Difference between revisions of "ApCoCoA-1:NC.NR"
| Line 2: | Line 2: | ||
<title>NC.NR</title> | <title>NC.NR</title> | ||
<short_description> | <short_description> | ||
| − | Normal remainder polynomial with respect to a list of polynomials over a free associative K-algebra. | + | Normal remainder polynomial with respect to a list of polynomials over a free associative <tt>K</tt>-algebra. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 40: | Line 40: | ||
<see>NC.Intersection</see> | <see>NC.Intersection</see> | ||
<see>NC.IsGB</see> | <see>NC.IsGB</see> | ||
| + | <see>NC.KernelOfHomomorphism</see> | ||
<see>NC.LC</see> | <see>NC.LC</see> | ||
<see>NC.LT</see> | <see>NC.LT</see> | ||
Revision as of 10:02, 20 July 2010
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.
@param F: a polynomial in K<X>. Each polynomial in K<X> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in K and w is a word in X*. Unit in X* is empty word represented as an empty STRING "". 0 polynomial is represented as an empty LIST []. For example, polynomial F:=xy-y+1 in K<x,y> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].
@param Polynomials: a LIST of polynomials in K<X>.
@return: a LIST which represents normal remainder of F with respect to Polynomials.
Example
NC.RingEnv(); Coefficient ring : Q (float type in C++) Alphabet : abc Ordering : LLEX ------------------------------- F:=[[1,<quotes>ab</quotes>],[1,<quotes>aca</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>],[1,<quotes></quotes>]]; F1 := [[1,<quotes>a</quotes>],[1,<quotes>c</quotes>]]; F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; Polynomials:=[F1,F2]; NC.NR(F,Polynomials); [[1, <quotes>bcb</quotes>], [-1, <quotes>ccc</quotes>], [-1, <quotes>bb</quotes>], [1, <quotes>cb</quotes>], [-1, <quotes></quotes>]] ------------------------------- NC.SetOrdering(<quotes>ELIM</quotes>); NC.NR(F,Polynomials); [[1, <quotes>bcb</quotes>], [-1, <quotes>bb</quotes>], [1, <quotes>cb</quotes>], [-1, <quotes>ccc</quotes>], [-1, <quotes></quotes>]] -------------------------------
See also
