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Check whether a polynomial of a list of polynomials is homogeneous 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 or a LIST of polynomials 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 BOOL value which is True if F is homogeneous and False otherwise. Note that if F is a set of homogeneous polynomials, then F generates a homogeneous ideal. It is false contrarily.
NC.SetX("xy");
F1 := [[1,"x"], [1,"y"]];
F2 := [[1,"xx"],[1,"xy"],[1,"x"]];
F := [F1,F2];
NC.IsHomog(F);
False
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NC.IsHomog(F1);
True
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NC.IsHomog(F2);
False
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