def __new__(cls, expr, *symbols, **assumptions):
expr = sympify(expr)
if not symbols: return expr
symbols = Derivative._symbolgen(*symbols)
if not assumptions.get("evaluate", False) and not isinstance(
expr, Derivative):
obj = Basic.__new__(cls, expr, *symbols)
return obj
unevaluated_symbols = []
for s in symbols:
s = sympify(s)
if not isinstance(s, Symbol):
raise ValueError(
'Invalid literal: %s is not a valid variable' % s)
if not expr.has(s):
return S.Zero
obj = expr._eval_derivative(s)
if obj is None:
unevaluated_symbols.append(s)
elif obj is S.Zero:
return S.Zero
else:
expr = obj
if not unevaluated_symbols:
return expr
return Basic.__new__(cls, expr, *unevaluated_symbols)
def __new__(cls, expr, *symbols, **assumptions):
expr = Basic.sympify(expr)
if not symbols: return expr
symbols = map(Basic.sympify, symbols)
if not assumptions.get("evaluate", True):
obj = Basic.__new__(cls, expr, *symbols)
return obj
for s in symbols:
assert isinstance(s, Basic.Symbol),`s`
if not expr.has(s):
return Basic.Zero()
unevaluated_symbols = []
for s in symbols:
obj = expr._eval_derivative(s)
if obj is None:
unevaluated_symbols.append(s)
else:
expr = obj
if not unevaluated_symbols:
return expr
return Basic.__new__(cls, expr, *unevaluated_symbols)
def __new__(cls, *args, **options):
# NOTE: this __new__ is twofold:
#
# 1 -- it can create another *class*, which can then be instantiated by
# itself e.g. Function('f') creates a new class f(Function)
#
# 2 -- on the other hand, we instantiate -- that is we create an
# *instance* of a class created earlier in 1.
#
# So please keep, both (1) and (2) in mind.
# (1) create new function class
# UC: Function('f')
if cls is Function:
#when user writes Function("f"), do an equivalent of:
#taking the whole class Function(...):
#and rename the Function to "f" and return f, thus:
#In [13]: isinstance(f, Function)
#Out[13]: False
#In [14]: isinstance(f, FunctionClass)
#Out[14]: True
if len(args) == 1 and isinstance(args[0], str):
#always create Function
return FunctionClass(Function, *args)
return FunctionClass(Function, *args, **options)
else:
print args
print type(args[0])
raise Exception("You need to specify exactly one string")
# (2) create new instance of a class created in (1)
# UC: Function('f')(x)
# UC: sin(x)
args = map(sympify, args)
# these lines should be refactored
for opt in [
"nargs", "dummy", "comparable", "noncommutative", "commutative"
]:
if opt in options:
del options[opt]
# up to here.
if options.get('evaluate') is False:
return Basic.__new__(cls, *args, **options)
r = cls.canonize(*args)
if isinstance(r, Basic):
return r
elif r is None:
# Just undefined functions have nargs == None
if not cls.nargs and hasattr(cls, 'undefined_Function'):
r = Basic.__new__(cls, *args, **options)
r.nargs = len(args)
return r
pass
elif not isinstance(r, tuple):
args = (r, )
return Basic.__new__(cls, *args, **options)
def __new__(cls, *args, **options):
# NOTE: this __new__ is twofold:
#
# 1 -- it can create another *class*, which can then be instantiated by
# itself e.g. Function('f') creates a new class f(Function)
#
# 2 -- on the other hand, we instantiate -- that is we create an
# *instance* of a class created earlier in 1.
#
# So please keep, both (1) and (2) in mind.
# (1) create new function class
# UC: Function('f')
if cls is Function:
#when user writes Function("f"), do an equivalent of:
#taking the whole class Function(...):
#and rename the Function to "f" and return f, thus:
#In [13]: isinstance(f, Function)
#Out[13]: False
#In [14]: isinstance(f, FunctionClass)
#Out[14]: True
if len(args) == 1 and isinstance(args[0], str):
#always create Function
return FunctionClass(Function, *args)
return FunctionClass(Function, *args, **options)
else:
print args
print type(args[0])
raise Exception("You need to specify exactly one string")
# (2) create new instance of a class created in (1)
# UC: Function('f')(x)
# UC: sin(x)
args = map(sympify, args)
# these lines should be refactored
for opt in ["nargs", "dummy", "comparable", "noncommutative", "commutative"]:
if opt in options:
del options[opt]
