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

Line 2: | Line 2: | ||

<title>NCo.LW</title> | <title>NCo.LW</title> | ||

<short_description> | <short_description> | ||

− | The leading word of a non-zero polynomial in a free monoid ring. | + | The leading word (or term) of a non-zero polynomial in a free monoid ring. |

</short_description> | </short_description> | ||

<syntax> | <syntax> | ||

NCo.LW(F:LIST):STRING | NCo.LW(F:LIST):STRING | ||

+ | NCo.LT(F:LIST):STRING | ||

</syntax> | </syntax> | ||

<description> | <description> |

## Revision as of 15:25, 2 May 2013

## NCo.LW

The leading word (or term) of a non-zero polynomial in a free monoid ring.

### Syntax

NCo.LW(F:LIST):STRING NCo.LT(F:LIST):STRING

### 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 the 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 LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). 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 STRING which represents the leading term of F with respect to the current word ordering. If

`F=0`, the function returns nothing.

#### Example

NCo.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[1,<quotes>aa</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>]]; NCo.LW(F); -- LLEX ordering (default ordering) bab ------------------------------- NCo.SetOrdering(<quotes>ELIM</quotes>); NCo.LW(F); aa ------------------------------- NCo.LW([]);

### See also