If you already have the binary file you can load it in Mathematica by
Install["FLink"]. Now you have a list of

functions you can use from Mathematica.

FInit[path, variables]: starts Fermat with the
listed variables as polynomials variables; the variables are submitted as a
comma-separated string and should be all lower-case;

FEval[expression]: performs an external evaluation
of the expression; both the input and output should be strings;

FClose[]: closes Fermat; should be always called at
the the end of your calculations, otherwise you will end with a process working
in background and using CPU time.