Difference between revisions of "ApCoCoA-1:NC.NR"
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| − | Normal remainder of polynomial with respect to a | + | Normal remainder of polynomial with respect to a LIST of polynomials in a non-commutative polynomial ring. |
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<see>NC.SetOrdering</see> | <see>NC.SetOrdering</see> | ||
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<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
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<type>non_commutative</type> | <type>non_commutative</type> | ||
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| − | <key> | + | <key>ncpoly.NR</key> |
<key>NC.NR</key> | <key>NC.NR</key> | ||
<key>NR</key> | <key>NR</key> | ||
| − | <wiki-category> | + | <wiki-category>Package_ncpoly</wiki-category> |
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Revision as of 15:30, 25 April 2013
NC.NR
Normal remainder of polynomial with respect to a LIST of polynomials in a non-commutative polynomial 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
