oppositeRing -- Creates the opposite ring of a noncommutative ring

Synopsis

• Usage:
Aop = oppositeRing A
• Inputs:
• Outputs:

Description

Given a noncommutative ring A, this creates a noncommutative ring whose defining ideal is generated by the "opposites" - elements whose noncommutative monomial terms have been reversed - of the generators of the defining ideal of A.

 i1 : R = QQ[q]/ideal{q^4+q^3+q^2+q+1} o1 = R o1 : QuotientRing i2 : A = skewPolynomialRing(R,q,{x,y,z,w}) Using GC ring in VectorArithmetic. o2 = A o2 : FreeAlgebraQuotient i3 : x*y == q*y*x o3 = true i4 : Aop = oppositeRing A Using GC ring in VectorArithmetic. o4 = Aop o4 : FreeAlgebraQuotient i5 : y*x == q*x*y o5 = true