Difference between revisions of "ApCoCoA-1:NC.LC"
| Line 2: | Line 2: | ||
<title>NC.LC</title> | <title>NC.LC</title> | ||
<short_description> | <short_description> | ||
| − | Leading coefficient of a polynomial | + | Leading coefficient of a polynomial in a free monoid ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 21: | Line 21: | ||
NC.LC(F); | NC.LC(F); | ||
2 | 2 | ||
| − | |||
------------------------------- | ------------------------------- | ||
NC.SetOrdering(<quotes>LLEX</quotes>); | NC.SetOrdering(<quotes>LLEX</quotes>); | ||
NC.LC(F); | NC.LC(F); | ||
4 | 4 | ||
| − | |||
------------------------------- | ------------------------------- | ||
NC.LC([]); -- 0 polynomial | NC.LC([]); -- 0 polynomial | ||
0 | 0 | ||
| − | |||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
| Line 42: | Line 39: | ||
<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 59: | Line 57: | ||
<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 15:34, 8 June 2012
NC.LC
Leading coefficient of a polynomial in a free monoid 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
