This method constructs a skew polynomial ring with coefficient ring R and generators elements of L. The relations all have the form a*b - f*b*a where a and b are in L. If R is a Bergman coefficient ring, an NCGroebnerBasis is computed for B.
i1 : R = QQ[q]/ideal{q^4+q^3+q^2+q+1} o1 = R o1 : QuotientRing |
i2 : A = skewPolynomialRing(R,promote(2,R),{x,y,z,w}) Using GC ring in VectorArithmetic. o2 = A o2 : FreeAlgebraQuotient |
i3 : x*y == 2*y*x o3 = true |
i4 : B = skewPolynomialRing(R,q,{x,y,z,w}) Using GC ring in VectorArithmetic. o4 = B o4 : FreeAlgebraQuotient |
i5 : x*y == q*y*x o5 = true |
i6 : Bop = oppositeRing B Using GC ring in VectorArithmetic. o6 = Bop o6 : FreeAlgebraQuotient |
i7 : y*x == q*x*y o7 = true |
i8 : C = skewPolynomialRing(QQ,2_QQ, {x,y,z,w}) o8 = C o8 : FreeAlgebraQuotient |
i9 : x*y == 2*y*x o9 = true |
i10 : D = skewPolynomialRing(QQ,1_QQ, {x,y,z,w}) o10 = D o10 : FreeAlgebraQuotient |
i11 : isCommutative C o11 = false |
i12 : isCommutative D o12 = false |
i13 : Cop = oppositeRing C o13 = Cop o13 : FreeAlgebraQuotient |
i14 : y*x == 2*x*y o14 = true |