Given a ring A, an Ore extension of A by x is the quotient of the free extension A<x> by the relations x*a - sigma(a)*x-delta(a) where sigma is an automorphism of A and delta is a sigma-derivation. This method returns the defining ideal (in the appropriate tensor algebra) of an Ore extension of A by x. The current version assumes the sigma-derivation delta is 0.
i1 : B = skewPolynomialRing(QQ,(-1)_QQ,{x,y,z,w}) --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12432-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12432-0/3.ter ... Complete! o1 = B o1 : NCQuotientRing |
i2 : sigma = ncMap(B,B,{y,z,w,x}) o2 = NCRingMap B <--- B o2 : NCRingMap |
i3 : C = oreIdeal(B,sigma,a) o3 = Two-sided ideal {yx+xy, zx+xz, zy+yz, wx+xw, wy+yw, wz+zw, ax-ya, ay-za, az-wa, aw-xa} o3 : NCIdeal |