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DGAlgebras :: torAlgebra

torAlgebra -- Computes the Tor algebra of a ring

Synopsis

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

The above example calculates the Tor algebra of R and S up to degree 3, by default. One can also specify the maximum degree to compute generators of the Tor algebra by specifying the GenDegreeLimit option.

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

Ways to use torAlgebra :

For the programmer

The object torAlgebra is a method function with options.