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

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<title>Weyl.Inw</title>
 
<title>Weyl.Inw</title>
 
<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>
 
<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>
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       <see>ApCoCoA-1:Weyl.InIw|Weyl.InIw</see>
       <see>Weyl.WNormalForm</see>
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     <key>inw</key>
 
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Latest revision as of 10:35, 7 October 2020

This article is about a function from ApCoCoA-1.

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