# Difference between revisions of "ApCoCoA-1:Weyl.InIw"

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<command> | <command> | ||

<title>Weyl.InIw</title> | <title>Weyl.InIw</title> | ||

− | <short_description>Computes the initial ideal of a D-ideal I in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).</short_description> | + | <short_description>Computes the initial ideal of a D-ideal <tt>I</tt> 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.InIw(I:IDEAL,W:LIST):IDEAL | Weyl.InIw(I:IDEAL,W:LIST):IDEAL | ||

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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 ideal of a D-ideal I in the Weyl algebra D with respect to weight vector W:=[u,v] such that u+v> | + | Computes the initial ideal of a D-ideal <tt>I</tt> 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>InIw(P,W)</tt> is an ideal of graded ring of D with respect to weight vector <tt>W</tt>. Due to limitations in CoCoA4, all <tt>u_i</tt> and <tt>v_i</tt> should be positive integers. Computation of initial ideal if <tt>u+v= 0</tt> is not implemented yet. |

<itemize> | <itemize> | ||

<item>@param <em>I</em> An ideal in the Weyl algebra.</item> | <item>@param <em>I</em> An ideal 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 An ideal, which is the initial ideal of I with respect to W.</item> | + | <item>@return An ideal, which is the initial ideal of <tt>I</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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<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||

<type>ideal</type> | <type>ideal</type> | ||

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</types> | </types> | ||

<key>weyl.InIw</key> | <key>weyl.InIw</key> | ||

− | <key> | + | <key>iniw</key> |

<wiki-category>Package_weyl</wiki-category> | <wiki-category>Package_weyl</wiki-category> | ||

</command> | </command> |

## Revision as of 13:15, 10 July 2009

## Weyl.InIw

Computes the initial ideal of a D-ideal `I` in Weyl algebra `A_n` with respect to the weight vector `W=(u_i,v_i)`.

### Syntax

Weyl.InIw(I:IDEAL,W:LIST):IDEAL

### 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 ideal of a D-ideal `I` 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 `InIw(P,W)` is an ideal of graded ring of D with respect to weight vector `W`. Due to limitations in CoCoA4, all `u_i` and `v_i` should be positive integers. Computation of initial ideal if `u+v= 0` is not implemented yet.

@param

*I*An ideal in the Weyl algebra.@param

*W*A list of n positive integers, where n = number of indeterminates.@return An ideal, which is the initial ideal of

`I`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 A4::=QQ[x[1..4],d[1..4]]; I4:=Ideal(d[2]d[3]-d[1]d[4],x[1]d[1]-x[4]d[4]-1,x[2]d[2]+x[4]d[4]+1,x[3]d[3]+x[4]d[4]+2); Weyl.InIw(I4,[0,0,0,0,1,1,1,1]); --This function is implemented only for positive weights! ERROR: All weights shoud be strictly positive CONTEXT: Error("All weights shoud be strictly positive") ------------------------------- Weyl.InIw(I4,[1,1,1,1,2,2,1,1]); -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Ideal(x[2]x[3]x[4]d[4]^2 - x[1]x[4]^2d[4]^2, x[1]x[4]d[3]d[4] + x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4], x[2]d[1]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1], x[2]d[2], x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4]) ------------------------------- Weyl.InIw(I4,[1,2,1,1,2,2,1,1]); -- CoCoAServer: computing Cpu Time = 0.032 ------------------------------- Ideal(x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4], x[2]d[1]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1], x[2]d[2], x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4]) ------------------------------- Weyl.InIw(I4,[2,2,2,2,1,1,1,1]); -- CoCoAServer: computing Cpu Time = 0.031 ------------------------------- Ideal(x[2]x[3]x[4]d[4]^2 - x[1]x[4]^2d[4]^2, x[1]x[4]d[3]d[4] + x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4] + x[3]x[4]d[4]^2, x[2]d[1]d[4] + x[4]d[3]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1] - x[4]d[4], x[2]d[2] + x[4]d[4], x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4]) -------------------------------

### See also