Coverage for sympy/core/sympify.py : 41%

"""sympify -- convert objects SymPy internal format""" 

from __future__ import print_function, division 

from inspect import getmro 

from .core import all_classes as sympy_classes 

from .compatibility import iterable, string_types, range 

from .evaluate import global_evaluate 

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. 

class CantSympify(object): 

""" 

Mix in this trait to a class to disallow sympification of its instances. 

Examples 

======== 

>>> from sympy.core.sympify import sympify, CantSympify 

>>> class Something(dict): 

... pass 

... 

>>> sympify(Something()) 

{} 

>>> class Something(dict, CantSympify): 

... pass 

... 

>>> sympify(Something()) 

Traceback (most recent call last): 

... 

SympifyError: SympifyError: {} 

""" 

pass 

def sympify(a, locals=None, convert_xor=True, strict=False, rational=False, 

evaluate=None): 

"""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 

- standard numeric python types: int, long, float, Decimal 

- strings (like "0.09" or "2e-19") 

- booleans, including ``None`` (will leave ``None`` 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'" 

Locals 

------ 

The sympification happens with access to everything that is loaded 

by ``from sympy import *``; anything used in a string that is not 

defined by that import will be converted to a symbol. In the following, 

the ``bitcount`` function is treated as a symbol and the ``O`` is 

interpreted as the Order object (used with series) and it raises 

an error when used improperly: 

>>> s = 'bitcount(42)' 

>>> sympify(s) 

bitcount(42) 

>>> sympify("O(x)") 

O(x) 

>>> sympify("O + 1") 

Traceback (most recent call last): 

... 

TypeError: unbound method... 

In order to have ``bitcount`` be recognized it can be imported into a 

namespace dictionary and passed as locals: 

>>> from sympy.core.compatibility import exec_ 

>>> ns = {} 

>>> exec_('from sympy.core.evalf import bitcount', ns) 

>>> sympify(s, locals=ns) 

6 

In order to have the ``O`` interpreted as a Symbol, identify it as such 

in the namespace dictionary. This can be done in a variety of ways; all 

three of the following are possibilities: 

>>> from sympy import Symbol 

>>> ns["O"] = Symbol("O") # method 1 

>>> exec_('from sympy.abc import O', ns) # method 2 

>>> ns.update(dict(O=Symbol("O"))) # method 3 

>>> sympify("O + 1", locals=ns) 

O + 1 

If you want *all* single-letter and Greek-letter variables to be symbols 

then you can use the clashing-symbols dictionaries that have been defined 

there as private variables: _clash1 (single-letter variables), _clash2 

(the multi-letter Greek names) or _clash (both single and multi-letter 

names that are defined in abc). 

>>> from sympy.abc import _clash1 

>>> _clash1 

{'C': C, 'E': E, 'I': I, 'N': N, 'O': O, 'Q': Q, 'S': S} 

>>> sympify('I & Q', _clash1) 

And(I, Q) 

Strict 

------ 

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. 

>>> print(sympify(None)) 

None 

>>> sympify(None, strict=True) 

Traceback (most recent call last): 

... 

SympifyError: SympifyError: None 

Evaluation 

---------- 

If the option ``evaluate`` is set to ``False``, then arithmetic and 

operators will be converted into their SymPy equivalents and the 

``evaluate=False`` option will be added. Nested ``Add`` or ``Mul`` will 

be denested first. This is done via an AST transformation that replaces 

operators with their SymPy equivalents, so if an operand redefines any 

of those operations, the redefined operators will not be used. 

>>> sympify('2**2 / 3 + 5') 

19/3 

>>> sympify('2**2 / 3 + 5', evaluate=False) 

2**2/3 + 5 

Extending 

--------- 

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()) 

Matrix([ 

[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()) 

Matrix([ 

[1], 

[2]]) 

Notes 

===== 

Sometimes autosimplification during sympification results in expressions 

that are very different in structure than what was entered. Until such 

autosimplification is no longer done, the ``kernS`` function might be of 

some use. In the example below you can see how an expression reduces to 

-1 by autosimplification, but does not do so when ``kernS`` is used. 

