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 of polynomial with respect to a list of polynomials | + | Normal remainder of polynomial with respect to a list of polynomials in a free monoid ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 23: | Line 23: | ||
Alphabet : abc | Alphabet : abc | ||
Ordering : LLEX | Ordering : LLEX | ||
| − | |||
------------------------------- | ------------------------------- | ||
F:=[[1,<quotes>ab</quotes>],[1,<quotes>aca</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>],[1,<quotes></quotes>]]; | F:=[[1,<quotes>ab</quotes>],[1,<quotes>aca</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>],[1,<quotes></quotes>]]; | ||
| Line 31: | Line 30: | ||
NC.NR(F,G); | NC.NR(F,G); | ||
[[1, <quotes>bcb</quotes>], [-1, <quotes>ccc</quotes>], [-1, <quotes>bb</quotes>], [1, <quotes>cb</quotes>], [-1, <quotes></quotes>]] | [[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.SetOrdering(<quotes>ELIM</quotes>); | ||
| Line 47: | Line 45: | ||
<see>NC.Interreduction</see> | <see>NC.Interreduction</see> | ||
<see>NC.Intersection</see> | <see>NC.Intersection</see> | ||
| + | <see>NC.IsFinite</see> | ||
<see>NC.IsGB</see> | <see>NC.IsGB</see> | ||
<see>NC.IsHomog</see> | <see>NC.IsHomog</see> | ||
| Line 64: | Line 63: | ||
<see>NC.SetX</see> | <see>NC.SetX</see> | ||
<see>NC.Subtract</see> | <see>NC.Subtract</see> | ||
| + | <see>NC.TruncatedGB</see> | ||
<see>NC.UnsetFp</see> | <see>NC.UnsetFp</see> | ||
<see>NC.UnsetOrdering</see> | <see>NC.UnsetOrdering</see> | ||
Revision as of 15:45, 8 June 2012
NC.NR
Normal remainder of polynomial with respect to a list of polynomials in a free monoid ring.
Syntax
NC.NR(F:LIST, G: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.
Please set ring environment coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a polynomial in K<X>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <X> 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 [].
@param G: a LIST of non-zero polynomials in K<X>.
@return: a LIST which represents the normal remainder of F w.r.t. G.
Example
NC.SetX(<quotes>abc</quotes>); NC.RingEnv(); Coefficient ring : Q 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>]]; G:=[F1,F2]; NC.NR(F,G); [[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,G); [[1, <quotes>bcb</quotes>], [-1, <quotes>bb</quotes>], [1, <quotes>cb</quotes>], [-1, <quotes>ccc</quotes>], [-1, <quotes></quotes>]] -------------------------------
See also
