torAlgebra -- Computes the Tor algebra of a ring

Synopsis

• Usage:

  torR = torAlgebra(R)

• Inputs:
  • R, a ring,
• Optional inputs:
  • GenDegreeLimit => ..., default value infinity, Option to specify the maximum degree to look for generators
  • RelDegreeLimit => ..., default value infinity, Option to specify the maximum degree to look for relations
• Outputs:
  • torR, a ring,

Description

i1 : R = ZZ/101[a,b,c,d]

o1 = R

o1 : PolynomialRing

i2 : TorR = torAlgebra(R)

o2 = TorR

o2 : PolynomialRing, 4 skew commutative variables

i3 : S = R/ideal{a^3,b^3,c^3,d^5}

o3 = S

o3 : QuotientRing

i4 : TorS = torAlgebra(S)

o4 = TorS

o4 : PolynomialRing, 4 skew commutative variables

i5 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a^2*b^2*c^3*d^2}

o5 = R

o5 : QuotientRing

i6 : TorR = torAlgebra(R,GenDegreeLimit=>5)

o6 = TorR

o6 : PolynomialRing, 4 skew commutative variables