Difference between revisions of "ApCoCoA-1:NCo.BLC"
(New page: <command> <title>NCo.BLC</title> <short_description> The leading coefficient of a polynomial in a free monoid ring over the binary field F_{2}={0,1}. </short_description> <syntax> NCo.BLC(...) |
|||
| Line 2: | Line 2: | ||
<title>NCo.BLC</title> | <title>NCo.BLC</title> | ||
<short_description> | <short_description> | ||
| − | The leading coefficient of a polynomial in a free monoid ring over the binary field F_{2}={0,1}. | + | The leading coefficient of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 10: | Line 10: | ||
Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is the length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is the length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | ||
<itemize> | <itemize> | ||
| − | <item>@param <em>F:</em> a polynomial in the free monoid ring <tt>F_{2}<X></tt>. Each polynomial is represented as a LIST of words (or terms) in <tt><X></tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[<quotes>xy</quotes>, <quotes>y</quotes>, <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 the free monoid ring <tt>F_{2}<X></tt>. Each polynomial is represented as a LIST of words (or terms) in <tt><X></tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[<quotes>xy</quotes>, <quotes>y</quotes>, <quotes></quotes>]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
| − | <item>@return: a INT which represents | + | <item>@return: a INT which represents the leading coefficient of F with respect to the current word ordering. Actually, the function returns 0 if F=0 and returns 1 otherwise.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Revision as of 17:05, 30 April 2013
NCo.BLC
The leading coefficient of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}.
Syntax
NCo.BLC(F:LIST):INT
Description
Please set ring environment alphabet (or set of indeterminates) X and word ordering via the functions NCo.SetX and NCo.SetOrdering, respectively, before calling this function. The default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a non-zero polynomial in the free monoid ring F_{2}<X>. Each polynomial is represented as a LIST of words (or terms) in <X>. Each word is represented as a STRING. For example, xy^2x is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial f=xy-y+1 is represented as F:=["xy", "y", ""]. The zero polynomial 0 is represented as the empty LIST [].
@return: a INT which represents the leading coefficient of F with respect to the current word ordering. Actually, the function returns 0 if F=0 and returns 1 otherwise.
Example
NCo.SetX(<quotes>xX</quotes>); NCo.SetOrdering(<quotes>LLEX</quotes>); F1:=[<quotes>xX</quotes>,<quotes></quotes>]; NCo.BLC(F1); 1 ------------------------------- NCo.BLC([]); 0 -------------------------------
See also
