i1 : B = threeDimSklyanin(QQ,{1,1,-1},{x,y,z})
--Calling Bergman for NCGB calculation.
Complete!
o1 = B
o1 : NCQuotientRing
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i2 : M = ncMatrix {{x, y, z}}
o2 = | x y z |
o2 : NCMatrix
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i3 : sigma = ncMap(B,B,{y,z,x})
o3 = NCRingMap B <--- B
o3 : NCRingMap
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i4 : N = ncMatrix {{M},{sigma M}, {sigma sigma M}}
o4 = | x y z |
| y z x |
| z x y |
o4 : NCMatrix
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i5 : N' = ncMatrix {{sigma sigma M}, {sigma M}, {M}}
o5 = | z x y |
| y z x |
| x y z |
o5 : NCMatrix
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i6 : N*N'
o6 = | 2*y^2 2*x^2 2*y*x+2*x*y |
| 2*x^2 2*y*x+2*x*y 2*y^2 |
| 2*y*x+2*x*y 2*y^2 2*x^2 |
o6 : NCMatrix
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i7 : N'*N
o7 = | y*z+y^2-x*z+x*y -y*z+y*x+x*z+x^2 y^2+y*x+x*y+x^2 |
| -y*z+y*x+x*z+x^2 y^2+y*x+x*y+x^2 y*z+y^2-x*z+x*y |
| y^2+y*x+x*y+x^2 y*z+y^2-x*z+x*y -y*z+y*x+x*z+x^2 |
o7 : NCMatrix
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