Difference between revisions of "ApCoCoA-1:Weyl.WNR"
From ApCoCoAWiki
(Change Wiki-category) |
|||
| Line 2: | Line 2: | ||
<title>Weyl.WNR</title> | <title>Weyl.WNR</title> | ||
<short_description>Computes normal remainder of a Weyl polynomial F with respect | <short_description>Computes normal remainder of a Weyl polynomial F with respect | ||
| − | to a polynomial | + | to a polynomial or a set of polnomials. </short_description> |
<syntax> | <syntax> | ||
| − | Weyl.WNR(F:POLY,G:LIST | + | Weyl.WNR(F:POLY,G:POLY):POLY |
| + | Weyl.WNR(F:POLY,G:LIST):POLY | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | Computes normal remainder of a Weyl polynomial F with respect to a polynomial | + | 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 | + | If G is Groebner basis then this function is used for ideal membership problem. |
| − | + | <itemize> | |
| + | <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>@return The remainder as a weyl polynomial using normal remainder algorithm in Weyl algebra A_n.</item> | ||
| + | </itemize> | ||
| − | + | <em>Note:</em> All polynomials that are not in normal form should be first converted in to normal form using <ref>Weyl.WNormalForm</ref>, otherwise you may get unexpected results. | |
| − | |||
<example> | <example> | ||
W3::=ZZ/(7)[x[1..3],d[1..3]]; | W3::=ZZ/(7)[x[1..3],d[1..3]]; | ||
| Line 35: | Line 39: | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
| − | + | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
Revision as of 12:39, 23 April 2009
Weyl.WNR
Computes normal remainder of a Weyl polynomial F with respect
to a polynomial or a set of polnomials.
Syntax
Weyl.WNR(F:POLY,G:POLY):POLY Weyl.WNR(F:POLY,G:LIST):POLY
Description
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 in to 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
