# Difference between revisions of "ApCoCoA-1:NCo.BLC"

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<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> | ||

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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