This command lifts an NCMatrix to a matrix over its ambient NCRing.
i1 : A = QQ{x,y,z,w} o1 = A o1 : NCPolynomialRing |
i2 : B = A/ncIdeal{y*z + z*y - x^2, x*z + z*x - y^2, z^2 - x*y - y*x} --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12252-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12252-0/3.ter ... Complete! o2 = B o2 : NCQuotientRing |
i3 : M = ncMatrix {{x,y,z,w},{y,z,w,x}} o3 = | x y z w | | | | y z w x | o3 : NCMatrix |
i4 : N = M || 2*M || -3*M o4 = | x y z w | | | | y z w x | | | | 2x 2y 2z 2w | | | | 2y 2z 2w 2x | | | | -3x -3y -3z -3w | | | | -3y -3z -3w -3x | o4 : NCMatrix |
i5 : ring N o5 = B o5 : NCQuotientRing |
i6 : ring lift N o6 = A o6 : NCPolynomialRing |