def test_fuzzy_group(): from sympy.utilities.iterables import cartes v = [T, F, U] for i in cartes(*[v]*3): assert _fuzzy_group(i) is (None if None in i else (True if all(j for j in i) else False)) assert _fuzzy_group(i, quick_exit=True) is \ (None if (i.count(False) > 1) else (None if None in i else (True if all(j for j in i) else False))) it = (True if (i == 0) else None for i in range(2)) assert _torf(it) is None it = (True if (i == 1) else None for i in range(2)) assert _torf(it) is None
class MinMaxBase(Expr, LatticeOp): def __new__(cls, *args, **assumptions): if not args: raise ValueError("The Max/Min functions must have arguments.") args = (sympify(arg) for arg in args) # first standard filter, for cls.zero and cls.identity # also reshape Max(a, Max(b, c)) to Max(a, b, c) try: _args = frozenset(cls._new_args_filter(args)) except ShortCircuit: return cls.zero # second filter # variant I: remove ones which can be removed # args = cls._collapse_arguments(set(_args), **assumptions) # variant II: find local zeros args = cls._find_localzeros(set(_args), **assumptions) if not args: return cls.identity elif len(args) == 1: return args.pop() else: # base creation # XXX should _args be made canonical with sorting? _args = frozenset(args) obj = Expr.__new__(cls, _args, **assumptions) obj._argset = _args return obj def _eval_simplify(self, ratio, measure): # simplify Min(foo, y, Max(foo, x)) to Min(foo, y) # Like And/Or, anything in common between the two # is cause to eliminate the opposite arg. cls = self.func if cls == Min: op = Max elif cls == Max: op = Min else: op = None if op: unnested = set() nested = [] remove = [] for a in self.args: if isinstance(a, op): nested.append(a) else: unnested.add(a) N = len(nested) - 1 for i, n in enumerate(reversed(nested)): if set(n.args) & unnested: nested.pop(N - i) return cls(*(list(unnested) + nested)) @classmethod def _new_args_filter(cls, arg_sequence): """ Generator filtering args. first standard filter, for cls.zero and cls.identity. Also reshape Max(a, Max(b, c)) to Max(a, b, c), and check arguments for comparability """ for arg in arg_sequence: # pre-filter, checking comparability of arguments if (not isinstance(arg, Expr)) or (arg.is_real is False) or ( arg is S.ComplexInfinity): raise ValueError("The argument '%s' is not comparable." % arg) if arg == cls.zero: raise ShortCircuit(arg) elif arg == cls.identity: continue elif arg.func == cls: for x in arg.args: yield x else: yield arg @classmethod def _find_localzeros(cls, values, **options): """ Sequentially allocate values to localzeros. When a value is identified as being more extreme than another member it replaces that member; if this is never true, then the value is simply appended to the localzeros. """ localzeros = set() for v in values: is_newzero = True localzeros_ = list(localzeros) for z in localzeros_: if id(v) == id(z): is_newzero = False else: con = cls._is_connected(v, z) if con: is_newzero = False if con is True or con == cls: localzeros.remove(z) localzeros.update([v]) if is_newzero: localzeros.update([v]) return localzeros @classmethod def _is_connected(cls, x, y): """ Check if x and y are connected somehow. """ from sympy.core.exprtools import factor_terms def hit(v, t, f): if not v.is_Relational: return t if v else f for i in range(2): if x == y: return True r = hit(x >= y, Max, Min) if r is not None: return r r = hit(y <= x, Max, Min) if r is not None: return r r = hit(x <= y, Min, Max) if r is not None: return r r = hit(y >= x, Min, Max) if r is not None: return r # simplification can be expensive, so be conservative # in what is attempted x = factor_terms(x - y) y = S.Zero return False def _eval_derivative(self, s): # f(x).diff(s) -> x.diff(s) * f.fdiff(1)(s) i = 0 l = [] for a in self.args: i += 1 da = a.diff(s) if da is S.Zero: continue try: df = self.fdiff(i) except ArgumentIndexError: df = Function.fdiff(self, i) l.append(df * da) return Add(*l) def evalf(self, prec=None, **options): return self.func(*[a.evalf(prec, **options) for a in self.args]) n = evalf _eval_is_algebraic = lambda s: _torf(i.is_algebraic for i in s.args) _eval_is_antihermitian = lambda s: _torf(i.is_antihermitian for i in s.args) _eval_is_commutative = lambda s: _torf(i.is_commutative for i in s.args) _eval_is_complex = lambda s: _torf(i.is_complex for i in s.args) _eval_is_composite = lambda s: _torf(i.is_composite for i in s.args) _eval_is_even = lambda s: _torf(i.is_even for i in s.args) _eval_is_finite = lambda s: _torf(i.is_finite for i in s.args) _eval_is_hermitian = lambda s: _torf(i.is_hermitian for i in s.args) _eval_is_imaginary = lambda s: _torf(i.is_imaginary for i in s.args) _eval_is_infinite = lambda s: _torf(i.is_infinite for i in s.args) _eval_is_integer = lambda s: _torf(i.is_integer for i in s.args) _eval_is_irrational = lambda s: _torf(i.is_irrational for i in s.args) _eval_is_negative = lambda s: _torf(i.is_negative for i in s.args) _eval_is_noninteger = lambda s: _torf(i.is_noninteger for i in s.args) _eval_is_nonnegative = lambda s: _torf(i.is_nonnegative for i in s.args) _eval_is_nonpositive = lambda s: _torf(i.is_nonpositive for i in s.args) _eval_is_nonzero = lambda s: _torf(i.is_nonzero for i in s.args) _eval_is_odd = lambda s: _torf(i.is_odd for i in s.args) _eval_is_polar = lambda s: _torf(i.is_polar for i in s.args) _eval_is_positive = lambda s: _torf(i.is_positive for i in s.args) _eval_is_prime = lambda s: _torf(i.is_prime for i in s.args) _eval_is_rational = lambda s: _torf(i.is_rational for i in s.args) _eval_is_real = lambda s: _torf(i.is_real for i in s.args) _eval_is_transcendental = lambda s: _torf(i.is_transcendental for i in s.args) _eval_is_zero = lambda s: _torf(i.is_zero for i in s.args)
def test_torf(): from sympy.utilities.iterables import cartes v = [T, F, U] for i in cartes(*[v]*3): assert _torf(i) is (True if all(j for j in i) else (False if all(j is False for j in i) else None))