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In your case, we can say that Singular library is called, see:

sage: from sage.misc.citation import get_systems
sage: get_systems('I.groebner_basis()')
['Singular']

But then, i am not sure which algorithm is called there, though apparently Singular ships F5, see https://en.wikipedia.org/wiki/Faugère's_F4_and_F5_algorithms

Note that you can chose which implementation, see

sage: I.groebner_basis?

For example, you can specify:

sage: I.groebner_basis(algorithm='libsingular:slimgb')
[x - 5*y - 5, y^2 - 2*y]

Though the name slimgb is not particularly self-contained.

In your case, we can say that Singular library is called, see:

sage: from sage.misc.citation import get_systems
sage: get_systems('I.groebner_basis()')
['Singular']

But then, i am not sure which algorithm is called there, though apparently Singular ships F5, see https://en.wikipedia.org/wiki/Faugère's_F4_and_F5_algorithms

Note that you can chose which implementation, see

sage: I.groebner_basis?

For example, you can specify:

sage: I.groebner_basis(algorithm='libsingular:slimgb')
[x - 5*y - 5, y^2 - 2*y]

Though the name slimgb is not particularly self-contained.self-contained (see https://singular.mathematik.uni-kl.de/Manual/4-2-0/sing_351.htm#SEC391for more details).

In your case, we can say that Singular library is called, see:

sage: from sage.misc.citation import get_systems
sage: get_systems('I.groebner_basis()')
['Singular']

But then, i am not sure which algorithm is called there, though apparently Singular ships F5, see https://en.wikipedia.org/wiki/Faugère's_F4_and_F5_algorithms

Note that you can chose which implementation, see

sage: I.groebner_basis?

For example, you can specify:specify (i just pick a random algorithm among all possible choices):

sage: I.groebner_basis(algorithm='libsingular:slimgb')
[x - 5*y - 5, y^2 - 2*y]

Though the name slimgb is not particularly self-contained (see https://singular.mathematik.uni-kl.de/Manual/4-2-0/sing_351.htm#SEC391for more details).