up previous next
Computes reduced Groebner basis of a D-ideal in Weyl algebra
A_n.
Weyl.WRedGB(GB:LIST):LIST
|
This function converts Groebner basis
GB computed by ApCoCoAServer into the reduced 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).
Note: This function is faster than
Weyl.WRGB for a list
GB of large size.
- @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.WRedGB(L);
[1]
-------------------------------
-- Done.
-------------------------------
|
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);
-------------------------------
-- CoCoAServer: computing Cpu Time = 0.485
-------------------------------
42 -- size of complete GB of the ideal I
-------------------------------
Time GbI:=Weyl.WRedGB(GbI);
Cpu time = 10.89, User time = 11
-------------------------------
11 -- GbI is now reduced Groebner Basis of the ideal I.
-------------------------------
-- Done.
-------------------------------
|