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Interreduce a LIST of polynomials in a free monoid ring.
NCo.Interreduction(G:LIST):LIST
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Note that, given a word ordering
Ordering, a set of non-zero polynomials
G is called
interreduced with respect to
Ordering if no element of
Supp(g) is contained in the leading word ideal
LW(G\{g}) for all
g in
G.
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 set of indeterminates)
X and
ordering via the functions
NCo.SetFp,
NCo.SetX and
NCo.SetOrdering, respectively, before using this function. The default coefficient field is
Q, and the default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
- @param G: a LIST of polynomials in K. Each polynomial is represented as a LIST of monomials, which are LISTs 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 LIST of interreduced polynomials with respect to the current word ordering.
NCo.SetX("abc");
NCo.SetOrdering("ELIM");
G:=[[[1,"ba"]], [[1,"b"],[1,""]], [[1,"c"]]];
NCo.Interreduction(G);
[[[1, "a"]], [[1, "b"], [1, ""]], [[1, "c"]]]
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