# up to here.
if options.get('evaluate') is False:
return Basic.__new__(cls, *args, **options)
r = cls.eval(*args)
if isinstance(r, Basic):
return r
elif r is None:
# Just undefined functions have nargs == None
if not cls.nargs and hasattr(cls, 'undefined_Function'):
r = Basic.__new__(cls, *args, **options)
r.nargs = len(args)
return r
pass
elif not isinstance(r, tuple):
args = (r,)
return Basic.__new__(cls, *args, **options)
def __new__(cls, b, e, **assumptions):
b = _sympify(b)
e = _sympify(e)
if assumptions.get("evaluate") is False:
return Basic.__new__(cls, b, e, **assumptions)
if e is S.Zero:
return S.One
if e is S.One:
return b
obj = b._eval_power(e)
if obj is None:
obj = Basic.__new__(cls, b, e, **assumptions)
obj.is_commutative = b.is_commutative and e.is_commutative
return obj
def __new__(cls, a, b, **assumptions):
a = _sympify(a)
b = _sympify(b)
if assumptions.get("evaluate") is False:
return Basic.__new__(cls, a, b, **assumptions)
if b is S.Zero:
return S.One
if b is S.One:
return a
obj = a._eval_power(b)
if obj is None:
obj = Basic.__new__(cls, a, b, **assumptions)
obj.is_commutative = a.is_commutative and b.is_commutative
return obj
def __new__(cls, a, b, **assumptions):
a = _sympify(a)
b = _sympify(b)
if assumptions.get('evaluate') is False:
return Basic.__new__(cls, a, b, **assumptions)
if b is S.Zero:
return S.One
if b is S.One:
return a
obj = a._eval_power(b)
if obj is None:
obj = Basic.__new__(cls, a, b, **assumptions)
obj.is_commutative = (a.is_commutative and b.is_commutative)
return obj
def __new__(cls, b, e, **assumptions):
b = _sympify(b)
e = _sympify(e)
if assumptions.get('evaluate') is False:
return Basic.__new__(cls, b, e, **assumptions)
if e is S.Zero:
return S.One
if e is S.One:
return b
obj = b._eval_power(e)
if obj is None:
obj = Basic.__new__(cls, b, e, **assumptions)
obj.is_commutative = (b.is_commutative and e.is_commutative)
return obj
def _new(cls, _mpf_, _prec):
if _mpf_ == mlib.fzero:
return S.Zero
obj = Basic.__new__(cls)
obj._mpf_ = _mpf_
obj._prec = _prec
return obj
def __new__(cls, p, q = None):
if q is None:
if isinstance(p, str):
p, q = _parse_rational(p)
else:
return Integer(p)
if q==0:
if p==0:
if _errdict["divide"]:
raise ValueError("Indeterminate 0/0")
else:
return S.NaN
if p<0: return S.NegativeInfinity
return S.Infinity
if q<0:
q = -q
p = -p
n = igcd(abs(p), q)
if n>1:
p //= n
q //= n
if q==1: return Integer(p)
if p==1 and q==2: return S.Half
obj = Basic.__new__(cls)
obj.p = int(p)
obj.q = int(q)
#obj._args = (p, q)
return obj
def __new__(cls, start, end, left_open=False, right_open=False):
start = _sympify(start)
end = _sympify(end)
# Only allow real intervals (use symbols with 'is_real=True').
if not start.is_real or not end.is_real:
raise ValueError("Only real intervals are supported")
# Make sure that the created interval will be valid.
if end.is_comparable and start.is_comparable:
if end < start:
return S.EmptySet
if end == start and (left_open or right_open):
return S.EmptySet
if end == start and not (left_open or right_open):
return FiniteSet(end)
# Make sure infinite interval end points are open.
if start == S.NegativeInfinity:
left_open = True
if end == S.Infinity:
right_open = True
return Basic.__new__(cls, start, end, left_open, right_open)
def _new(cls, _mpf_, _prec):
if _mpf_ == mlib.fzero:
return S.Zero
obj = Basic.__new__(cls)
obj._mpf_ = _mpf_
obj._prec = _prec
return obj
def __new__(cls, p, q = None):
if q is None:
if isinstance(p, str):
p, q = _parse_rational(p)
else:
return Integer(p)
if q==0:
if p==0:
if _errdict["divide"]:
raise Exception("Indeterminate 0/0")
else:
return S.NaN
if p<0: return S.NegativeInfinity
return S.Infinity
if q<0:
q = -q
p = -p
n = igcd(abs(p), q)
if n>1:
p //= n
q //= n
if q==1: return Integer(p)
if p==1 and q==2: return S.Half
obj = Basic.__new__(cls)
obj.p = int(p)
obj.q = int(q)
#obj._args = (p, q)
return obj
def __new__(cls, start, end, left_open=False, right_open=False):
start = _sympify(start)
end = _sympify(end)
