Difference between revisions of "ApCoCoA-1:Weyl.WDim"
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| − | <command> | + | {{Version|1}} |
| + | <command> | ||
<title>Weyl.WDim</title> | <title>Weyl.WDim</title> | ||
| − | <short_description>Computes the dimension ideal I in Weyl algebra < | + | <short_description>Computes the dimension of an ideal <tt>I</tt> in Weyl algebra <tt>A_n</tt>.</short_description> |
<syntax> | <syntax> | ||
Weyl.WDim(I:IDEAL):INT | Weyl.WDim(I:IDEAL):INT | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | + | <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/> | ||
| + | This function computes the dimension of an Ideal <tt>I = (f_1,f_2, ..., f_r)</tt> which represents the module <tt>A_n/I</tt> where every generator <tt>f_i</tt> should be a Weyl polynomial in Normal form. This dimension of <tt>I</tt> is equal to the dimension of the associated graded module with respect to the Bernstein filtration. | ||
| − | + | <itemize> | |
| + | <item>@param <em>I</em> An ideal in the Weyl algebra.</item> | ||
| + | <item>@return The dimension of the given ideal.</item> | ||
| + | </itemize> | ||
<example> | <example> | ||
W3::=ZZ/(7)[x[1..3],d[1..3]]; | W3::=ZZ/(7)[x[1..3],d[1..3]]; | ||
Use W3; | Use W3; | ||
| − | Cpu time = 0.00, User time = 0 | + | -- Cpu time = 0.00, User time = 0 |
------------------------------- | ------------------------------- | ||
F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; | F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; | ||
| Line 45: | Line 51: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Weyl.WNormalForm</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| − | <see>Weyl.WGB</see> | + | <see>ApCoCoA-1:Weyl.WNormalForm|Weyl.WNormalForm</see> |
| − | <see>Weyl.IsHolonomic</see> | + | <see>ApCoCoA-1:Weyl.WGB|Weyl.WGB</see> |
| + | <see>ApCoCoA-1:Weyl.IsHolonomic|Weyl.IsHolonomic</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| − | <type> | + | <type>apcocoaserver</type> |
| + | <type>ideal</type> | ||
</types> | </types> | ||
<key>weyl.wdim</key> | <key>weyl.wdim</key> | ||
| − | <wiki-category>Package_weyl</wiki-category> | + | <key>wdim</key> |
| + | <wiki-category>ApCoCoA-1:Package_weyl</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 10:38, 7 October 2020
| This article is about a function from ApCoCoA-1. |
Weyl.WDim
Computes the dimension of an ideal I in Weyl algebra A_n.
Syntax
Weyl.WDim(I:IDEAL):INT
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.
This function computes the dimension of an Ideal I = (f_1,f_2, ..., f_r) which represents the module A_n/I where every generator f_i should be a Weyl polynomial in Normal form. This dimension of I is equal to the dimension of the associated graded module with respect to the Bernstein filtration.
@param I An ideal in the Weyl algebra.
@return The dimension of the given ideal.
Example
W3::=ZZ/(7)[x[1..3],d[1..3]]; Use W3; -- Cpu time = 0.00, User time = 0 ------------------------------- F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; F2:=-3x[2]d[2]^5d[3]^5+x[2]d[1]^3; F3:=-2d[1]^4d[2]^5-x[1]d[2]^7+x[3]^3d[3]^5; I:=Ideal(F1,F2,F3); Weyl.WDim(I); -- CoCoAServer: computing Cpu Time = 2.36 ------------------------------- 2 -------------------------------
Example
A3::=QQ[x[1..2],d[1..2]]; Use A3; ------------------------------- I:=Ideal(x[1]d[1] + 2x[2]d[2] - 5, d[1]^2 - d[2]); ------------------------------- Weyl.WDim(I); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- 2 ------------------------------- -- If the dimension is ZERO, -1 will be returned Weyl.WDim(Ideal(x[1],d[1])); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- -1 -------------------------------
See also
