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Leading term of a polynomial over a free associative
K-algebra.
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 field
K, alphabet (or indeterminates)
X and ordering through the functions
NC.SetFp(Prime),
NC.SetX(X) and
NC.SetOrdering(Ordering), respectively, before calling the function. Default coefficient field is
Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
- @param F: a polynomial in K. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", unit is represented as an empty string "". Then, polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. 0 polynomial is represented as an empty LIST [].
- @return: a STRING which represents a leading term of F with respect to current ordering. If F=0, the function returns nothing.
NC.SetX("abc");
F:=[[1,"ab"],[1,"aa"],[1,"bb"],[1,"bab"]];
NC.LT(F); -- LLEX ordering (default ordering)
bab
-------------------------------
NC.SetOrdering("ELIM");
NC.LT(F);
aa
-------------------------------
NC.LT([]);
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