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 sympify(a, locals=None, convert_xor=True, strict=False, rational=False):
"""
Converts an arbitrary expression to a type that can be used inside sympy.
For example, it will convert python ints into instance of sympy.Rational,
floats into instances of sympy.Float, etc. It is also able to coerce symbolic
expressions which inherit from Basic. This can be useful in cooperation
with SAGE.
It currently accepts as arguments:
- any object defined in sympy (except matrices [TODO])
- standard numeric python types: int, long, float, Decimal
- strings (like "0.09" or "2e-19")
- booleans, including ``None`` (will leave them unchanged)
- lists, sets or tuples containing any of the above
If the argument is already a type that sympy understands, it will do
nothing but return that value. This can be used at the beginning of a
function to ensure you are working with the correct type.
>>> from sympy import sympify
>>> sympify(2).is_integer
True
>>> sympify(2).is_real
True
>>> sympify(2.0).is_real
True
>>> sympify("2.0").is_real
True
>>> sympify("2e-45").is_real
True
If the expression could not be converted, a SympifyError is raised.
>>> sympify("x***2")
Traceback (most recent call last):
...
SympifyError: SympifyError: "could not parse u'x***2'"
If the option ``strict`` is set to ``True``, only the types for which an
explicit conversion has been defined are converted. In the other
cases, a SympifyError is raised.
>>> sympify(True)
True
>>> sympify(True, strict=True)
Traceback (most recent call last):
...
SympifyError: SympifyError: True
To extend `sympify` to convert custom objects (not derived from `Basic`),
the static dictionary `convert` is provided. The custom converters are
usually added at import time, and will apply to all objects of the given
class or its derived classes.
For example, all geometry objects derive from `GeometryEntity` class, and
should not be altered by the converter, so we add the following after
defining that class:
>>> from sympy.core.sympify import converter
>>> from sympy.geometry.entity import GeometryEntity
>>> converter[GeometryEntity] = lambda x: x
"""
try:
cls = a.__class__
except AttributeError: #a is probably an old-style class object
cls = type(a)
if cls in sympy_classes:
return a
if cls in (bool, type(None)):
if strict:
raise SympifyError(a)
else:
return a
try:
return converter[cls](a)
except KeyError:
for superclass in getmro(cls):
try:
return converter[superclass](a)
except KeyError:
continue
try:
return a._sympy_()
except AttributeError:
pass
if not isinstance(a, basestring):
for coerce in (float, int):
try:
return sympify(coerce(a))
except (TypeError, ValueError, AttributeError, SympifyError):
continue
if strict:
raise SympifyError(a)
if isinstance(a, tuple):
from containers import Tuple
return Tuple(*[sympify(x, locals=locals, convert_xor=convert_xor,
rational=rational) for x in a])
if iterable(a):
try:
return type(a)([sympify(x, locals=locals, convert_xor=convert_xor,
rational=rational) for x in a])
except TypeError:
# Not all iterables are rebuildable with their type.
pass
if isinstance(a, dict):
try:
return type(a)([sympify(x, locals=locals, convert_xor=convert_xor,
rational=rational) for x in a.iteritems()])
except TypeError:
# Not all iterables are rebuildable with their type.
pass
# At this point we were given an arbitrary expression
# which does not inherit from Basic and doesn't implement
# _sympy_ (which is a canonical and robust way to convert
# anything to SymPy expression).
#
# As a last chance, we try to take "a"'s normal form via unicode()
# and try to parse it. If it fails, then we have no luck and
# return an exception
try:
a = unicode(a)
except Exception, exc:
raise SympifyError(a, exc)