ApCoCoA-1:Weyl.WRGB
From ApCoCoAWiki
Weyl.WRGB
Reduced Groebner basis of an ideal I in Weyl algebra A_n.
Syntax
Weyl.WRGB(GB:LIST):LIST
Description
This function converts a Weyl Groebner basis GB computed by ApCoCoAServer into the reduced Weyl Groebner Basis. If GB is not a Groebner basis then the output will not be the reduced Groebner basis. In fact, this function reduces a list GB of Weyl polynomials using Weyl.WNR into a new list L such that Ideal(L) = Ideal(GB), every polynomial is reduced with respect to the remaining polynomials in the list L and leading coefficient of each polynomial in L is 1.
@param GB Groebner Basis of an ideal in the Weyl algebra.
@result The reduced Groebner Basis of the given ideal.
Example
A1::=QQ[x,d]; --Define appropriate ring Use A1; L:=[x,d,1]; Weyl.WRGB(L); [1] -------------------------------
Example
A2::=ZZ/7[x[1..2],y[1..2]]; -- define appropriate ring
Use A2;
I:=Ideal(2x[1]^14y[1]^7,x[1]^2y[1]^3+x[1]^2-1,y[2]^7-1,x[2]^3y[2]^2-x[2]y[2]-3x[2]-1);
GbI:=Weyl.WGB(I,0);Len(GbI);
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-- CoCoAServer: computing Cpu Time = 0.485
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42 -- size of complete GB of the ideal I
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Time GbI:=Weyl.WRGB(GbI);Len(GbI);
Cpu time = 9.61, User time = 10
-------------------------------
11
-------------------------------
-- Done.
-------------------------------
Time GbI:=Weyl.WRGBS(GbI);Len(GbI); -- Weyl.WRGBS() can now be used for calling same implementation in ApCoCoALib
-- note that this speeds up the computations
-------------------------------
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Cpu time = 0.04, User time = 0
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11 -- this is now size of reduced GB of the ideal I
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-- Done.
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See also
Introduction to Groebner Basis in CoCoA
