ((r[1]==0) & (r[2]==3) & (r[3]==4) & (r[4]==1))
psi <-
36*a23^2*a24*a33 + 9*a22*a24*a33^2 + 24*a23^3*a34 + 36*a22*a23*a33*a34
if ((r[1]==0) & (r[2]==3) & (r[3]==3) & (r[4]==2))
psi <-
3*(12*a23^2*a24*a34 + 6*a22*a24*a33*a34 + 2*a23^3*a44 + 
  3*a23*(2*a24^2*a33 + 2*a22*a34^2 + a22*a33*a44))
if ((r[1]==0) & (r[2]==3) & (r[3]==2) & (r[4]==3))
psi <-
3*(2*a24^3*a33 + 12*a23*a24^2*a34 + 6*a22*a23*a34*a44 + 
  3*a24*(2*a22*a34^2 + 2*a23^2*a44 + a22*a33*a44))
if ((r[1]==0) & (r[2]==3) & (r[3]==1) & (r[4]==4))
psi <-
24*a24^3*a34 + 36*a23*a24^2*a44 + 36*a22*a24*a34*a44 + 9*a22*a23*a44^2
if ((r[1]==0) & (r[2]==3) & (r[3]==0) & (r[4]==5))
psi <-
15*a24*a44*(4*a24^2 + 3*a22*a44)
if ((r[1]==0) & (r[2]==2) & (r[3]==6) & (r[4]==0))
psi <-
15*a33^2*(6*a23^2 + a22*a33)
if ((r[1]==0) & (r[2]==2) & (r[3]==5) & (r[4]==1))
psi <-
15*a33*(2*a23*a24*a33 + 4*a23^2*a34 + a22*a33*a34)
if ((r[1]==0) & (r[2]==2) & (r[3]==4) & (r[4]==2))
psi <-
3*(2*a24^2*a33^2 + 16*a23*a24*a33*a34 + 4*a23^2*(2*a34^2 + a33*a44) + 
  a22*a33*(4*a34^2 + a33*a44))
if ((r[1]==0) & (r[2]==2) & (r[3]==3) & (r[4]==3))
psi <-
3*(6*a24^2*a33*a34 + 6*a23*a24*(2*a34^2 + a33*a44) + 
  a34*(2*a22*a34^2 + 6*a23^2*a44 + 3*a22*a33*a44))
if ((r[1]==0) & (r[2]==2) & (r[3]==2) & (r[4]==4))
psi <-
3*(16*a23*a24*a34*a44 + 4*a24^2*(2*a34^2 + a33*a44) + 
  a44*(4*a22*a34^2 + 2*a23^2*a44 + a22*a33*a44))
if ((r[1]==0) & (r[2]==2) & (r[3]==1) & (r[4]==5))
psi <-
15*a44*(4*a24^2*a34 + 2*a23*a24*a44 + a22*a34*a44)
if ((r[1]==0) & (r[2]==2) & (r[3]==0) & (r[4]==6))
psi <-
15*a44^2*(6*a24^2 + a22*a44)
if ((r[1]==0) & (r[2]==1) & (r[3]==7) & (r[4]==0))
psi <-
105*a23*a33^3
if ((r[1]==0) & (r[2]==1) & (r[3]==6) & (r[4]==1))
psi <-
15*a33^2*(a24*a33 + 6*a23*a34)
  if ((r[1]==0) & (r[2]==1) & (r[3]==5) & (r[4]==2))
psi <-
15*a33*(2*a24*a33*a34 + 4*a23*a34^2 + a23*a33*a44)
if ((r[1]==0) & (r[2]==1) & (r[3]==4) & (r[4]==3))
psi <-
9*a24*a33*(4*a34^2 + a33*a44) + 12*a23*a34*(2*a34^2 + 3*a33*a44)
if ((r[1]==0) & (r[2]==1) & (r[3]==3) & (r[4]==4))
psi <-
9*a23*a44*(4*a34^2 + a33*a44) + 12*a24*(2*a34^3 + 3*a33*a34*a44)
if ((r[1]==0) & (r[2]==1) & (r[3]==2) & (r[4]==5))
psi <-
15*a44*(4*a24*a34^2 + a24*a33*a44 + 2*a23*a34*a44)
if ((r[1]==0) & (r[2]==1) & (r[3]==1) & (r[4]==6))
psi <-
15*a44^2*(6*a24*a34 + a23*a44)
if ((r[1]==0) & (r[2]==1) & (r[3]==0) & (r[4]==7))
psi <-
105*a24*a44^3
