def __new__(cls, *args):
from sympy.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 sympify(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 __new__(cls, sets, polar=False):
from sympy import symbols, Dummy, sympify, sin, cos
x, y, r, theta = symbols('x, y, r, theta', cls=Dummy)
I = S.ImaginaryUnit
polar = sympify(polar)
# Rectangular Form
if polar == False:
if all(_a.is_FiniteSet
for _a in sets.args) and (len(sets.args) == 2):
# ** ProductSet of FiniteSets in the Complex Plane. **
# For Cases like ComplexRegion({2, 4}*{3}), It
# would return {2 + 3*I, 4 + 3*I}
complex_num = []
for x in sets.args[0]:
for y in sets.args[1]:
complex_num.append(x + I * y)
obj = FiniteSet(*complex_num)
else:
obj = ImageSet.__new__(cls, Lambda((x, y), x + I * y), sets)
obj._variables = (x, y)
obj._expr = x + I * y
# Polar Form
elif polar == True:
new_sets = []
# sets is Union of ProductSets
if not sets.is_ProductSet:
for k in sets.args:
new_sets.append(k)
# sets is ProductSets
else:
new_sets.append(sets)
# Normalize input theta
for k, v in enumerate(new_sets):
from sympy.sets import ProductSet
new_sets[k] = ProductSet(v.args[0],
normalize_theta_set(v.args[1]))
sets = Union(*new_sets)
obj = ImageSet.__new__(
cls, Lambda((r, theta), r * (cos(theta) + I * sin(theta))),
sets)
obj._variables = (r, theta)
obj._expr = r * (cos(theta) + I * sin(theta))
else:
raise ValueError("polar should be either True or False")
obj._sets = sets
obj._polar = polar
return obj
def __new__(cls, sets, polar=False):
from sympy import symbols, Dummy, sympify, sin, cos
x, y, r, theta = symbols('x, y, r, theta', cls=Dummy)
I = S.ImaginaryUnit
polar = sympify(polar)
# Rectangular Form
if polar == False:
if all(_a.is_FiniteSet for _a in sets.args) and (len(sets.args) == 2):
# ** ProductSet of FiniteSets in the Complex Plane. **
# For Cases like ComplexRegion({2, 4}*{3}), It
# would return {2 + 3*I, 4 + 3*I}
complex_num = []
for x in sets.args[0]:
for y in sets.args[1]:
complex_num.append(x + I*y)
obj = FiniteSet(*complex_num)
else:
obj = ImageSet.__new__(cls, Lambda((x, y), x + I*y), sets)
obj._variables = (x, y)
obj._expr = x + I*y
# Polar Form
elif polar == True:
new_sets = []
# sets is Union of ProductSets
if not sets.is_ProductSet:
for k in sets.args:
new_sets.append(k)
# sets is ProductSets
else:
new_sets.append(sets)
# Normalize input theta
for k, v in enumerate(new_sets):
from sympy.sets import ProductSet
new_sets[k] = ProductSet(v.args[0],
normalize_theta_set(v.args[1]))
sets = Union(*new_sets)
obj = ImageSet.__new__(cls, Lambda((r, theta),
r*(cos(theta) + I*sin(theta))),
sets)
obj._variables = (r, theta)
obj._expr = r*(cos(theta) + I*sin(theta))
else:
raise ValueError("polar should be either True or False")
obj._sets = sets
obj._polar = polar
return obj
def __new__(cls, *args):
from sympy.functions.elementary.integers import ceiling
if len(args) == 1:
if isinstance(args[0], range if PY3 else xrange):
args = args[0].__reduce__()[1] # use pickle method
# 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 sympify(
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 _contains(self, other):
from sympy.functions import arg, Abs
# self in rectangular form
if not self.polar:
re, im = other.as_real_imag()
for element in self.psets:
if And(element.args[0]._contains(re),
element.args[1]._contains(im)):
return True
return False
# self in polar form
elif self.polar:
if sympify(other).is_zero:
r, theta = S.Zero, S.Zero
else:
r, theta = Abs(other), arg(other)
for element in self.psets:
if And(element.args[0]._contains(r),
element.args[1]._contains(theta)):
return True
return False
def _contains(self, other):
from sympy.functions import arg, Abs
# self in rectangular form
if not self.polar:
re, im = other.as_real_imag()
for element in self.psets:
if And(element.args[0]._contains(re),
element.args[1]._contains(im)):
return True
return False
# self in polar form
elif self.polar:
if sympify(other).is_zero:
r, theta = S.Zero, S.Zero
else:
r, theta = Abs(other), arg(other)
for element in self.psets:
if And(element.args[0]._contains(r),
element.args[1]._contains(theta)):
return True
return False
