def reduce_inequalities(inequalities, symbols=[]):
    if not iterable(inequalities):
        inequalities = [inequalities]
    inequalities = [sympify(i) for i in inequalities]

    gens = set().union(*[i.free_symbols for i in inequalities])

    if not iterable(symbols):
        symbols = [symbols]
    symbols = (set(symbols) or gens) & gens
    if any(i.is_real is False for i in symbols):
        raise TypeError(filldedent('''
            inequalities cannot contain symbols that are not real.'''))

    # make vanilla symbol real
    recast = dict([(i, Dummy(i.name, real=True))
        for i in gens if i.is_real is None])
    inequalities = [i.xreplace(recast) for i in inequalities]
    symbols = {i.xreplace(recast) for i in symbols}

    # prefilter
    keep = []
    for i in inequalities:
        if isinstance(i, Relational):
            i = i.func(i.lhs.as_expr() - i.rhs.as_expr(), 0)
        elif i not in (True, False):
            i = Eq(i, 0)
        if i == True:
            continue
        elif i == False:
            return S.false
        if i.lhs.is_number:
            raise NotImplementedError(
                "could not determine truth value of %s" % i)
        keep.append(i)
    inequalities = keep
    del keep

    # solve system
    rv = _reduce_inequalities(inequalities, symbols)

    # restore original symbols and return
    return rv.xreplace({v: k for k, v in recast.items()})
Reduce a system of inequalities with rational coefficients.
dataset/ETHPy150Open sympy/sympy/sympy/solvers/inequalities.py/reduce_inequalities