oppositeRing -- Creates the opposite ring of a noncommutative ring

Synopsis

Usage:

Aop = oppositeRing A
Inputs:
- A, an instance of the type NCRing,
Outputs:
- Aop, an instance of the type NCRing,

Description

Given an NCRing A, this creates an NCRing whose defining NCIdeal is generated by the "opposites" - elements whose noncommutative monomial terms have been reversed - of the generators of the defining NCIdeal of A. If the coefficient ring of A is a Bergman ring, an NCGroebnerBasis is computed for Aop.

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})

o2 = A

o2 : NCQuotientRing

i3 : x*y == q*y*x

o3 = true

i4 : Aop = oppositeRing A

o4 = Aop

o4 : NCQuotientRing

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

o5 = true

Ways to use oppositeRing :

oppositeRing(NCRing)

For the programmer

The object oppositeRing is a method function.

oppositeRing -- Creates the opposite ring of a noncommutative ring

Synopsis

Description

See also

Ways to use oppositeRing :

For the programmer