ApCoCoA-1:Weyl.WLT: Difference between revisions
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New page: <command> <title>Weyl.WLT</title> <short_description>Computes the leading term ideal of a D-ideal I in Weyl algebra <tt>A_n</tt>.</short_description> <syntax> Weyl.WLT(I:IDEAL):I... |
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<command> | {{Version|1}} | ||
<command> | |||
<title>Weyl.WLT</title> | <title>Weyl.WLT</title> | ||
<short_description>Computes the leading term ideal of a D-ideal I in Weyl algebra <tt>A_n</tt>.</short_description> | <short_description>Computes the leading term ideal of a D-ideal <tt>I</tt> in Weyl algebra <tt>A_n</tt>.</short_description> | ||
<syntax> | <syntax> | ||
Weyl.WLT(I:IDEAL):IDEAL | Weyl.WLT(I:IDEAL):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/> | ||
This function computes the ideal of leading monomials of all the polynomials of a D-ideal I in the Weyl algebra D. | This function computes the ideal of leading monomials of all the polynomials of a D-ideal <tt>I</tt> in the Weyl algebra D. | ||
<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>@return An ideal, which is leading term ideal of I.</item> | <item>@return An ideal, which is leading term ideal of <tt>I</tt>.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
A1::=QQ[x,d];Use A1; | |||
L:=x^2(x-1)(x-3)d^2-(6x^3-20x^2+12x)d+(12x^2-32x+12); | |||
I:=Ideal(L,d^5); | |||
Weyl.WLT(I); | |||
-- CoCoAServer: computing Cpu Time = 0.016 | |||
------------------------------- | |||
Ideal(xd^4, x^3d^2, x^2d^3, d^5) | |||
------------------------------- | |||
ChI:=Weyl.CharI(I);ChI; | |||
-- CoCoAServer: computing Cpu Time = 0 | |||
------------------------------- | |||
The characteristic ideal lies in QQ[x,d] | |||
-------------------------------------------------- | |||
------------------------------- | |||
Ideal(d^5, x^4d^2 - 4x^3d^2 + 3x^2d^2, xd^3) | |||
------------------------------- | |||
</example> | </example> | ||
<example> | <example> | ||
A2::=QQ[x[1..2],d[1..2]]; | |||
Use A2; | |||
I:=Ideal(x[1]d[2],x[2]d[1]); | |||
Weyl.WLT(I); | |||
-- CoCoAServer: computing Cpu Time = 0.016 | |||
------------------------------- | |||
Ideal(x[2]^2d[2], x[2]d[2]^2, x[1]d[1], x[2]d[1], x[1]d[2]) | |||
------------------------------- | |||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
<see>Weyl.InIw</see> | <see>ApCoCoA-1:Weyl.InIw|Weyl.InIw</see> | ||
<see>ApCoCoA-1:Weyl.CharI|Weyl.CharI</see> | |||
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
<type>ideal</type> | <type>ideal</type> | ||
</types> | </types> | ||
<key>weyl. | <key>weyl.wlt</key> | ||
<key> | <key>wlt</key> | ||
<wiki-category>Package_weyl</wiki-category> | <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.WLT
Computes the leading term ideal of a D-ideal I in Weyl algebra A_n.
Syntax
Weyl.WLT(I:IDEAL):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.
This function computes the ideal of leading monomials of all the polynomials of a D-ideal I in the Weyl algebra D.
@param I An ideal in the Weyl algebra.
@return An ideal, which is leading term ideal of I.
Example
A1::=QQ[x,d];Use A1; L:=x^2(x-1)(x-3)d^2-(6x^3-20x^2+12x)d+(12x^2-32x+12); I:=Ideal(L,d^5); Weyl.WLT(I); -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Ideal(xd^4, x^3d^2, x^2d^3, d^5) ------------------------------- ChI:=Weyl.CharI(I);ChI; -- CoCoAServer: computing Cpu Time = 0 ------------------------------- The characteristic ideal lies in QQ[x,d] -------------------------------------------------- ------------------------------- Ideal(d^5, x^4d^2 - 4x^3d^2 + 3x^2d^2, xd^3) -------------------------------
Example
A2::=QQ[x[1..2],d[1..2]]; Use A2; I:=Ideal(x[1]d[2],x[2]d[1]); Weyl.WLT(I); -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Ideal(x[2]^2d[2], x[2]d[2]^2, x[1]d[1], x[2]d[1], x[1]d[2]) -------------------------------
See also
