toNCRing -- Converts a Ring to an NCRing

Synopsis

• Usage:

  S = toNCRing R

• Inputs:
  • R, a ring,
• Outputs:
  • S, an instance of the type NCRing,

Description

i1 : R = QQ[a,b,c,d]

o1 = R

o1 : PolynomialRing

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' = toNCRing(S)
--Calling Bergman for NCGB calculation.
Complete!

o4 = S'

o4 : NCQuotientRing

i5 : ideal S'

o5 = Two-sided ideal {-ba+ab, -ca+ac, -cb+bc, -da+ad, -db+bd, -dc+cd, -bc+ad}

o5 : NCIdeal

See also

• toM2Ring -- Compute the abelianization of an NCRing and returns a Ring.