-- Hilbert functions and series

restart
R=QQ[x,y,z]
J=matrix{{x,x^3+y^3+z^3}}
coker J
Mr=res coker J -- the resolution
Mr.dd -- the maps
betti Mr -- shifts in the resolution

-- primary component supported on the irrelevant ideal
m=ideal(x,y,z)
(m^2 : ideal(x+y) ) -- different form m^2

-- Koszul complex of three elements
restart
R=QQ[f1,f2,f3]
I=ideal(f1,f2,f3)
res I
oo.dd


R=QQ[f1,f2,f3,f4]
I=ideal(f1,f2,f3,f4)
res I
oo.dd

-- cubic and conic
R=QQ[x,y,z,w]
C=random(3,R)
Q=random(2,R)
I=ideal(Q,C)
res I
oo.dd
hilbertPolynomial(I,Projective=>false)