-- -*- M2-comint -*- hash: 6658333707190688636

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})

o2 = A

o2 : FreeAlgebraQuotient

i3 : x*y == 2*y*x

o3 = true

i4 : B = skewPolynomialRing(R,q,{x,y,z,w})

o4 = B

o4 : FreeAlgebraQuotient

i5 : x*y == q*y*x

o5 = true

i6 : Bop = oppositeRing B
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.

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
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.

o13 = Cop

o13 : FreeAlgebraQuotient

i14 : y*x == 2*x*y

o14 = true

i15 : 
