This command allows for the product of composable NCMatrices (or ordinary matrices over the base).
i1 : B = threeDimSklyanin(QQ,{1,1,-1},{x,y,z})
--Calling Bergman for NCGB calculation.
--running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12438-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12438-0/3.ter ... 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'
| 2 2 |
o6 = | 2y 2x 2yx+2xy |
| |
| 2 2 |
| 2x 2yx+2xy 2y |
| |
| 2 2 |
| 2yx+2xy 2y 2x |
o6 : NCMatrix
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i7 : N'*N
| 2 2 2 2 |
o7 = | yz+y -xz+xy -yz+yx+xz+x y +yx+xy+x |
| |
| 2 2 2 2 |
| -yz+yx+xz+x y +yx+xy+x yz+y -xz+xy |
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| 2 2 2 2 |
| y +yx+xy+x yz+y -xz+xy -yz+yx+xz+x |
o7 : NCMatrix
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