# 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 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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</description> | </description> | ||

<seealso> | <seealso> | ||

− | <see>Weyl.InIw</see> | + | <see>ApCoCoA-1:Weyl.InIw|Weyl.InIw</see> |

− | <see>Weyl.WNormalForm</see> | + | <see>ApCoCoA-1:Weyl.WNormalForm|Weyl.WNormalForm</see> |

</seealso> | </seealso> | ||

<types> | <types> | ||

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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>ApCoCoA-1:Package_weyl</wiki-category> |

</command> | </command> |

## 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