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

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<title>NC.Interreduction</title> | <title>NC.Interreduction</title> | ||

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− | Interreduce a | + | Interreduce a list (set) of polynomials in a free monoid ring. Note that, given an admissible ordering <tt>Ordering</tt>, a set of non-zero polynomial <tt>G</tt> is called <em>interreduced</em> w.r.t. <tt>Ordering</tt> if no element of <tt>Supp(g)</tt> is contained in <tt>LT(G\{g})</tt> for all <tt>g</tt> in <tt>G</tt>. |

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

<syntax> | <syntax> |

## Revision as of 10:58, 11 June 2012

## NC.Interreduction

Interreduce a list (set) of polynomials in a free monoid ring. Note that, given an admissible ordering `Ordering`, a set of non-zero polynomial `G` is called *interreduced* w.r.t. `Ordering` if no element of `Supp(g)` is contained in `LT(G\{g})` for all `g` in `G`.

### Syntax

NC.Interreduction(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 *coefficient field* `K`, *alphabet* (or set of indeterminates) `X` and *ordering* via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is `Q`. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*G*: a LIST of polynomials in`K<X>`. Each polynomial is represented as a LIST of monomials, which are pairs 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 LIST of interreduced polynomials.

#### Example

NC.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); G:=[[[1,<quotes>ba</quotes>]], [[1,<quotes>b</quotes>],[1,<quotes></quotes>]], [[1,<quotes>c</quotes>]]]; NC.Interreduction(G); [[[1, <quotes>a</quotes>]], [[1, <quotes>b</quotes>], [1, <quotes></quotes>]], [[1, <quotes>c</quotes>]]] -------------------------------

### See also