```
"""sympify -- convert objects SymPy internal format"""
from inspect import getmro
from core import all_classes as sympy_classes
from sympy.core.compatibility import iterable
class SympifyError(ValueError):
def __init__(self, expr, base_exc=None):
self.expr = expr
self.base_exc = base_exc
def __str__(self):
if self.base_exc is None:
return "SympifyError: %r" % (self.expr,)
return ("Sympify of expression '%s' failed, because of exception being "
"raised:\n%s: %s" % (self.expr, self.base_exc.__class__.__name__,
str(self.base_exc)))
converter = {} #See sympify docstring.
[docs]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``),
just define a ``_sympy_`` method to your class. You can do that even to
classes that you do not own by subclassing or adding the method at runtime.
>>> from sympy import Matrix
>>> class MyList1(object):
... def __iter__(self):
... yield 1
... yield 2
... raise StopIteration
... def __getitem__(self, i): return list(self)[i]
... def _sympy_(self): return Matrix(self)
>>> sympify(MyList1())
[1]
[2]
If you do not have control over the class definition you could also use the
``converter`` global dictionary. The key is the class and the value is a
function that takes a single argument and returns the desired SymPy
object, e.g. ``converter[MyList] = lambda x: Matrix(x)``.
>>> class MyList2(object): # XXX Do not do this if you control the class!
... def __iter__(self): # Use _sympy_!
... yield 1
... yield 2
... raise StopIteration
... def __getitem__(self, i): return list(self)[i]
>>> from sympy.core.sympify import converter
>>> converter[MyList2] = lambda x: Matrix(x)
>>> sympify(MyList2())
[1]
[2]
"""
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 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)
from sympy.parsing.sympy_parser import parse_expr, TokenError
try:
a = a.replace('\n', '')
expr = parse_expr(a, locals or {}, rational, convert_xor)
except (TokenError, SyntaxError):
raise SympifyError('could not parse %r' % a)
return expr
def _sympify(a):
"""Short version of sympify for internal usage for __add__ and __eq__
methods where it is ok to allow some things (like Python integers
and floats) in the expression. This excludes things (like strings)
that are unwise to allow into such an expression.
>>> from sympy import Integer
>>> Integer(1) == 1
True
>>> Integer(1) == '1'
False
>>> from sympy import Symbol
>>> from sympy.abc import x
>>> x + 1
x + 1
>>> x + '1'
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for +: 'Symbol' and 'str'
see: sympify
"""
return sympify(a, strict=True)
```