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

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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||

<par/> | <par/> | ||

− | Please set ring | + | Please set non-commutative polynomial ring (via the command <ref>Use</ref>) and word ordering (via the function <ref>NC.SetOrdering</ref>) before calling this function. The default word ordering is the length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant commands and functions. |

<itemize> | <itemize> | ||

− | <item>@param <em>F</em>: a polynomial | + | <item>@param <em>F</em>: a non-zero non-commutative polynomial. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |

− | <item>@return: a | + | <item>@return: a LIST, which is the leading word of F with respect to the current word ordering.</item> |

</itemize> | </itemize> | ||

<example> | <example> | ||

Line 29: | Line 29: | ||

</description> | </description> | ||

<seealso> | <seealso> | ||

+ | <see>Use</see> | ||

<see>NC.SetOrdering</see> | <see>NC.SetOrdering</see> | ||

<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> |

## Revision as of 18:31, 25 April 2013

## NC.LW

Leading word of a non-zero polynomial in a non-commutative polynomial ring.

### Syntax

NC.LW(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 non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.

@param

*F*: a non-zero non-commutative polynomial. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial`f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5`is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial`0`is represented as the empty LIST [].@return: a LIST, which is the leading word of F with respect to the current word ordering.

#### Example

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

### See also