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Computes a Gröbner Bases over a prime field using the degree reverse lexicographic term ordering in parallel.
$apcocoa/pgbc.ParallelGBC(Polys:LIST,Threads:INT):LIST;
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This command computed the Gröbner Basis of the ideal generated by
Polys using the degree reverse lexicographic term ordering.
The computation can be performed in parallel using
Threads threads, at which the number of threads should be less or equal the
number of processors/cores which are available on the used system.
To compute the Gröbner Basis of
F as defined below using two cores you can enter the following sequence of commands:
Use R::=ZZ/(32003)[x[1..9],h];
F:=[x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + 2*x[6]^2 + 2*x[7]^2 + 2*x[8]^2 + 2*x[9]^2 - x[1]*h,
2*x[1]*x[2] + 2*x[2]*x[3] + 2*x[3]*x[4] + 2*x[4]*x[5] + 2*x[5]*x[6] + 2*x[6]*x[7] + 2*x[7]*x[8] + 2*x[8]*x[9]- x[2]*h,
x[2]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] + 2*x[3]*x[5] + 2*x[4]*x[6] + 2*x[5]*x[7] + 2*x[6]*x[8] + 2*x[7]*x[9] - x[3]*h,
2*x[2]*x[3] + 2*x[1]*x[4] + 2*x[2]*x[5] + 2*x[3]*x[6] + 2*x[4]*x[7] + 2*x[5]*x[8] + 2*x[6]*x[9] - x[4]*h,
x[3]^2 + 2*x[2]*x[4] + 2*x[1]*x[5] + 2*x[2]*x[6] + 2*x[3]*x[7] + 2*x[4]*x[8] + 2*x[5]*x[9] - x[5]*h,
2*x[3]*x[4] + 2*x[2]*x[5] + 2*x[1]*x[6] + 2*x[2]*x[7] + 2*x[3]*x[8] + 2*x[4]*x[9] -x[6]*h,
x[4]^2 + 2*x[3]*x[5] + 2*x[2]*x[6] + 2*x[1]*x[7] + 2*x[2]*x[8] + 2*x[3]*x[9] - x[7]*h,
2*x[4]*x[5] + 2*x[3]*x[6] + 2*x[2]*x[7] + 2*x[1]*x[8] + 2*x[2]*x[9] - x[8]*h,
x[1] + 2*x[2] + 2*x[3] + 2*x[4] + 2*x[5] + 2*x[6] + 2*x[7] + 2*x[8] + 2*x[9] - h
];
G:=$apcocoa/pgbc.ParallelGBC(F,2);
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The result you obtain is a set of polynomials which is not associated to the ideal of F. But you can set the computed basis as property of the ideal:
I:=Ideal(F);
I.GBasis:=G;
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