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

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

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− | Note that, given a word ordering, a set <tt>G</tt> of non-zero polynomials is called <em>interreduced</em> if no element of <tt>Supp(g)</tt> is contained in the leading word ideal <tt> | + | Note that, given a word ordering, a set <tt>G</tt> of non-zero polynomials is called <em>interreduced</em> if no element of <tt>Supp(g)</tt> is contained in the leading word ideal <tt>BLW(G\{g})</tt> for all <tt>g</tt> in <tt>G</tt>. |

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

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+ | <see>NCo.BLW</see> | ||

<see>NCo.SetOrdering</see> | <see>NCo.SetOrdering</see> | ||

<see>NCo.SetX</see> | <see>NCo.SetX</see> |

## Revision as of 18:27, 30 April 2013

## NCo.BInterreduction

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

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`.

### Syntax

NCo.BInterreduction(G:LIST):LIST

### 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 *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