# filename = Z2Nmatrix
# The Pfaffian form for the system $Z_2$ is given in the matrix form
#    N1*dt1 + N2*dt2

N1[1, 1] = 0:
N1[1, 2] = 1:
N1[1, 3] = 0:
N1[1, 4] = 0:
N1[1, 5] = 0:
N1[1, 6] = 0:

N1[2, 1] = 0:
N1[2, 2] = 0:
N1[2, 3] = 0:
N1[2, 4] = 1:
N1[2, 5] = 0:
N1[2, 6] = 0:

N1[3, 1] = 0:
N1[3, 2] = 0:
N1[3, 3] = 0:
N1[3, 4] = 0:
N1[3, 5] = 1:
N1[3, 6] = 0:

N1[4, 1] = (1/2)*(-a2+a1-a3)*(2+a0)/((t1-1)*(t1+1)*(t1-t2)):
N1[4, 2] = -(a0*t1+t1*a1-t2*a1+a0*t2+a0^2*t1-a3*t1+a3*t2)/((t1-1)*(t1+1)*(t1-t2)):
N1[4, 3] = -a2/((t1-1)*(t1+1)):
N1[4, 4] = (-2+2*a0*t1^2-a0+2*t1*t2-t1*a0*t2)/((t1-1)*(t1+1)*(t1-t2)):
N1[4, 5] = -(2-2*t1*a0*t2+a0+a0*t1^2-2*t2^2)/((t1-1)*(t1+1)*(t1-t2)):
N1[4, 6] = (-2*t1*t2+1+t1^2)/((t1-1)*(t1+1)):

N1[5, 1] = 0:
N1[5, 2] = 0:
N1[5, 3] = 0:
N1[5, 4] = 0:
N1[5, 5] = 0:
N1[5, 6] = 1:

N1[6, 1] = -(1/2)*(-a0*a2-2*a2+2*a1-2*a3+a0*a1-a0*a3+2*a2*a3)/((t1-t2)^2*(t1-1)*(t1+1)):
N1[6, 2] = (1/2)*(-2*a1-2*a3+4*a1*t2^2-4*t1*a0*t2+2*t1^2*a1+2*a0^2*t1^2+4*a0*t1^2+2*t1*t2*a0*a1+2*t1*t2*a3*a0-a0*a1+a0*a2-a0*a3+2*a2-2*a3*t1^2+2*t1^2*a2-4*t1*t2*a1+4*t1*t2*a3-4*t1*t2*a2-2*t1*t2*a0^2-a0*a1*t1^2-a0*a2*t1^2-a0*a3*t1^2)/((t1-t2)^3*(t1-1)*(t1+1)):
N1[6, 3] = (1/2)*(2*a2+2*a3+2*a2*t2^2+4*t1^2*a2-2*t2^2*a3-2*t1*t2*a0*a2-a0*a1+a0*a2+a0*a3-2*a1-8*t1*t2*a2+a0*a1*t2^2+a0*a2*t2^2-a0*t2^2*a3+2*a1*t2^2)/((t1-t2)^3*(t1-1)*(t1+1)):
N1[6, 4] = -(a0*t1^2-t1^2*a1-t1^2*a2+2*t1^2+2*t1*t2*a1-2-a1+a2-a0)/((t1-t2)^2*(t1-1)*(t1+1)):
N1[6, 5] = -(-3*a0*t1^2-t1^2*a2+4*t1*a0*t2+t1*t2*a0^2+a0*t2^2-a1-2*a0+a2-2+a1*t2^2+a3-a0^2+2*t2^2-t2^2*a3)/((t1-t2)^2*(t1-1)*(t1+1)):
N1[6, 6] = (-4*t1^2+a0*t1^2+t1*a0*t2+4*t1*t2-2*a0)/((t1-1)*(t1+1)*(t1-t2)):

N2[1, 1] = 0:
N2[1, 2] = 0:
N2[1, 3] = 1:
N2[1, 4] = 0:
N2[1, 5] = 0:
N2[1, 6] = 0:

N2[2, 1] = 0:
N2[2, 2] = 0:
N2[2, 3] = 0:
N2[2, 4] = 0:
N2[2, 5] = 1:
N2[2, 6] = 0:

N2[3, 1] = a3/((t2-1)*(t2+1)):
N2[3, 2] = a0*t1/((t2-1)*(t2+1)):
N2[3, 3] = a0*t2/((t2-1)*(t2+1)):
N2[3, 4] = -(t1-1)*(t1+1)/((t2-1)*(t2+1)):
N2[3, 5] = -2*(t1*t2-1)/((t2-1)*(t2+1)):
N2[3, 6] = 0:

N2[4, 1] = 0:
N2[4, 2] = 0:
N2[4, 3] = 0:
N2[4, 4] = 0:
N2[4, 5] = 0:
N2[4, 6] = 1:

N2[5, 1] = -(1/2)*(-a2+a1-a3)*(2+a0)/((t1-t2)*(t2-1)*(t2+1)):
N2[5, 2] = (2*a0*t1+t1*a1-t2*a1+a0^2*t1)/((t1-t2)*(t2-1)*(t2+1)):
N2[5, 3] = a2/((t2-1)*(t2+1)):
N2[5, 4] = -(t1-1)*(t1+1)*(2+a0)/((t1-t2)*(t2-1)*(t2+1)):
N2[5, 5] = (-2*t1*t2+2-t1*a0*t2+a0+a0*t1^2-a0*t2^2)/((t1-t2)*(t2-1)*(t2+1)):
N2[5, 6] = -(t1-1)*(t1+1)/((t2-1)*(t2+1)):
N2[6, 1] = -(1/2)*(-2*a0*a2+2*a0*a1-2*a0*a3-2*a2*a3-a0^2*a3-a0^2*a2+a0^2*a1)/((t2-1)*(t2+1)*(t1-t2)^2):
N2[6, 2] = (1/2)*(2*a1+2*a3-2*a1*t2^2-2*t2^2*a3+4*a0^2*t1^2-4*t1*t2*a0*a1-2*t1*t2*a0*a2+a0*a1-a0*a2+a0*a3-2*a2+2*a2*t2^2+a0*a1*t2^2+a0*a2*t2^2-a0*t2^2*a3-4*t1*t2*a0^2+2*a0*a1*t1^2+2*a0*a2*t1^2-2*a0^3*t1*t2+2*a0^3*t1^2)/((t1-t2)^3*(t2-1)*(t2+1)):
N2[6, 3] = -(1/2)*(2*a2+2*a3-2*a2*t2^2-2*t2^2*a3+2*t1*t2*a0*a2-a0*a1+a0*a2+a0*a3-2*a1-2*a0*a2*t1^2+a0*a1*t2^2-a0*a2*t2^2-a0*t2^2*a3+2*a1*t2^2)/((t1-t2)^3*(t2-1)*(t2+1)):
N2[6, 4] = -(a0^2*t1^2+t1^2*a2+2*a0*t1^2-2*a0+a1-a0^2-a2-a1*t2^2)/((t2-1)*(t2+1)*(t1-t2)^2):
N2[6, 5] = (a0^2*t1^2-2*t1*t2*a2-2*t1*a0*t2-t1*t2*a0^2+a0+a3+a2+a0*t2^2-a1+a2*t2^2-t2^2*a3+a1*t2^2)/((t2-1)*(t2+1)*(t1-t2)^2):
N2[6, 6] = -(t1^2+t2^2-2)*a0/((t1-t2)*(t2-1)*(t2+1)):