>>> from sympy.core.sympify import kernS 

>>> from sympy.abc import x 

>>> -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1 

-1 

>>> s = '-2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1' 

>>> sympify(s) 

-1 

>>> kernS(s) 

-2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1 

""" 

if evaluate is None: 

evaluate = global_evaluate[0] 

try: 

if a in sympy_classes: 

return a 

except TypeError: # Type of a is unhashable 

pass 

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 is 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 

if isinstance(a, CantSympify): 

raise SympifyError(a) 

try: 

return a._sympy_() 

except AttributeError: 

pass 

if not isinstance(a, string_types): 

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.items()]) 

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: 

from .compatibility import unicode 

a = unicode(a) 

except Exception as exc: 

raise SympifyError(a, exc) 

from sympy.parsing.sympy_parser import (parse_expr, TokenError, 

standard_transformations) 

from sympy.parsing.sympy_parser import convert_xor as t_convert_xor 

from sympy.parsing.sympy_parser import rationalize as t_rationalize 

transformations = standard_transformations 

if rational: 

transformations += (t_rationalize,) 

if convert_xor: 

transformations += (t_convert_xor,) 

try: 

a = a.replace('\n', '') 

expr = parse_expr(a, local_dict=locals, transformations=transformations, evaluate=evaluate) 

except (TokenError, SyntaxError) as exc: 

raise SympifyError('could not parse %r' % a, exc) 

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.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) 

def kernS(s): 

"""Use a hack to try keep autosimplification from joining Integer or 

minus sign into an Add of a Mul; this modification doesn't 

prevent the 2-arg Mul from becoming an Add, however. 

Examples 

======== 

>>> from sympy.core.sympify import kernS 

>>> from sympy.abc import x, y, z 

The 2-arg Mul allows a leading Integer to be distributed but kernS will 

prevent that: 

>>> 2*(x + y) 

2*x + 2*y 

>>> kernS('2*(x + y)') 

2*(x + y) 

If use of the hack fails, the un-hacked string will be passed to sympify... 

and you get what you get. 

XXX This hack should not be necessary once issue 4596 has been resolved. 

""" 

import re 

from sympy.core.symbol import Symbol 

hit = False 

if '(' in s: 

if s.count('(') != s.count(")"): 

raise SympifyError('unmatched left parenthesis') 

kern = '_kern' 

while kern in s: 

kern += "_" 

olds = s 

# digits*( -> digits*kern*( 

s = re.sub(r'(\d+)( *\* *)\(', r'\1*%s\2(' % kern, s) 

# negated parenthetical 

kern2 = kern + "2" 

while kern2 in s: 

kern2 += "_" 

# step 1: -(...) --> kern-kern*(...) 

target = r'%s-%s*(' % (kern, kern) 

s = re.sub(r'- *\(', target, s) 

# step 2: double the matching closing parenthesis 

# kern-kern*(...) --> kern-kern*(...)kern2 

i = nest = 0 

while True: 

j = s.find(target, i) 

if j == -1: 

break 

j = s.find('(') 

for j in range(j, len(s)): 

if s[j] == "(": 

nest += 1 

elif s[j] == ")": 

nest -= 1 

if nest == 0: 

break 

s = s[:j] + kern2 + s[j:] 

i = j 

# step 3: put in the parentheses 

# kern-kern*(...)kern2 --> (-kern*(...)) 

s = s.replace(target, target.replace(kern, "(", 1)) 

s = s.replace(kern2, ')') 

hit = kern in s 

for i in range(2): 

try: 

expr = sympify(s) 

break 

except: # the kern might cause unknown errors, so use bare except 

if hit: 

s = olds # maybe it didn't like the kern; use un-kerned s 

hit = False 

continue 

expr = sympify(s) # let original error raise 

if not hit: 

return expr 

rep = {Symbol(kern): 1} 

def _clear(expr): 

if isinstance(expr, (list, tuple, set)): 

return type(expr)([_clear(e) for e in expr]) 

if hasattr(expr, 'subs'): 

return expr.subs(rep, hack2=True) 

return expr 

expr = _clear(expr) 

# hope that kern is not there anymore 

return expr