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[[z31, z32, z33], [z21, z22, z23], [z11, z12, z13]]
[z31 z32 1]
[z21 1 0]
[ 1 0 0]
[(1, 0, 0), (0, 1, 0), (0, 0, 1)]
[1 0 0]
[0 2 0]
[0 0 3]
[[a11, a12], [a21, a22, a23], [a31, a32, a33, a34]]
[(a11*z31 + a12*z32, a11*z21 + a12, a11)]
(z31, a11*z31 + a12*z32)
(2*z21, a11*z21 + a12)
(3, a11)
(a11*z31 + a12*z32, z31)
(a11*z21 + a12, 2*z21)
(a11, 3)
3
-z21
Principal ideal (-z21*z32 + 2*z31) of Symbolic Ring
-z21*z32 + 3*z31
The cell of 321 in the Peterson variety is the set of all matrices of the form
[z31 z32 1]
[z21 1 0]
[ 1 0 0]
where z31 = -z21*z32 + 3*z31.