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Reduced Groebner basis of an ideal
I in Weyl algebra
A_n.
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.
A1::=QQ[x,d]; --Define appropriate ring
Use A1;
L:=[x,d,1];
Weyl.WRGB(L);
[1]
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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
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11
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-- Done.
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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
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-- CoCoAServer: computing Cpu Time = 0
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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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