Difference between revisions of "ApCoCoA-1:Weyl.Inw"

From ApCoCoAWiki
(New page: <command> <title>Weyl.Inw</title> <short_description>Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).</short_description> <syn...)
 
Line 1: Line 1:
 
   <command>
 
   <command>
 
<title>Weyl.Inw</title>
 
<title>Weyl.Inw</title>
<short_description>Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).</short_description>
+
<short_description>Computes the initial form of a polynomial in Weyl algebra <tt>A_n</tt> with respect to the weight vector <tt>W=(u_i,v_i)</tt>.</short_description>
 
<syntax>
 
<syntax>
 
Weyl.Inw(P:POLY,W:LIST):POLY
 
Weyl.Inw(P:POLY,W:LIST):POLY
Line 8: Line 8:
 
<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 initial form of a normally ordered Weyl polynomial P in the Weyl algebra D with respect to weight vector W=(u,v) such that u+v>=0. Here u=(u1,...,un) and v=(v1,...,vn) are weights of indeterminates [x1,...,xn] and [y1,...,yn] respectively. Note that Inw(P,W) is a polynomail in the graded ring of D with respet to weight vector W.
+
Computes the initial form of a normally ordered Weyl polynomial P in the Weyl algebra D with respect to weight vector <tt>W=(u,v)</tt> such that <tt>u+v &gt;= 0</tt>. Here <tt>u=(u1,...,un)</tt> and <tt>v=(v1,...,vn)</tt> are weights of indeterminates <tt>[x1,...,xn]</tt> and <tt>[y1,...,yn]</tt> respectively. Note that <tt>Inw(P,W)</tt> is a polynomial in the graded ring of D with respect to weight vector <tt>W</tt>.
 
<itemize>
 
<itemize>
 
<item>@param <em>P</em> A polynomial in the Weyl algebra.</item>
 
<item>@param <em>P</em> A polynomial in the Weyl algebra.</item>
 
<item>@param <em>W</em> A list of n positive integers, where n = number of indeterminates.</item>
 
<item>@param <em>W</em> A list of n positive integers, where n = number of indeterminates.</item>
<item>@return A polynomial, which is the initial form of P with respect to W.</item>
+
<item>@return A polynomial, which is the initial form of <tt>P</tt> with respect to <tt>W</tt>.</item>
 
</itemize>
 
</itemize>
 
<em>Beta Warning:</em> This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.
 
<em>Beta Warning:</em> This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.
Line 52: Line 52:
 
     </types>
 
     </types>
 
     <key>weyl.Inw</key>
 
     <key>weyl.Inw</key>
 
+
    <key>inw</key>
 
     <wiki-category>Package_weyl</wiki-category>
 
     <wiki-category>Package_weyl</wiki-category>
 
   </command>
 
   </command>

Revision as of 13:22, 10 July 2009

Weyl.Inw

Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).

Syntax

Weyl.Inw(P:POLY,W: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 initial form of a normally ordered Weyl polynomial P in the Weyl algebra D with respect to weight vector W=(u,v) such that u+v >= 0. Here u=(u1,...,un) and v=(v1,...,vn) are weights of indeterminates [x1,...,xn] and [y1,...,yn] respectively. Note that Inw(P,W) is a polynomial in the graded ring of D with respect to weight vector W.

  • @param P A polynomial in the Weyl algebra.

  • @param W A list of n positive integers, where n = number of indeterminates.

  • @return A polynomial, which is the initial form of P with respect to W.

Beta Warning: This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.

Example

Use A2::=QQ[x[1..2],d[1..2]];
W:=[0,0,1,1];
Weyl.Inw(x[1]d[1]+x[1],W);
x[1]d[1]
-------------------------------
Weyl.Inw(x[1]d[1]+d[1],W);
x[1]d[1] + d[1]
-------------------------------
Weyl.Inw(x[1]d[1]+x[2]d[2]+d[2]^2,W);
d[2]^2
-------------------------------
Weyl.Inw(3x[1]d[1]^2+4x[2]d[1]+d[2]^2,W);
3x[1]d[1]^2 + d[2]^2
-------------------------------
W2:=[-1,-1,1,1];
Weyl.Inw(3x[1]d[1]+4x[2]d[1]+6x[2]d[2],W2);
3x[1]d[1] + 4x[2]d[1] + 6x[2]d[2]
-------------------------------
Weyl.Inw(0,W);
0
-------------------------------


See also

Weyl.InIw

Weyl.WNormalForm