toCommRing -- Compute the abelianization of a Ring and returns a Ring.

Synopsis

• Usage:

  S = toCommRing R

• Inputs:
  • R, a quotient of a free algebra, or FreeAlgebra
• Optional inputs:
  • SkewCommutative => a Boolean value, default value false
• Outputs:
  • S, a ring,

Description

i1 : A = skewPolynomialRing(QQ,(-1)_QQ,{w,x,y,z})

o1 = A

o1 : FreeAlgebraQuotient

i2 : x*y-y*x

o2 = -2y*x

o2 : A

i3 : w^2

      2
o3 = w

o3 : A

i4 : B = toCommRing(A)

o4 = B

o4 : QuotientRing

i5 : x*y

o5 = 0

o5 : B

i6 : w^2

      2
o6 = w

o6 : B

i7 : C = toCommRing(A,SkewCommutative=>true)

o7 = C

o7 : PolynomialRing, 4 skew commutative variables

i8 : x*y-y*x

o8 = 2x*y

o8 : C

i9 : w^2

o9 = 0

o9 : C

See also

• toFreeAlgebraQuotient -- Converts a Ring to a noncommutative ring