up previous next
NC.LTIdeal

Enumerate a (partial) (two-sided) leading-term ideal of a finitely generated ideal in a free monoid ring.
Syntax
          
NC.LTIdeal(G:LIST):LIST
NC.LTIdeal(G:LIST, DegreeBound:INT, LoopBound:INT, Flag: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 coefficient fieldK, alphabet (or set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. Since this function is based on Groebner basis computations, we refer users to NC.GB or NC.ReducedGB for information about the following three optional parameters:

Example
NC.SetX("xyzt");  
F1 := [[1,"xx"], [-1,"yx"]];    
F2 := [[1,"xy"], [-1,"ty"]];   
F3 := [[1,"xt"], [-1, "tx"]];   
F4 := [[1,"yt"], [-1, "ty"]];   
G := [F1, F2,F3,F4]; -- over Q (default field), LLEX ordering (default ordering) 
NC.LTIdeal(G);
["yt", "xt", "xy", "xx", "tyy", "yyx"]
-------------------------------
NC.SetFp(); 
NC.LTIdeal(G); -- over F2
["yt", "xt", "xy", "xx", "tyy", "yyx"]
-------------------------------
NC.SetFp(3); 
NC.LTIdeal(G); -- over F3
["yt", "xt", "xy", "xx", "tyy", "yyx"]
-------------------------------


See Also