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Packages » AssociativeAlgebras :: toCommRing
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toCommRing -- Compute the abelianization of a Ring and returns a Ring.

Synopsis

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})
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.

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

See also

Ways to use toCommRing :

For the programmer

The object toCommRing is a method function with options.