# Only allow real intervals (use symbols with 'is_real=True').
if not start.is_real or not end.is_real:
raise ValueError("Only real intervals are supported")
# Make sure that the created interval will be valid.
if end.is_comparable and start.is_comparable:
if end < start:
return S.EmptySet
if end == start and (left_open or right_open):
return S.EmptySet
if end == start and not (left_open or right_open):
return FiniteSet(end)
# Make sure infinite interval end points are open.
if start == S.NegativeInfinity:
left_open = True
if end == S.Infinity:
right_open = True
return Basic.__new__(cls, start, end, left_open, right_open)
def __new__(cls, *args):
def flatten(arg):
if is_flattenable(arg):
return sum(map(flatten, arg), [])
return [arg]
args = flatten(list(args))
# Sympify Arguments
args = map(sympify, args)
# Turn tuples into Tuples
args = [Tuple(*arg) if arg.__class__ is tuple else arg for arg in args]
if len(args) == 0:
return EmptySet()
try:
if all([arg.is_real and arg.is_number for arg in args]):
cls = RealFiniteSet
except AttributeError:
pass
elements = frozenset(map(sympify, args))
obj = Basic.__new__(cls, elements)
obj.elements = elements
return obj
def __new__(cls, *args):
# Flatten out Iterators and Unions to form one list of sets
args = list(args)
def flatten(arg):
if arg == S.EmptySet:
return []
if isinstance(arg, Set):
if arg.is_Union:
return sum(map(flatten, arg.args), [])
else:
return [arg]
if is_flattenable(arg): # and not isinstance(arg, Set) (implicit)
return sum(map(flatten, arg), [])
raise TypeError("Input must be Sets or iterables of Sets")
args = flatten(args)
if len(args) == 0:
return S.EmptySet
# Only real parts? Return a RealUnion
if all(arg.is_real for arg in args):
return RealUnion(args)
# Lets find and merge real elements if we have them
# Separate into finite, real and other sets
finite_set = sum([s for s in args if s.is_FiniteSet], S.EmptySet)
real_sets = [s for s in args if s.is_real]
other_sets = [s for s in args if not s.is_FiniteSet and not s.is_real]
# Separate finite_set into real and other part
real_finite = RealFiniteSet(i for i in finite_set if i.is_real)
other_finite = FiniteSet(i for i in finite_set if not i.is_real)
# Merge real part of set
real_union = RealUnion(real_sets+[real_finite])
if not real_union: # Real part was empty
sets = other_sets + [other_finite]
elif real_union.is_FiniteSet: # Real part was just a FiniteSet
sets = other_sets + [real_union+other_finite]
elif real_union.is_Interval: # Real part was just an Interval
sets = [real_union] + other_sets + [other_finite]
# If is_RealUnion then separate
elif real_union.is_Union and real_union.is_real:
intervals = [s for s in real_union.args if s.is_Interval]
finite_set = sum([s for s in real_union.args if s.is_FiniteSet] +
[other_finite], S.EmptySet) # Join FiniteSet back together
sets = intervals + [finite_set] + other_sets
# Clear out Empty Sets
sets = [set for set in sets if set != S.EmptySet]
# If a single set is left over, don't create a new Union object but
# rather return the single set.
if len(sets) == 1:
return sets[0]
return Basic.__new__(cls, *sets)
def __new__(cls, *args):
# Flatten out Iterators and Unions to form one list of sets
args = list(args)
def flatten(arg):
if arg == S.EmptySet:
return []
if isinstance(arg, Set):
if arg.is_Union:
return sum(map(flatten, arg.args), [])
else:
return [arg]
if is_flattenable(arg): # and not isinstance(arg, Set) (implicit)
return sum(map(flatten, arg), [])
raise TypeError("Input must be Sets or iterables of Sets")
args = flatten(args)
if len(args) == 0:
return S.EmptySet
# Only real parts? Return a RealUnion
if all(arg.is_real for arg in args):
return RealUnion(args)
# Lets find and merge real elements if we have them
# Separate into finite, real and other sets
finite_set = sum([s for s in args if s.is_FiniteSet], S.EmptySet)
real_sets = [s for s in args if s.is_real]
other_sets = [s for s in args if not s.is_FiniteSet and not s.is_real]
# Separate finite_set into real and other part
real_finite = RealFiniteSet(i for i in finite_set if i.is_real)
other_finite = FiniteSet(i for i in finite_set if not i.is_real)
# Merge real part of set
real_union = RealUnion(real_sets+[real_finite])
if not real_union: # Real part was empty
sets = other_sets + [other_finite]
elif real_union.is_FiniteSet: # Real part was just a FiniteSet
sets = other_sets + [real_union+other_finite]
elif real_union.is_Interval: # Real part was just an Interval
sets = [real_union] + other_sets + [other_finite]
# If is_RealUnion then separate
elif real_union.is_Union and real_union.is_real:
intervals = [s for s in real_union.args if s.is_Interval]
finite_set = sum([s for s in real_union.args if s.is_FiniteSet] +
[other_finite], S.EmptySet) # Join FiniteSet back together
sets = intervals + [finite_set] + other_sets
# Clear out Empty Sets
sets = [set for set in sets if set != S.EmptySet]
