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

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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 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 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>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. |

<itemize> | <itemize> | ||

<item>@param <em>G:</em> a LIST of polynomials 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>G:</em> a LIST of polynomials 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> | ||

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

<seealso> | <seealso> | ||

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

## Revision as of 08:26, 7 October 2020

## NCo.BInterreduction

Interreduce a LIST of polynomials in a free monoid ring over the binary field.

### Syntax

NCo.BInterreduction(G:LIST):LIST

### Description

Note that, given a word ordering, a set `G` of non-zero polynomials is called *interreduced* if no element of `Supp(g)` is contained in the leading word ideal `BLW(G\{g})` for all `g` in `G`.

*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 *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 length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*G:*a LIST of polynomials 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 LIST of interreduced polynomials.

#### Example

NCo.SetX(<quotes>abc</quotes>); NCo.SetOrdering(<quotes>ELIM</quotes>); Polynomials:=[[<quotes>ba</quotes>,<quotes>c</quotes>],[<quotes>b</quotes>,<quotes></quotes>], [<quotes>c</quotes>]]; NCo.BInterreduction(Polynomials); [[<quotes>a</quotes>], [<quotes>b</quotes>, <quotes></quotes>], [<quotes>c</quotes>]] -------------------------------

### See also