Difference between revisions of "ApCoCoA-1:Weyl.WGB"
From ApCoCoAWiki
(Updated example(s).) |
|||
| Line 16: | Line 16: | ||
<example> | <example> | ||
| − | A1::=QQ[x,d]; --Define | + | 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 | ||
| Line 25: | Line 25: | ||
------------------------------- | ------------------------------- | ||
-- 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; | ||
| Line 38: | Line 40: | ||
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); -- | + | 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