# If a single set is left over, don't create a new Union object but
# rather return the single set.
if len(sets) == 1:
return sets[0]
return Basic.__new__(cls, *sets)
def __new__(cls, i):
if isinstance(i, Integer):
return i
if i==0: return S.Zero
if i==1: return S.One
if i==-1: return S.NegativeOne
obj = Basic.__new__(cls)
obj.p = i
return obj
def cls_new(cls):
try:
obj = getattr(SingletonFactory, cls.__name__)
except AttributeError:
obj = Basic.__new__(cls, *(), **{})
setattr(SingletonFactory, cls.__name__, obj)
return obj
def __new__(cls, lhs, rhs, rop=None, **assumptions):
lhs = _sympify(lhs)
rhs = _sympify(rhs)
if cls is not Relational:
rop_cls = cls
else:
rop_cls, swap = Relational.get_relational_class(rop)
if swap: lhs, rhs = rhs, lhs
obj = Basic.__new__(rop_cls, lhs, rhs, **assumptions)
return obj
def __new__(cls, *args, **assumptions):
if assumptions.get('evaluate') is False:
return Basic.__new__(cls, *map(_sympify, args), **assumptions)
if len(args)==0:
return cls.identity()
if len(args)==1:
return _sympify(args[0])
c_part, nc_part, order_symbols = cls.flatten(map(_sympify, args))
if len(c_part) + len(nc_part) <= 1:
if c_part: obj = c_part[0]
elif nc_part: obj = nc_part[0]
else: obj = cls.identity()
else:
obj = Basic.__new__(cls, *(c_part + nc_part), **assumptions)
obj.is_commutative = not nc_part
if order_symbols is not None:
obj = C.Order(obj, *order_symbols)
return obj
def __new__(cls, num):
if isinstance(num, (int, long)):
return Integer(num)
singleton_cls_name = decimal_to_Number_cls.get(num.as_tuple(), None)
if singleton_cls_name is not None:
return getattr(Basic, singleton_cls_name)()
obj = Basic.__new__(cls)
obj.num = num
return obj
def __new__(cls, *args, **assumptions):
if assumptions.get('evaluate') is False:
return Basic.__new__(cls, *map(_sympify, args), **assumptions)
if len(args)==0:
return cls.identity()
if len(args)==1:
return _sympify(args[0])
c_part, nc_part, order_symbols = cls.flatten(map(_sympify, args))
if len(c_part) + len(nc_part) <= 1:
if c_part: obj = c_part[0]
elif nc_part: obj = nc_part[0]
else: obj = cls.identity()
else:
obj = Basic.__new__(cls, *(c_part + nc_part), **assumptions)
obj.is_commutative = not nc_part
if order_symbols is not None:
obj = C.Order(obj, *order_symbols)
return obj
def __new__(cls, *args):
if len(args)==1 and args[0].__class__ is dict:
items = [Tuple(k, v) for k, v in args[0].iteritems()]
elif iterable(args) and all(len(arg) == 2 for arg in args):
items = [Tuple(k, v) for k, v in args]
else:
raise TypeError('Pass Dict args as Dict((k1, v1), ...) or Dict({k1: v1, ...})')
obj = Basic.__new__(cls, *items)
obj._dict = dict(items) # In case Tuple decides it wants to sympify
return obj
def __new__(cls, lhs, rhs, rop=None, **assumptions):
lhs = Basic.sympify(lhs)
rhs = Basic.sympify(rhs)
if cls is not Relational:
rop_cls = cls
else:
rop_cls, swap = Relational.get_relational_class(rop)
if swap: lhs, rhs = rhs, lhs
obj = Basic.__new__(rop_cls, lhs, rhs, **assumptions)
return obj
def __new__(cls, a, b, **assumptions):
a = Basic.sympify(a)
b = Basic.sympify(b)
if isinstance(b, Basic.Zero):
return S.One
if isinstance(b, Basic.One):
return a
obj = a._eval_power(b)
if obj is None:
obj = Basic.__new__(cls, a, b, **assumptions)
return obj
def __new__(cls, *args):
if len(args) == 1 and args[0].__class__ is dict:
items = [Tuple(k, v) for k, v in args[0].items()]
elif iterable(args) and all(len(arg) == 2 for arg in args):
