Difference between revisions of "ApCoCoA-1:NC.NR"
(New page: <command> <title>NC.NR</title> <short_description> Normal remainder polynomial with respect to a list of polynomials over a free associative K-algebra. </short_description> <syntax> NC.NR(...) |
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</itemize> | </itemize> | ||
<example> | <example> | ||
| − | |||
NC.RingEnv(); | NC.RingEnv(); | ||
Coefficient ring : Q (float type in C++) | Coefficient ring : Q (float type in C++) | ||
Alphabet : abc | Alphabet : abc | ||
| − | Ordering : | + | Ordering : LLEX |
------------------------------- | ------------------------------- | ||
| − | F:=[[1,<quotes>ab</quotes>],[1,<quotes> | + | F:=[[1,<quotes>ab</quotes>],[1,<quotes>aca</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>],[1,<quotes></quotes>]]; |
| − | NC. | + | 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> | + | NC.SetOrdering(<quotes>ELIM</quotes>); |
| − | NC. | + | NC.NR(F,Polynomials); |
| − | + | [[1, <quotes>bcb</quotes>], [-1, <quotes>bb</quotes>], [1, <quotes>cb</quotes>], [-1, <quotes>ccc</quotes>], [-1, <quotes></quotes>]] | |
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
Revision as of 11:22, 14 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 STRING 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
