Difference between revisions of "ApCoCoA-1:Weyl.WGB"
From ApCoCoAWiki
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<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. | <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 a Groebner Basis for an Ideal <tt>I = (f_1,f_2, ..., f_r)</tt> where every generator <tt>f_i</tt> should be a Weyl polynomial in Normal form. | This function computes a Groebner Basis for an Ideal <tt>I = (f_1,f_2, ..., f_r)</tt> where every generator <tt>f_i</tt> should be a Weyl polynomial in Normal form. | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
| + | <see>Introduction to Groebner Basis in CoCoA</see> | ||
| + | <see>Introduction to CoCoAServer</see> | ||
<see>Weyl.WNormalForm</see> | <see>Weyl.WNormalForm</see> | ||
</seealso> | </seealso> | ||
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<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
<type>ideal</type> | <type>ideal</type> | ||
| − | <type> | + | <type>groebner</type> |
</types> | </types> | ||
<key>weyl.wgb</key> | <key>weyl.wgb</key> | ||
Revision as of 12:13, 24 April 2009
Weyl.WGB
Computes the Groebner basis of an ideal I in Weyl algebra A_n.
Syntax
Weyl.WGB(I:IDEAL):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 I = (f_1,f_2, ..., f_r) where every generator f_i should be a Weyl polynomial in Normal form.
@param I An ideal in the Weyl algebra.
@return A Groebner Basis of the given ideal.
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
Introduction to Groebner Basis in CoCoA