items = [Tuple(k, v) for k, v in args]
else:
raise TypeError(
'Pass Dict args as Dict((k1, v1), ...) or Dict({k1: v1, ...})')
elements = frozenset(items)
obj = Basic.__new__(cls, elements)
obj.elements = elements
obj._dict = dict(items) # In case Tuple decides it wants to sympify
return obj
def __new__(cls, lhs, rhs, rop=None, **assumptions):
lhs = _sympify(lhs)
rhs = _sympify(rhs)
if cls is not Relational:
rop_cls = cls
else:
rop_cls, swap = Relational.get_relational_class(rop)
if swap: lhs, rhs = rhs, lhs
if lhs.is_real and lhs.is_number and rhs.is_real and rhs.is_number:
return rop_cls._eval_relation(lhs.evalf(), rhs.evalf())
else:
obj = Basic.__new__(rop_cls, lhs, rhs, **assumptions)
return obj
def __new__(cls, expr, *symbols, **assumptions):
expr = sympify(expr)
if not symbols:
return expr
symbols = Derivative._symbolgen(*symbols)
if expr.is_commutative:
assumptions["commutative"] = True
if "evaluate" in assumptions:
evaluate = assumptions["evaluate"]
del assumptions["evaluate"]
else:
evaluate = False
if not evaluate and not isinstance(expr, Derivative):
symbols = list(symbols)
if len(symbols) == 0:
# We make a special case for 0th derivative, because there
# is no good way to unambiguously print this.
return expr
obj = Basic.__new__(cls, expr, *symbols, **assumptions)
return obj
unevaluated_symbols = []
for s in symbols:
s = sympify(s)
if not isinstance(s, Symbol):
raise ValueError("Invalid literal: %s is not a valid variable" % s)
if not expr.has(s):
return S.Zero
obj = expr._eval_derivative(s)
if obj is None:
unevaluated_symbols.append(s)
elif obj is S.Zero:
return S.Zero
else:
expr = obj
if not unevaluated_symbols:
return expr
return Basic.__new__(cls, expr, *unevaluated_symbols, **assumptions)
def eval(cls,*args):
obj = Basic.__new__(cls, *args)
#use dummy variables internally, just to be sure
nargs = len(args)-1
expression = args[nargs]
funargs = [Symbol(arg.name, dummy=True) for arg in args[:nargs]]
#probably could use something like foldl here
for arg,funarg in zip(args[:nargs],funargs):
expression = expression.subs(arg,funarg)
funargs.append(expression)
obj._args = tuple(funargs)
return obj
def canonize(cls, *args):
obj = Basic.__new__(cls, *args)
#use dummy variables internally, just to be sure
nargs = len(args) - 1
expression = args[nargs]
funargs = [Symbol(arg.name, dummy=True) for arg in args[:nargs]]
#probably could use something like foldl here
for arg, funarg in zip(args[:nargs], funargs):
expression = expression.subs(arg, funarg)
funargs.append(expression)
obj._args = tuple(funargs)
return obj
def __new__(cls, *args, **assumptions):
args = (_sympify(arg) for arg in args)
try:
_args = frozenset(cls._new_args_filter(args))
except ShortCircuit:
return cls.zero
if not _args:
return cls.identity
elif len(_args) == 1:
return set(_args).pop()
else:
obj = Basic.__new__(cls, _args, **assumptions)
obj._argset = _args
return obj
def __new__(cls, expr, *args):
expr = Basic.sympify(expr)
args = tuple(map(Basic.sympify, args))
#if isinstance(expr, Apply):
# if expr[:]==args:
# return expr.func
dummy_args = []
for a in args:
if not isinstance(a, Basic.Symbol):
raise TypeError("%s %s-th argument must be Symbol instance (got %r)" \
% (cls.__name__, len(dummy_args)+1,a))
d = a.as_dummy()
expr = expr.subs(a, d)
dummy_args.append(d)
obj = Basic.__new__(cls, expr, *dummy_args, **expr._assumptions)
return obj
def __new__(cls, i):
try:
return _intcache[i]
except KeyError:
