Source code for sympy.core.sympify

"""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__,

converter = {}  # See sympify docstring.

class CantSympify(object):
    Mix in this trait to a class to disallow sympification of its instances.


    >>> 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: {}


[docs]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 .. warning:: Note that this function uses ``eval``, and thus shouldn't be used on unsanitized input. 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 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 import _clash1 >>> _clash1 {'C': C, 'E': E, 'I': I, 'N': N, 'O': O, 'Q': Q, 'S': S} >>> sympify('I & Q', _clash1) 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 ... return ... 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 ... return ... 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 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: if global_evaluate[0] is False: evaluate = global_evaluate[0] else: evaluate = True 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 #Support for basic numpy datatypes if type(a).__module__ == 'numpy': import numpy as np if np.isscalar(a): if not isinstance(a, np.floating): return sympify(np.asscalar(a)) else: try: from sympy.core.numbers import Float prec = np.finfo(a).nmant a = str(list(np.reshape(np.asarray(a), (1, np.size(a)))[0]))[1:-1] return Float(a, precision=prec) except NotImplementedError: raise SympifyError('Translation for numpy float : %s ' 'is not implemented' % 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 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 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