Difference between revisions of "ApCoCoA-1:Weyl.WMul"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
| − | <title>Weyl. | + | <title>Weyl.WGB</title> |
| − | <short_description>Computes the Groebner basis of | + | <short_description>Computes the Groebner basis of an ideal I in Weyl algebra <math>A_n</math>, using corresponding |
implementation in CoCoALib.</short_description> | implementation in CoCoALib.</short_description> | ||
<syntax> | <syntax> | ||
| − | Weyl. | + | Weyl.WGB(I):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
{{ApCoCoAServer}} | {{ApCoCoAServer}} | ||
| − | This function computes a Groebner Basis for | + | This function computes a Groebner Basis for an Ideal <math>I = (f_1,f_2, ..., f_r)</math> where every generator <math>f_i</math> should be a Weyl polynomial in Normal form. |
<example> | <example> | ||
| Line 18: | Line 18: | ||
-- CoCoAServer: computing Cpu Time = 0 | -- CoCoAServer: computing Cpu Time = 0 | ||
------------------------------- | ------------------------------- | ||
| − | [d, x, 1] | + | [1] |
| + | ------------------------------- | ||
| + | Note that Groebner basis you obtained is minimal. | ||
| + | A2::=QQ[x[1..2],y[1..2]]; | ||
| + | Use A2; | ||
| + | I1:=Ideal(x[1]^7,y[1]^7); | ||
| + | Weyl.WGB(I1); | ||
| + | -- CoCoAServer: computing Cpu Time = 0.094 | ||
| + | ------------------------------- | ||
| + | [1] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | <example> | ||
| + | W3::=ZZ/(7)[x[1..3],d[1..3]]; | ||
| + | Use W3; | ||
| + | I2:=Ideal(x[1]^7,d[1]^7); --is a 2-sided ideal in W3 | ||
| + | Weyl.WGB(I2); --ApCoCOAServer should be running | ||
| + | -- CoCoAServer: computing Cpu Time = 0 | ||
| + | ------------------------------- | ||
| + | [x[1]^7, d[1]^7] | ||
------------------------------- | ------------------------------- | ||
| − | |||
| + | I3:=Ideal(x[1]^3d[2],x[2]*d[1]^2); | ||
| + | |||
| + | Weyl.WGB(I3); | ||
| + | -- CoCoAServer: computing Cpu Time = 0 | ||
| + | ------------------------------- | ||
| + | [x[2]^2d[2], x[2]d[2]^2 + 2d[2], x[1]^3d[1]^2 + x[1]^2x[2]d[1]d[2] + x[1]x[2]d[2], x[1]^3d[2], x[2]d[1]^2] | ||
| + | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Weyl. | + | <see>Weyl.WNormalForm</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>cocoaserver</type> | <type>cocoaserver</type> | ||
</types> | </types> | ||
| − | <key>weyl. | + | <key>weyl.wgb</key> |
<wiki-category>Package_Weyl</wiki-category> | <wiki-category>Package_Weyl</wiki-category> | ||
</command> | </command> | ||
Revision as of 09:50, 20 April 2009
Weyl.WGB
Computes the Groebner basis of an ideal I in Weyl algebra , using corresponding
implementation in CoCoALib.
Syntax
Weyl.WGB(I):LIST
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 a Groebner Basis for an Ideal where every generator should be a Weyl polynomial in Normal form.
Example
A1::=QQ[x,d]; --Define appropraite ring Use A1; I:=Ideal(x,d); -- Now start ApCoCoA server for executing next command Weyl.WeylGB(I); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [1] ------------------------------- Note that Groebner basis you obtained is minimal. A2::=QQ[x[1..2],y[1..2]]; Use A2; I1:=Ideal(x[1]^7,y[1]^7); Weyl.WGB(I1); -- CoCoAServer: computing Cpu Time = 0.094 ------------------------------- [1] -------------------------------
Example
W3::=ZZ/(7)[x[1..3],d[1..3]]; Use W3; I2:=Ideal(x[1]^7,d[1]^7); --is a 2-sided ideal in W3 Weyl.WGB(I2); --ApCoCOAServer should be running -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [x[1]^7, d[1]^7] ------------------------------- I3:=Ideal(x[1]^3d[2],x[2]*d[1]^2); Weyl.WGB(I3); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [x[2]^2d[2], x[2]d[2]^2 + 2d[2], x[1]^3d[1]^2 + x[1]^2x[2]d[1]d[2] + x[1]x[2]d[2], x[1]^3d[2], x[2]d[1]^2] -------------------------------
See also
