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Leading coefficient of a polynomial in a free monoid ring.
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.
- @param F: a polynomial in K. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in and C is the coefficient of W. For example, the polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].
- @return: a INT or RAT which represents the leading coefficient of F w.r.t. the current ordering. If F=0, the function returns 0.
NC.SetX("abc");
F:=[[1,"ab"],[2,"aa"],[3,"bb"],[4,"bab"]];
NC.SetOrdering("ELIM");
NC.LC(F);
2
-------------------------------
NC.SetOrdering("LLEX");
NC.LC(F);
4
-------------------------------
NC.LC([]); -- 0 polynomial
0
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