Numbers

Fraction(R:GcdDomain): FractionFieldCategory R == add {
        Rep == Record(Numer:R, Denom:R);

        local mkquot(a:R, b:R):%        == { import from Rep; per [a, b]; }
        local numden(x:%):(R, R)        == { import from Rep; explode rep x; }


        0:%                             == { import from R; mkquot(0, 1); }
        1:%                             == { import from R; mkquot(1, 1); }

        numerator(x:%):R                == { import from Rep; rep(x).Numer; }
        denominator(x:%):R              == { import from Rep; rep(x).Denom; }

        coerce(a:R):%                   == mkquot(a, 1);
        coerce(a:Z):%                   == a::R::%;
        normalize(x:%):%                == x;


        local canon(n:R, d:R):% == {
                assert(~zero? d);
                assert(unit? gcd(n, d));
                mkquot(n, d);
        }

        (a:R) / (b:R):% == {
                assert(~zero? b);
                zero? a => 0;
                one? b => a::%;
                (g, a1, b1) := gcdquo(a, b);
                canon(a1, b1);
        }

        (x:%) = (y:%):Boolean == {
                import from R;
                (u, v) := numden x;
                (w, t) := numden y;
                u = w and v = t => true;
                u * t = v * w;
        }

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