Difference between revisions of "ApCoCoA-1:Weyl.Inw"
(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...) |
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<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 | ||
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<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 | + | 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 >= 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. | ||
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</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
