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NC.GHF

Hilbert function of F2/(Gb).
Syntax
          
NC.GHF(Gb:LIST):LIST
NC.GHF(Gb:LIST, DegreeBound:INT):LIST

          

Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Please set ring environment alphabet (or indeterminates) X and ordering through the functions NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

Example
NC.SetX("ab");
NC.SetOrdering("LLEX");
F1:=["aa", ""];
F2:=["bbb", ""];
F3:=["abababbabbabababbabb", ""];
G:=[F1,F2,F3]; -- a generalized triangle group 
NC.GHF(G);

Warning: the input is not a Groeber basis, and error might occur consequently.
[1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 464, 614, 812, 
1074, 1421, 1879, 2486, 3288, 4349, 5753, 7610, 10067, 13317]
-------------------------------
-- Done.
-------------------------------
GB:=NC.GGB(G);
NC.GHF(GB);

[1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 24, 27, 31, 35, 37, 38, 41, 43, 41, 34, 30, 32, 31, 23, 15, 9, 4, 1, 0]
-------------------------------
-- Done.
-------------------------------
RGB:=NC.GReducedGB(G);
NC.GHF(RGB);

[1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 24, 27, 31, 35, 37, 38, 41, 43, 41, 34, 30, 32, 31, 23, 15, 9, 4, 1, 0]
-------------------------------
-- Done.
-------------------------------
Sum(It);

576
-------------------------------
-- Done.
-------------------------------


See Also