# torAlgebra -- Computes the Tor algebra of a ring

## Synopsis

• Usage:
torR = torAlgebra(R)
• Inputs:
• 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:

## 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 :

• "torAlgebra(Ring)"
• torAlgebra(Ring,Ring) -- Computes Tor_R(S,k) up to a specified generating and relating degree.

## For the programmer

The object torAlgebra is .