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
