that is either a polynomial ring or a quotient of a polynomial ring, and suppose that
has the standard grading.
as a list.
to return the entire Hilbert function (i.e., until the Hilbert function is zero) of
as a list. The user can override this by using the
option to bound the highest degree considered.
through degree 20. Again, the user can select a different upper bound for the degree by using the
option.
in order to compute with the Hilbert series, which is much faster than repeatedly computing the Hilbert function.
i1 : R=ZZ/32003[a..c];
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i2 : hilbertFunct ideal(a^3,b^3,c^3)
o2 = {1, 3, 6, 7, 6, 3, 1}
o2 : List
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i3 : hilbertFunct ideal(a^3,a*b^2)
o3 = {1, 3, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
------------------------------------------------------------------------
24, 25}
o3 : List
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i4 : hilbertFunct(ideal(a^3,a*b^2),Degree=>4)
o4 = {1, 3, 6, 8, 9}
o4 : List
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i5 : M=ideal(a^3,b^4,a*c);
o5 : Ideal of R
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i6 : Q=R/M;
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i7 : hilbertFunct ideal(c^4)
o7 = {1, 3, 5, 6, 5, 3, 1}
o7 : List
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i8 : hilbertFunct ideal(b*c,a*b)
o8 = {1, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
o8 : List
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