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 |
i2 : M = ncMatrix {{x, y, z}} o2 = | x y z | o2 : NCMatrix |
i3 : sigma = ncMap(B,B,{y,z,x}) o3 = NCRingMap B <--- B o3 : NCRingMap |
i4 : N = ncMatrix {{M},{sigma M}, {sigma sigma M}} o4 = | x y z | | | | y z x | | | | z x y | o4 : NCMatrix |
i5 : N' = ncMatrix {{sigma sigma M}, {sigma M}, {M}} o5 = | z x y | | | | y z x | | | | x y z | o5 : NCMatrix |
i6 : N*N' | 2 2 | o6 = | 2y 2x 2yx+2xy | | | | 2 2 | | 2x 2yx+2xy 2y | | | | 2 2 | | 2yx+2xy 2y 2x | o6 : NCMatrix |
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 | | | | 2 2 2 2 | | y +yx+xy+x yz+y -xz+xy -yz+yx+xz+x | o7 : NCMatrix |