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AssociativeAlgebras :: toFreeAlgebraQuotient

toFreeAlgebraQuotient -- Converts a Ring to a noncommutative ring

Synopsis

Description

This function converts commutative rings and quotients of exterior algebras (i.e. quotients of PolynomialRing) to a ring of type FreeAlgebraQuotient.

i1 : R = QQ[a,b,c,d, SkewCommutative=>{2,3}]

o1 = R

o1 : PolynomialRing, 2 skew commutative variables
i2 : I = ideal(a*d-b*c)

o2 = ideal(- b*c + a*d)

o2 : Ideal of R
i3 : S = R/I

o3 = S

o3 : QuotientRing
i4 : S' = toFreeAlgebraQuotient(S)

o4 = S'

o4 : FreeAlgebraQuotient
i5 : ideal S'

                                                                             
o5 = ideal (a*b - b*a, a*c - c*a, b*c - c*b, a*d - d*a, b*d - d*b, c*d + d*c,
     ------------------------------------------------------------------------
      2   2
     c , d , - c*b + d*a)

o5 : Ideal of QQ <|a, b, c, d|>

See also

Ways to use toFreeAlgebraQuotient :

For the programmer

The object toFreeAlgebraQuotient is a method function.