simplify.py 文件源码

def _real_to_rational(expr, tolerance=None):
    """
    Replace all reals in expr with rationals.

    >>> from sympy import nsimplify
    >>> from sympy.abc import x

    >>> nsimplify(.76 + .1*x**.5, rational=True)
    sqrt(x)/10 + 19/25

    """
    p = expr
    reps = {}
    reduce_num = None
    if tolerance is not None and tolerance < 1:
        reduce_num = ceiling(1/tolerance)
    for float in p.atoms(C.Float):
        key = float
        if reduce_num is not None:
            r = Rational(float).limit_denominator(reduce_num)
        elif (tolerance is not None and tolerance >= 1 and
                float.is_Integer is False):
            r = Rational(tolerance*round(float/tolerance)
                ).limit_denominator(int(tolerance))
        else:
            r = nsimplify(float, rational=False)
            # e.g. log(3).n() -> log(3) instead of a Rational
            if not r.is_Rational:
                if float < 0:
                    float = -float
                    d = Pow(10, int((mpmath.log(float)/mpmath.log(10))))
                    r = -Rational(str(float/d))*d
                elif float > 0:
                    d = Pow(10, int((mpmath.log(float)/mpmath.log(10))))
                    r = Rational(str(float/d))*d
                else:
                    r = Integer(0)
        reps[key] = r
    return p.subs(reps, simultaneous=True)