Difference between revisions of "ApCoCoA-1:NC.LC"
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| − | Leading coefficient of a polynomial in a | + | Leading coefficient of a non-zero polynomial in a non-commutative polynomial ring. |
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<syntax> | <syntax> | ||
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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> | ||
</types> | </types> | ||
| − | <key> | + | <key>ncpoly.LC</key> |
<key>NC.LC</key> | <key>NC.LC</key> | ||
<key>LC</key> | <key>LC</key> | ||
| − | <wiki-category> | + | <wiki-category>Package_ncpoly</wiki-category> |
</command> | </command> | ||
Revision as of 15:26, 25 April 2013
NC.LC
Leading coefficient of a non-zero polynomial in a non-commutative polynomial ring.
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 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 [].
@return: a INT or RAT which represents the leading coefficient of F w.r.t. the current ordering. If F=0, the function returns 0.
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
