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