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. 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' 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 |
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 |