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Ideally, FGb should be included in Singular. However it is possible to include it directly in Sage ! There seems to be a C library, so it should not be too hard with cython. If you feel able to do that by yourself, that would be an awesome contribution, you can have a first look at http://doc.sagemath.org/html/en/thematic_tutorials/cython_interface.html We can help you in the process of letting your work enter Sage source code.

Ideally, FGb should be included in Singular. However it is possible to include it directly in Sage ! There seems to be a C library, so it should not be too hard with cython. If you feel able to do that by yourself, that would be an awesome contribution, you can have a first look at http://doc.sagemath.org/html/en/thematic_tutorials/cython_interface.html We can help you in the process of letting your work enter Sage source code.

sage -i giacpy

sage: G = I.groebner_basis(algorithm='giac:gbasis')

Ideally, FGb should be included in Singular. However it is possible to include it directly in Sage ! There seems to be a C library, so it should not be too hard with cython. If you feel able to do that by yourself, that would be an awesome contribution, you can have a first look at http://doc.sagemath.org/html/en/thematic_tutorials/cython_interface.html We can help you in the process of letting your work enter Sage source code.

EDIT Regarding the computation of the Groebner basis of thus this ideal, actually there is a way to let Sage compute it, using the interface with giac:

First install giacpy from your terminal:

sage -i giacpy

Then, you can get the Groebner Basis (in about one minute) from within Sage as follows:

sage: G = I.groebner_basis(algorithm='giac:gbasis')

Ideally, FGb should be included in Singular. Singular or Sage but it is closed source... However it is still possible to include interface it directly in with Sage ! There seems to be a C library, so it should not be too hard with cython. If you feel able to do that by yourself, that would be an awesome contribution, you can have a first look at http://doc.sagemath.org/html/en/thematic_tutorials/cython_interface.html We can help you in the process of letting your work enter Sage source code.

EDIT Regarding the computation of the Groebner basis of this ideal, actually there is a way to let Sage compute it, using the interface with giac:

First install giacpy from your terminal:

sage -i giacpy

Then, you can get the Groebner Basis (in about one minute) from within Sage as follows:

sage: G = I.groebner_basis(algorithm='giac:gbasis')