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

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

This method takes a noncommutative ring and returns the quotient of a commutative polynomial ring (or an exterior algebra, if SkewCommutative=>true) on the same generators by the defining relations of the input ring.

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 variable(s)

i8 : x*y-y*x

o8 = 2x*y

o8 : C

i9 : w^2

o9 = 0

o9 : C

Ways to use toCommRing:

toCommRing(FreeAlgebra)
toCommRing(FreeAlgebraQuotient)

For the programmer

The object toCommRing is a method function with options.

The source of this document is in AssociativeAlgebras/doc.m2:901:0.

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

Description

See also

Ways to use toCommRing:

For the programmer