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

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<command> | <command> | ||

<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> | ||

<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 environment <em>coefficient field</em> <tt> K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is <tt>Q</tt>, and the default ordering is the length-lexicographic ordering ( | + | Please set ring environment <em>coefficient field</em> <tt> K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>ApCoCoA-1:NCo.SetFp|NCo.SetFp</ref>, <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is <tt>Q</tt>, and the default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. |

<itemize> | <itemize> | ||

− | <item>@param <em>F</em>: a non-zero polynomial in <tt>K<X></tt>. 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 <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1, | + | <item>@param <em>F</em>: a non-zero polynomial in <tt>K<X></tt>. 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 <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |

− | <item>@return: a STRING which represents the leading term of F with respect to the current ordering. If <tt>F=0</tt>, the function returns nothing.</item> | + | <item>@return: a STRING which represents the leading term of F with respect to the current word ordering. If <tt>F=0</tt>, the function returns nothing.</item> |

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

<example> | <example> | ||

− | NCo.SetX( | + | NCo.SetX("abc"); |

− | F:=[[1, | + | F:=[[1,"ab"],[1,"aa"],[1,"bb"],[1,"bab"]]; |

NCo.LW(F); -- LLEX ordering (default ordering) | NCo.LW(F); -- LLEX ordering (default ordering) | ||

bab | bab | ||

------------------------------- | ------------------------------- | ||

− | NCo.SetOrdering( | + | NCo.SetOrdering("ELIM"); |

NCo.LW(F); | NCo.LW(F); | ||

aa | aa | ||

Line 29: | Line 31: | ||

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

<seealso> | <seealso> | ||

− | <see>NCo.SetFp</see> | + | <see>ApCoCoA-1:NCo.SetFp|NCo.SetFp</see> |

− | <see>NCo.SetOrdering</see> | + | <see>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</see> |

− | <see>NCo.SetX</see> | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |

− | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |

</seealso> | </seealso> | ||

<types> | <types> | ||

Line 42: | Line 44: | ||

<key>NCo.LW</key> | <key>NCo.LW</key> | ||

<key>LW</key> | <key>LW</key> | ||

− | <wiki-category>Package_gbmr</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_gbmr</wiki-category> |

</command> | </command> |

## Latest revision as of 13:40, 29 October 2020

This article is about a function from ApCoCoA-1. |

## 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("abc"); F:=[[1,"ab"],[1,"aa"],[1,"bb"],[1,"bab"]]; NCo.LW(F); -- LLEX ordering (default ordering) bab ------------------------------- NCo.SetOrdering("ELIM"); NCo.LW(F); aa ------------------------------- NCo.LW([]);

### See also