# We only work with well-behaved integer types. This converts, for
# example, numpy.int32 instances.
ival = int(i)
if ival == 0: obj = S.Zero
elif ival == 1: obj = S.One
elif ival == -1: obj = S.NegativeOne
else:
obj = Basic.__new__(cls)
obj.p = ival
_intcache[i] = obj
return obj
def __new__(cls, *sets, **assumptions):
def flatten(arg):
if isinstance(arg, Set):
if arg.is_ProductSet:
return sum(map(flatten, arg.args), [])
else:
return [arg]
elif is_flattenable(arg):
return sum(map(flatten, arg), [])
raise TypeError("Input must be Sets or iterables of Sets")
sets = flatten(list(sets))
if EmptySet() in sets or len(sets)==0:
return EmptySet()
return Basic.__new__(cls, *sets, **assumptions)
def __new__(cls, num, prec=15):
prec = mpmath.settings.dps_to_prec(prec)
if isinstance(num, (int, long)):
return Integer(num)
if isinstance(num, (str, decimal.Decimal)):
_mpf_ = mlib.from_str(str(num), prec, rnd)
elif isinstance(num, tuple) and len(num) == 4:
_mpf_ = num
else:
_mpf_ = mpmath.mpf(num)._mpf_
if not num:
return C.Zero()
obj = Basic.__new__(cls)
obj._mpf_ = _mpf_
obj._prec = prec
return obj
def __new__(cls, num, prec=15):
prec = mpmath.settings.dps_to_prec(prec)
if isinstance(num, (int, long)):
return Integer(num)
if isinstance(num, (str, decimal.Decimal)):
_mpf_ = mlib.from_str(str(num), prec, rnd)
elif isinstance(num, tuple) and len(num) == 4:
_mpf_ = num
else:
_mpf_ = mpmath.mpf(num)._mpf_
if not num:
return C.Zero()
obj = Basic.__new__(cls)
obj._mpf_ = _mpf_
obj._prec = prec
return obj
def __new__(cls, *sets, **assumptions):
def flatten(arg):
if isinstance(arg, Set):
if arg.is_ProductSet:
return sum(map(flatten, arg.args), [])
else:
return [arg]
elif is_flattenable(arg):
return sum(map(flatten, arg), [])
raise TypeError("Input must be Sets or iterables of Sets")
sets = flatten(list(sets))
if EmptySet() in sets or len(sets)==0:
return EmptySet()
return Basic.__new__(cls, *sets, **assumptions)
def __new__(cls, *args, **assumptions):
if len(args)==0:
return cls.identity()
if len(args)==1:
return Basic.sympify(args[0])
c_part, nc_part, lambda_args, order_symbols = cls.flatten(map(Basic.sympify, args))
if len(c_part) + len(nc_part) <= 1:
if c_part: obj = c_part[0]
elif nc_part: obj = nc_part[0]
else: obj = cls.identity()
else:
assumptions['commutative'] = not nc_part
obj = Basic.__new__(cls, *(c_part + nc_part), **assumptions)
if order_symbols is not None:
obj = Basic.Order(obj, *order_symbols)
if lambda_args is not None:
obj = Basic.Lambda(obj, *lambda_args)
return obj
def __new__(cls, i):
try:
return _intcache[i]
except KeyError:
# The most often situation is when Integers are created from Python
# int or long
if isinstance(i, (int, long)):
obj = Basic.__new__(cls)
obj.p = i
_intcache[i] = obj
return obj
# Also, we seldomly need the following to work:
# UC: Integer(Integer(4)) <-- sympify('4')
elif isinstance(i, Integer):
return i
else:
raise ValueError('invalid argument for Integer: %r' % (i,))
def __new__(cls, i):
try:
return _intcache[i]
except KeyError:
# The most often situation is when Integers are created from Python
# int or long
if isinstance(i, (int, long)):
obj = Basic.__new__(cls)
obj.p = i
_intcache[i] = obj
return obj
# Also, we seldomly need the following to work:
# UC: Integer(Integer(4)) <-- sympify('4')
elif isinstance(i, Integer):
return i
else:
raise ValueError('invalid argument for Integer: %r' % (i,))
def __new__(cls, name, commutative=True, dummy=False, **assumptions):
"""if dummy == True, then this Symbol is totally unique, i.e.::
>>> bool(Symbol("x") == Symbol("x")) == True
True
but with the dummy variable ::
>>> bool(Symbol("x", dummy = True) == Symbol("x", dummy = True)) == True
False
"""
obj = Basic.__new__(cls, commutative=commutative, dummy=dummy, **assumptions)
if dummy:
Symbol.dummycount += 1
obj.dummy_index = Symbol.dummycount
assert isinstance(name, str), ` type(name) `
obj.name = name
return obj
def _new_rawargs(self, *args):
"""create new instance of own class with args exactly as provided by caller
This is handy when we want to optimize things, e.g.
