# Difference between revisions of "ApCoCoA-1:NC.LC"

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Before calling the function, please set ring environment coefficient field <tt>K</tt>, alphabet <tt>X</tt> and ordering through the functions <ref>NC.SetFp</ref>(Prime) (or <ref>NC.UnsetFp</ref>()), <ref>NC.SetX</ref>(X) and <ref>NC.SetOrdering</ref>(Ordering) respectively. Default coefficient field is <tt>Q</tt>. Default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | Before calling the function, please set ring environment coefficient field <tt>K</tt>, alphabet <tt>X</tt> and ordering through the functions <ref>NC.SetFp</ref>(Prime) (or <ref>NC.UnsetFp</ref>()), <ref>NC.SetX</ref>(X) and <ref>NC.SetOrdering</ref>(Ordering) respectively. Default coefficient field is <tt>Q</tt>. 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 in <tt>K<X></tt> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in <tt>K</tt> and w is a word in <tt>X*</tt>. Unit in <tt>X*</tt> is empty word represented as an empty STRING <quotes></quotes>. <tt>0</tt> polynomial is represented as an empty LIST []. For example, polynomial <tt>F:=xy-y+1</tt> in <tt>K<x,y></tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]].</item> | + | <item>@param <em>F</em>: a polynomial in <tt>K<X></tt>. Each polynomial in <tt>K<X></tt> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in <tt>K</tt> and w is a word in <tt>X*</tt>. Unit in <tt>X*</tt> is empty word represented as an empty STRING <quotes></quotes>. <tt>0</tt> polynomial is represented as an empty LIST []. For example, polynomial <tt>F:=xy-y+1</tt> in <tt>K<x,y></tt> is represented as <tt>F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]</tt>.</item> |

<item>@return: an element of K which is leading term of <tt>F</tt> with respect to current ordering. If <tt>F=0</tt>, then return <tt>0</tt>. </item> | <item>@return: an element of K which is leading term of <tt>F</tt> with respect to current ordering. If <tt>F=0</tt>, then return <tt>0</tt>. </item> | ||

</itemize> | </itemize> |

## Revision as of 12:56, 26 July 2010

## NC.LC

Leading coefficient of a polynomial over a free associative K-algebra.

### Syntax

NC.LC(F:LIST):K

### 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.

Before calling the function, please set ring environment coefficient field `K`, alphabet `X` and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is `Q`. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*F*: a polynomial in`K<X>`. Each polynomial in`K<X>`is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in`K`and w is a word in`X*`. Unit in`X*`is empty word represented as an empty STRING "".`0`polynomial is represented as an empty LIST []. For example, polynomial`F:=xy-y+1`in`K<x,y>`is represented as`F:=[[1,"xy"], [-1, "y"], [1,""]]`.@return: an element of K which is leading term of

`F`with respect to current ordering. If`F=0`, then return`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