lattice reduction RealField

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I have a basis for a lattice in three dimensional space and I need to keep it with very high precision and so I'm using RealField. I then tranform the basis linearly. I'd like to find the reduced basis for the lattice. My understanding is the LLL algorithms apply only to integer matrices. Is this correct?

To get around this I currently scale the basis by a very large number and round to the closest integer and reduce this approximation, find the transformation to the reduced basis and finally apply it to the exact basis.