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NC.NR

Normal remainder polynomial with respect to a list of polynomials over a free associative K-algebra.
Syntax
          
NC.NR(F:LIST, Polynomials:LIST):LIST

          

Description
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.

Before calling the function, please set ring environment coefficient field K, alphabet X and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

Example
NC.SetX("abc");
NC.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : LLEX

-------------------------------
F:=[[1,"ab"],[1,"aca"],[1,"bb"],[1,"bab"],[1,""]];
F1 := [[1,"a"],[1,"c"]]; 
F2 := [[1,"b"],[1,"ba"]];
Polynomials:=[F1,F2];
NC.NR(F,Polynomials);
[[1, "bcb"], [-1, "ccc"], [-1, "bb"], [1, "cb"], [-1, ""]]
-------------------------------
NC.SetOrdering("ELIM");
NC.NR(F,Polynomials);
[[1, "bcb"], [-1, "bb"], [1, "cb"], [-1, "ccc"], [-1, ""]]
-------------------------------


See Also