>>> from sympy import Mul, symbols
>>> x,y = symbols('xy')
>>> e = Mul(3,x,y)
>>> e.args
(3, x, y)
>>> Mul(*e.args[1:])
x*y
>>> e._new_rawargs(*e.args[1:]) # the same as above, but faster
x*y
"""
obj = Basic.__new__(type(self), *args) # NB no assumptions for Add/Mul
obj.is_commutative = self.is_commutative
return obj
def _new_rawargs(self, *args):
"""create new instance of own class with args exactly as provided by caller
This is handy when we want to optimize things, e.g.
>>> from sympy import Mul, symbols
>>> x,y = symbols('xy')
>>> e = Mul(3,x,y)
>>> e.args
(3, x, y)
>>> Mul(*e.args[1:])
x*y
>>> e._new_rawargs(*e.args[1:]) # the same as above, but faster
x*y
"""
obj = Basic.__new__(type(self), *args) # NB no assumptions for Add/Mul
obj.is_commutative = self.is_commutative
return obj
def __new__(cls, *args, **options):
if cls is SingleValuedFunction or cls is Function:
#when user writes SingleValuedFunction("f"), do an equivalent of:
#taking the whole class SingleValuedFunction(...):
#and rename the SingleValuedFunction to "f" and return f, thus:
#In [13]: isinstance(f, SingleValuedFunction)
#Out[13]: False
#In [14]: isinstance(f, FunctionClass)
#Out[14]: True
if len(args) == 1 and isinstance(args[0], str):
#always create SingleValuedFunction
return FunctionClass(SingleValuedFunction, *args)
return FunctionClass(SingleValuedFunction, *args, **options)
else:
print args
print type(args[0])
raise Exception("You need to specify exactly one string")
args = map(Basic.sympify, args)
# these lines should be refactored
if "nofargs" in options:
del options["nofargs"]
if "dummy" in options:
del options["dummy"]
if "comparable" in options:
del options["comparable"]
if "noncommutative" in options:
del options["noncommutative"]
if "commutative" in options:
del options["commutative"]
# up to here.
r = cls._eval_apply(*args, **options)
if isinstance(r, Basic):
return r
elif r is None:
pass
elif not isinstance(r, tuple):
args = (r,)
return Basic.__new__(cls, *args, **options)
def __new__(cls, *args):
def flatten(arg):
if is_flattenable(arg):
return sum(map(flatten, arg), [])
return [arg]
args = flatten(list(args))
# Sympify Arguments
args = map(sympify, args)
# Turn tuples into Tuples
args = [Tuple(*arg) if arg.__class__ is tuple else arg for arg in args]
if len(args) == 0:
return EmptySet()
if all(arg.is_number and arg.is_real for arg in args):
cls = RealFiniteSet
elements = frozenset(map(sympify, args))
obj = Basic.__new__(cls, elements)
obj.elements = elements
return obj
def __new__(cls, *args, **assumptions):
intervals, other_sets = [], []
for arg in args:
if isinstance(arg, EmptySet):
continue
elif isinstance(arg, Interval):
intervals.append(arg)
elif isinstance(arg, Union):
intervals += arg.args
elif isinstance(arg, Set):
other_sets.append(arg)
else:
raise ValueError, "Unknown argument '%s'" % arg
# Any non-empty sets at all?
if len(intervals) == 0 and len(other_sets) == 0:
return S.EmptySet
# Sort intervals according to their infimum
intervals.sort(lambda i, j: cmp(i.start, j.start))
# Merge comparable overlapping intervals
i = 0
while i < len(intervals) - 1:
cur = intervals[i]
next = intervals[i + 1]
merge = False
if cur._is_comparable(next):
if next.start < cur.end:
merge = True
elif next.start == cur.end:
