isNormal(RingElement) -- Determines if an element of a noncommutative ring is normal

i1 : A = QQ<|a,b,c|>

o1 = A

o1 : FreeAlgebra

i2 : I = ideal {a*b+b*a,a*c+c*a,b*c+c*b}

o2 = ideal (a*b + b*a, a*c + c*a, b*c + c*b)

o2 : Ideal of A

i3 : B = A/I
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.

o3 = B

o3 : FreeAlgebraQuotient

i4 : sigma = map(B,B,{b,c,a})

o4 = map (B, B, {b, c, a})

o4 : RingMap B <-- B

i5 : C = oreExtension(B,sigma,w)
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.

o5 = C

o5 : FreeAlgebraQuotient

i6 : isCentral w

o6 = false

i7 : isNormal w

o7 = true