if ((r[1]==0) & (r[2]==0) & (r[3]==8) & (r[4]==0))
psi <-
105*a33^4
if ((r[1]==0) & (r[2]==0) & (r[3]==7) & (r[4]==1))
psi <-
105*a33^3*a34
if ((r[1]==0) & (r[2]==0) & (r[3]==6) & (r[4]==2))
psi <-
15*a33^2*(6*a34^2 + a33*a44)
if ((r[1]==0) & (r[2]==0) & (r[3]==5) & (r[4]==3))
psi <-
15*a33*a34*(4*a34^2 + 3*a33*a44)
if ((r[1]==0) & (r[2]==0) & (r[3]==4) & (r[4]==4))
psi <-
24*a34^4 + 72*a33*a34^2*a44 + 9*a33^2*a44^2
if ((r[1]==0) & (r[2]==0) & (r[3]==3) & (r[4]==5))
psi <-
15*a34*a44*(4*a34^2 + 3*a33*a44)
if ((r[1]==0) & (r[2]==0) & (r[3]==2) & (r[4]==6))
psi <-
15*a44^2*(6*a34^2 + a33*a44)
if ((r[1]==0) & (r[2]==0) & (r[3]==1) & (r[4]==7))
psi <- 105*a34*a44^3
if ((r[1]==0) & (r[2]==0) & (r[3]==0) & (r[4]==8))
psi <- 105*a44^4


  return(psi)
}



psins.6d.part6 <- function(r, a11, a22, a33, a44, a55, a66, a12, a13, a14, a15,
                           a16, a23, a24, a25, a26, a34, a35, a36, a45, a46, a56)
{
  if ((r[1]==6) & (r[2]==0) & (r[3]==0) & (r[4]==0) & (r[5]==0) & (r[6]==0))
    psi <--15*a11^3
if ((r[1]==5) & (r[2]==1) & (r[3]==0) & (r[4]==0) & (r[5]==0) & (r[6]==0))
    psi <- -15*a11^2*a12
if ((r[1]==5) & (r[2]==0) & (r[3]==1) & (r[4]==0) & (r[5]==0) & (r[6]==0))
psi <-
-15*a11^2*a13
if ((r[1]==5) & (r[2]==0) & (r[3]==0) & (r[4]==1) & (r[5]==0) & (r[6]==0))
psi <-
-15*a11^2*a14
if ((r[1]==5) & (r[2]==0) & (r[3]==0) & (r[4]==0) & (r[5]==1) & (r[6]==0))
psi <-
-15*a11^2*a15
if ((r[1]==5) & (r[2]==0) & (r[3]==0) & (r[4]==0) & (r[5]==0) & (r[6]==1))
psi <-
-15*a11^2*a16
if ((r[1]==4) & (r[2]==2) & (r[3]==0) & (r[4]==0) & (r[5]==0) & (r[6]==0))
psi <-
-3*a11*(4*a12^2 + a11*a22)
if ((r[1]==4) & (r[2]==1) & (r[3]==1) & (r[4]==0) & (r[5]==0) & (r[6]==0))
psi <-
-3*a11*(4*a12*a13 + a11*a23)
if ((r[1]==4) & (r[2]==1) & (r[3]==0) & (r[4]==1) & (r[5]==0) & (r[6]==0))
psi <-
-3*a11*(4*a12*a14 + a11*a24)
if ((r[1]==4) & (r[2]==1) & (r[3]==0) & (r[4]==0) & (r[5]==1) & (r[6]==0))
psi <-
-3*a11*(4*a12*a15 + a11*a25)
if ((r[1]==4) & (r[2]==1) & (r[3]==0) & (r[4]==0) & (r[5]==0) & (r[6]==1))
psi <-
-3*a11*(4*a12*a16 + a11*a26)
if ((r[1]==4) & (r[2]==0) & (r[3]==2) & (r[4]==0) & (r[5]==0) & (r[6]==0))
psi <-
-3*a11*(4*a13^2 + a11*a33)
if ((r[1]==4) & (r[2]==0) & (r[3]==1) & (r[4]==1) & (r[5]==0) & (r[6]==0))
psi <-
-3*a11*(4*a13*a14 + a11*a34)
if ((r[1]==4) & (r[2]==0) & (r[3]==1) & (r[4]==0) & (r[5]==1) & (r[6]==0))
psi <-