regularityVar computes the Castelnuovo-Mumford regularity of homogeneous ideals in a polynomial ring by computing the shifts and degrees of generators in a minimal free resolution of the homogeneous ideal.
The list of variables
l contains the variables of the ring having degree 1. Those variables on the ring not in
l have automatically degree 0, as well as the the elements on the coefficient ring
i1 : R=QQ[a..i,x,y,z]
o1 = R
o1 : PolynomialRing
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i2 : f1 = a*x+b*y+c*z
o2 = a*x + b*y + c*z
o2 : R
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i3 : f2 = d*x+e*y+f*z
o3 = d*x + e*y + f*z
o3 : R
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i4 : f3 = g*x+h*y+i*z
o4 = g*x + h*y + i*z
o4 : R
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i5 : I = ideal(f1,f2,f3)
o5 = ideal (a*x + b*y + c*z, d*x + e*y + f*z, g*x + h*y + i*z)
o5 : Ideal of R
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i6 : l = {x,y,z}
o6 = {x, y, z}
o6 : List
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i7 : regularityVar (l,I)
o7 = 1
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