Difference between revisions of "ApCoCoA-1:NCo.LC"
| Line 2: | Line 2: | ||
<title>NCo.LC</title> | <title>NCo.LC</title> | ||
<short_description> | <short_description> | ||
| − | The leading coefficient of a polynomial in a free monoid ring. | + | The leading coefficient of a non-zero polynomial in a free monoid ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 12: | Line 12: | ||
Please set ring environment <em>coefficient field</em> <tt> K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is <tt>Q</tt>, and the default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | Please set ring environment <em>coefficient field</em> <tt> K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is <tt>Q</tt>, and the default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | ||
<itemize> | <itemize> | ||
| − | <item>@param <em>F</em>: a polynomial in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | + | <item>@param <em>F</em>: a non-zero polynomial in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
<item>@return: a INT or RAT, which represents the leading coefficient of F with respect to the current word ordering. If <tt>F=0</tt>, the function returns <tt>0</tt>.</item> | <item>@return: a INT or RAT, which represents the leading coefficient of F with respect to the current word ordering. If <tt>F=0</tt>, the function returns <tt>0</tt>.</item> | ||
</itemize> | </itemize> | ||
Revision as of 16:42, 29 April 2013
NCo.LC
The leading coefficient of a non-zero polynomial in a free monoid ring.
Syntax
NCo.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 NCo.SetFp, NCo.SetX and NCo.SetOrdering, respectively, before using this function. The default coefficient field is Q, and the default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a non-zero polynomial in K<X>. Each polynomial is represented as a LIST of monomials, which are LISTs 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 with respect to the current word ordering. If F=0, the function returns 0.
Example
NCo.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NCo.SetOrdering(<quotes>ELIM</quotes>); NCo.LC(F); 2 ------------------------------- NCo.SetOrdering(<quotes>LLEX</quotes>); NCo.LC(F); 4 ------------------------------- NCo.LC([]); -- 0 polynomial 0 -------------------------------
See also
