Difference between revisions of "ApCoCoA-1:Weyl.WGB"

From ApCoCoAWiki
(Updated example(s).)
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<example>
 
<example>
A1::=QQ[x,d]; --Define appropraite ring
+
A1::=QQ[x,d]; --Define appropriate ring
 
Use A1;
 
Use A1;
 
I:=Ideal(x,d);  -- Now start ApCoCoA server for executing next command
 
I:=Ideal(x,d);  -- Now start ApCoCoA server for executing next command
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-------------------------------
 
-------------------------------
 
-- Note that Groebner basis you obtained is minimal.
 
-- Note that Groebner basis you obtained is minimal.
 +
</example>
 +
<example>
 
A2::=QQ[x[1..2],y[1..2]];
 
A2::=QQ[x[1..2],y[1..2]];
 
Use A2;
 
Use A2;
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Use W3;
 
Use W3;
 
I2:=Ideal(x[1]^7,d[1]^7);  --is a 2-sided ideal in W3
 
I2:=Ideal(x[1]^7,d[1]^7);  --is a 2-sided ideal in W3
Weyl.WGB(I2);  --ApCoCOAServer should be running
+
Weyl.WGB(I2);  --ApCoCoAServer should be running
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------

Revision as of 14:35, 28 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 appropriate ring
Use A1;
I:=Ideal(x,d);  -- Now start ApCoCoA server for executing next command
Weyl.WGB(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[1]
-------------------------------
-- Note that Groebner basis you obtained is minimal.

Example

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

Introduction to CoCoAServer

Weyl.WNormalForm