UF function on Mathics #mma

UF_mathics.m

(*
 * UF[] by A. Smirnov.
 * U and F are obtained by computing the matrix determinant.
 *)
UF[xx_, yy_, z_] := Module[{degree, coeff, i, t2, t1, t0, zz},
    zz = Map[Rationalize[##,0]&, z, {0, Infinity}];
    degree = -Sum[yy[[i]]*x[i], {i, 1, Length[yy]}];
    coeff = 1;
    For[i = 1, i <= Length[xx], i++,
        t2 = Coefficient[degree, xx[[i]], 2];
        t1 = Coefficient[degree, xx[[i]], 1];
        t0 = Coefficient[degree, xx[[i]], 0];
        coeff = coeff*t2;
        degree = Together[t0 - ((t1^2)/(4 t2))];
    ];
    degree = Together[-coeff*degree] //. zz;
    coeff = Together[coeff] //. zz;
    {coeff, Expand[degree], Length[xx]}
];

(*
 * Rationalize[] is available in v1.0
 *)
(*
(* XXX: Ignore it!!! *)
Rationalize[x_, y_] := x;
*)

(* XXX: Polynomial only!!! *)
Coefficient[expr_, x_, n_] := Module[{e},
  e = expr;
  Do[
    e = D[e, x];
  , {i, n}];
  (e /. x -> 0) / n!
];

(* Test *)
UF[{p1, p2}, {p1^2, p2^2, (p2-q)^2, (p1-q)^2 ,(p1-p2)^2}, {}]