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

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Interreduction of a LIST of polynomials in a non-commutative polynomial ring. | Interreduction of a LIST of polynomials in a non-commutative polynomial ring. | ||

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

− | Note that, given a word ordering, a set of non-zero polynomial <tt>G</tt> is called <em>interreduced</em> if, for all <tt>g</tt> in <tt>G</tt>, no element of <tt>Supp(g)</tt> is a multiple of any element in <tt> | + | Note that, given a word ordering, a set of non-zero polynomial <tt>G</tt> is called <em>interreduced</em> if, for all <tt>g</tt> in <tt>G</tt>, no element of <tt>Supp(g)</tt> is a multiple of any element in <tt>LW{G\{g}}</tt>. |

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

<syntax> | <syntax> | ||

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<seealso> | <seealso> | ||

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

+ | <see>NC.LW</see> | ||

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

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

## Revision as of 18:43, 30 April 2013

## NC.Interreduction

Interreduction of a LIST of polynomials in a non-commutative polynomial ring.

Note that, given a word ordering, a set of non-zero polynomial `G` is called *interreduced* if, for all `g` in `G`, no element of `Supp(g)` is a multiple of any element in `LW{G\{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 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

*G*: a LIST of non-commutative polynomials. 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 an interreduced set of G.

#### 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