Difference between revisions of "ApCoCoA-1:NC.LC"
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<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
| − | <type> | + | <type>polynomial</type> |
| + | <type>non_commutative</type> | ||
</types> | </types> | ||
<key>gbmr.LC</key> | <key>gbmr.LC</key> | ||
Revision as of 14:56, 14 December 2010
NC.LC
Leading coefficient of a polynomial over a free associative K-algebra.
Syntax
NC.LC(F:LIST):INT or RAT
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 indeterminates) X and ordering through the functions NC.SetFp(Prime), NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. 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 is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", unit is represented as an empty string "". Then, polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. 0 polynomial is represented as an empty LIST [].
@return: a INT or RAT which represents a leading coefficient of F.
Example
NC.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NC.SetOrdering(<quotes>ELIM</quotes>); NC.LC(F); 2 ------------------------------- NC.SetOrdering(<quotes>LLEX</quotes>); NC.LC(F); 4 ------------------------------- NC.LC([]); -- 0 polynomial 0 -------------------------------
See also
