up previous next
Checks whether a polynomial of a list of polynomials is homogeneous 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 or a LIST of polynomials 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 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 system. 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
-------------------------------
NC.IsHomog(F1);
True
-------------------------------
NC.IsHomog(F2);
False
-------------------------------
|