This function returns the algebra that contains A and B as a subalgebra, with the commutation law on the images of A and B given by a*b = q*b*a for all a in A and b in B. In the case of A ** B, q = 1.
i1 : A = QQ{x,y} o1 = A o1 : NCPolynomialRing |
i2 : B = skewPolynomialRing(QQ,(-1)_QQ, {a,b}) --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/3.ter ... Complete! o2 = B o2 : NCQuotientRing |
i3 : C = qTensorProduct(A,B,-1_QQ) --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/5.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/8.ter ... Complete! --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/10.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/13.ter ... Complete! o3 = C o3 : NCQuotientRing |
i4 : ideal C o4 = Two-sided ideal {ba+ab, ax+xa, bx+xb, ay+ya, by+yb} o4 : NCIdeal |
i5 : D = A ** B --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/15.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/18.ter ... Complete! --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/20.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12303-0/23.ter ... Complete! o5 = D o5 : NCQuotientRing |
i6 : ideal D o6 = Two-sided ideal {ba+ab, ax-xa, bx-xb, ay-ya, by-yb} o6 : NCIdeal |