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DGAlgebras :: deviations

deviations -- Computes the deviations of the input ring

Synopsis

Description

This command computes the deviations of the ring R. The deviations are the same as the degrees of the generators of the acyclic closure of R, or the degrees of the generators of the Tor algebra of R. This function takes an option called Limit (default value 3) that specifies the largest deviation to compute.

i1 : R = ZZ/101[a,b,c,d]/ideal {a^3,b^3,c^3,d^3}

o1 = R

o1 : QuotientRing
i2 : deviations(R)

o2 = Tally{{1, 1} => 4}
           {2, 3} => 4

o2 : Tally
i3 : deviations(R,DegreeLimit=>4)

o3 = Tally{{1, 1} => 4}
           {2, 3} => 4

o3 : Tally
i4 : S = R/ideal{a^2*b^2*c^2*d^2}

o4 = S

o4 : QuotientRing
i5 : deviations(S,DegreeLimit=>4)

o5 = Tally{{1, 1} => 4 }
           {2, 3} => 4
           {2, 8} => 1
           {3, 9} => 4
           {4, 10} => 6
           {4, 11} => 4

o5 : Tally
i6 : T = ZZ/101[a,b]/ideal {a^2-b^3}

o6 = T

o6 : QuotientRing
i7 : deviations(T,DegreeLimit=>4)

o7 = Tally{{1} => 2}
           {2} => 1

o7 : Tally

Note that the deviations of T are not graded, since T is not graded.

Ways to use deviations :