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B Conversion between Generating Sets

We list the three sets of generators and relations among them. We first list below a, b, g, z:
a = (- 1,- z,- xz,1,xy, y), b = (- xy,- 1,- x,z,1,yz), (88) g = (- y,- yz,- 1,xz,x, 1), z = (- x,- y,- z,x,y,z).
We now express the ai and * bj in terms of a, b, g, z:
a1 = g - zz, a2 = a - zb, a3 = - za + b - xg + xzz, a4 = zz, (89) * b1 = - ya + yzb + g - zz, b*2 = (1- z2)b- xg + xzz, * b3 = b - yz.
Further we also list below a, b, g, z in terms of X(A):
a = X(3), (4) b = X , g = - X(1) + zX(2), (90) (2) z = X .
This proves that since the a i, b* j generate the required module, the a, b, g, z and X(A), A = 1,2,3,4, also generate the same module.

The Gröbner basis is given in terms of the above generators as follows: G(1) = z, G(2) = X(1), G(3) = b, G(4) = a, and G(5) = a3.


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