# Difference between revisions of "ApCoCoA-1:Weyl.WNR"

Line 1: | Line 1: | ||

<command> | <command> | ||

<title>Weyl.WNR</title> | <title>Weyl.WNR</title> | ||

− | <short_description>Computes the normal remainder of a Weyl polynomial F with respect | + | <short_description>Computes the normal remainder of a Weyl polynomial <tt>F</tt> with respect |

− | to a polynomial or a set of | + | to a polynomial or a set of polynomials.</short_description> |

<syntax> | <syntax> | ||

Weyl.WNR(F:POLY,G:POLY):POLY | Weyl.WNR(F:POLY,G:POLY):POLY | ||

Line 10: | Line 10: | ||

<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/> | ||

− | Computes the normal remainder of a Weyl polynomial F with respect to a polynomial G or a set of polynomials in the list G. | + | Computes the normal remainder of a Weyl polynomial <tt>F</tt> with respect to a polynomial <tt>G</tt> or a set of polynomials in the list <tt>G</tt>. |

− | If G is Groebner basis then this function is used for ideal membership problem. | + | If <tt>G</tt> is Groebner basis then this function is used for ideal membership problem. |

<itemize> | <itemize> | ||

<item>@param <em>F</em> A Weyl polynomial in normal form.</item> | <item>@param <em>F</em> A Weyl polynomial in normal form.</item> | ||

<item>@param <em>G</em> A Weyl polynomial or a list of Weyl polynomials.</item> | <item>@param <em>G</em> A Weyl polynomial or a list of Weyl polynomials.</item> | ||

− | <item>@return The remainder as a | + | <item>@return The remainder as a Weyl polynomial using normal remainder algorithm in Weyl algebra <tt>A_n</tt>.</item> |

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

## Revision as of 13:35, 10 July 2009

## Weyl.WNR

Computes the normal remainder of a Weyl polynomial `F` with respect

to a polynomial or a set of polynomials.

### Syntax

Weyl.WNR(F:POLY,G:POLY):POLY Weyl.WNR(F:POLY,G:LIST):POLY

### 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.

Computes the normal remainder of a Weyl polynomial `F` with respect to a polynomial `G` or a set of polynomials in the list `G`.

If `G` is Groebner basis then this function is used for ideal membership problem.

@param

*F*A Weyl polynomial in normal form.@param

*G*A Weyl polynomial or a list of Weyl polynomials.@return The remainder as a Weyl polynomial using normal remainder algorithm in Weyl algebra

`A_n`.

*Note:* All polynomials that are not in normal form should be first converted into normal form using Weyl.WNormalForm, otherwise you may get unexpected results.

#### Example

W3::=ZZ/(7)[x[1..3],d[1..3]]; Use W3; F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; F2:=-3x[2]d[2]^5d[3]^5+x[2]d[1]^3; F3:=-2d[1]^4d[2]^5-x[1]d[2]^7+x[3]^3d[3]^5; L:=[F1,F2,F3]; Weyl.WNR(F1,L); 0 ------------------------------- Weyl.WNR(F1,Gens(Ideal(F2,F3))); -d[1]^3d[2]^5d[3]^5 + x[2]^5 ------------------------------- Weyl.WNR(x[2]^5-d[1]^3,L); x[2]^5 - d[1]^3 ------------------------------- Weyl.WNR(x[2]^5-d[1]^3d[2]^7d[3]^6,F1); -x[2]^5d[2]^2d[3] - 3x[2]^4d[2]d[3] + x[2]^5 + x[2]^3d[3] -------------------------------

### See also