def __new__(cls, *args, **kwargs):
from diofant.geometry.point import Point
args = [
Tuple(*a)
if is_sequence(a) and not isinstance(a, Point) else sympify(a)
for a in args
]
return Basic.__new__(cls, *args)
def __new__(cls, *args):
from diofant.functions.elementary.integers import ceiling
# expand range
slc = slice(*args)
start, stop, step = slc.start or 0, slc.stop, slc.step or 1
try:
start, stop, step = [
w if w in [S.NegativeInfinity, S.Infinity] else Integer(
as_int(w)) for w in (start, stop, step)
]
except ValueError:
raise ValueError("Inputs to Range must be Integer Valued\n" +
"Use ImageSets of Ranges for other cases")
if not step.is_finite:
raise ValueError("Infinite step is not allowed")
if start == stop:
return S.EmptySet
n = ceiling((stop - start) / step)
if n <= 0:
return S.EmptySet
# normalize args: regardless of how they are entered they will show
# canonically as Range(inf, sup, step) with step > 0
if n.is_finite:
start, stop = sorted((start, start + (n - 1) * step))
else:
start, stop = sorted((start, stop - step))
step = abs(step)
if (start, stop) == (S.NegativeInfinity, S.Infinity):
raise ValueError("Both the start and end value of "
"Range cannot be unbounded")
else:
return Basic.__new__(cls, start, stop + step, step)
def eval(cls, *args):
try:
newargs = []
for x in args:
if isinstance(x, Number) or x in (0, 1):
newargs.append(True if x else False)
else:
newargs.append(x)
A, B = newargs
except ValueError:
raise ValueError("%d operand(s) used for an Implies "
"(pairs are required): %s" %
(len(args), str(args)))
if A == S.true or A == S.false or B == S.true or B == S.false:
return Or(Not(A), B)
elif A == B:
return S.true
elif A.is_Relational and B.is_Relational:
if A.canonical == B.canonical:
return S.true
if (~A).canonical == B.canonical:
return B
else:
return Basic.__new__(cls, *args)
def __new__(cls):
global instantiated
instantiated += 1
return Basic.__new__(cls)
def __new__(cls):
global instantiated
instantiated += 1
return Basic.__new__(cls)
def __new__(cls, lamda, base_set):
return Basic.__new__(cls, lamda, base_set)