# Must be careful with boundaries.
merge = not(next.left_open and cur.right_open)
if merge:
if cur.start == next.start:
left_open = cur.left_open and next.left_open
else:
left_open = cur.left_open
if cur.end < next.end:
right_open = next.right_open
end = next.end
elif cur.end > next.end:
right_open = cur.right_open
end = cur.end
else:
right_open = cur.right_open and next.right_open
end = cur.end
intervals[i] = Interval(cur.start, end, left_open, right_open)
del intervals[i + 1]
else:
i += 1
# If a single set is left over, don't create a new Union object but
# rather return the single set.
if len(intervals) == 1 and len(other_sets) == 0:
return intervals[0]
elif len(intervals) == 0 and len(other_sets) == 1:
return other_sets[0]
return Basic.__new__(cls, *(intervals + other_sets), **assumptions)
def __new__(cls, *args, **assumptions):
args = [sympify(arg) for arg in args]
obj = Basic.__new__(cls, *args, **assumptions)
return obj
def __new__(cls, *args):
intervals, finite_sets, other_sets = [], [], []
args = list(args)
for arg in args:
if isinstance(arg, Set):
if arg == S.EmptySet:
continue
elif arg.is_Union:
args += arg.args
elif arg.is_FiniteSet:
finite_sets.append(arg)
elif arg.is_Interval:
intervals.append(arg)
else:
other_sets.append(arg)
elif is_flattenable(arg):
args += arg
else:
raise TypeError("%s: Not a set or iterable of sets"%arg)
# Sort intervals according to their infimum
intervals.sort(key=lambda i: i.start)
# Merge comparable overlapping intervals
i = 0
while i < len(intervals) - 1:
cur = intervals[i]
next = intervals[i + 1]
merge = False
if cur._is_comparable(next):
if next.start < cur.end:
merge = True
elif next.start == cur.end:
# Must be careful with boundaries.
merge = not(next.left_open and cur.right_open)
if merge:
if cur.start == next.start:
left_open = cur.left_open and next.left_open
else:
left_open = cur.left_open
if cur.end < next.end:
right_open = next.right_open
end = next.end
elif cur.end > next.end:
right_open = cur.right_open
end = cur.end
else:
right_open = cur.right_open and next.right_open
end = cur.end
intervals[i] = Interval(cur.start, end, left_open, right_open)
del intervals[i + 1]
else:
i += 1
# Collect all elements in the finite sets not in any interval
if finite_sets:
# Merge Finite Sets
finite_set = sum(finite_sets, S.EmptySet)
# Close open intervals if boundary is in finite_set
for num, i in enumerate(intervals):
closeLeft = i.start in finite_set if i.left_open else False
closeRight = i.end in finite_set if i.right_open else False
if ((closeLeft and i.left_open)
or (closeRight and i.right_open)):
intervals[num] = Interval(i.start, i.end,
not closeLeft, not closeRight)
# All elements in finite_set not in any interval
finite_complement = FiniteSet(
el for el in finite_set
if not el.is_number
or not any(el in i for i in intervals))
if len(finite_complement)>0: # Anything left?
other_sets.append(finite_complement)
# Clear out empty sets
sets = [set for set in (intervals + other_sets) if set]
# If nothing is there then return the empty set
if not sets:
return S.EmptySet
# If a single set is left over, don't create a new Union object but
# rather return the single set.
if len(sets) == 1:
return sets[0]
return Basic.__new__(cls, *sets)
def __new__(cls, start, end, **assumptions):
start = _sympify(start)
end = _sympify(end)
return Basic.__new__(cls, start, end, **assumptions)
def __new_stage2__(cls, name, commutative=True, **assumptions):
assert isinstance(name, str), ` type(name) `
obj = Basic.__new__(cls, **assumptions)
obj.is_commutative = commutative
obj.name = name
return obj
def __new__(cls, expr, *symbols, **assumptions):
expr = sympify(expr)
if not symbols: return expr
symbols = Derivative._symbolgen(*symbols)
if expr.is_commutative:
assumptions["commutative"] = True
if "evaluate" in assumptions:
evaluate = assumptions["evaluate"]
del assumptions["evaluate"]
else:
evaluate = False
if not evaluate and not isinstance(expr, Derivative):
obj = Basic.__new__(cls, expr, *symbols, **assumptions)
return obj
unevaluated_symbols = []
for s in symbols:
s = sympify(s)
if not isinstance(s, Symbol):
raise ValueError('Invalid literal: %s is not a valid variable' % s)
if not expr.has(s):
return S.Zero
obj = expr._eval_derivative(s)
if obj is None:
unevaluated_symbols.append(s)
elif obj is S.Zero:
return S.Zero
else:
expr = obj
if not unevaluated_symbols:
return expr
return Basic.__new__(cls, expr, *unevaluated_symbols, **assumptions)