MTtranslateService/Lib/site-packages/sympy/core/sympify.py

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

import typing
if typing.TYPE_CHECKING:
    from typing import Any, Callable, Dict as tDict, Type

from inspect import getmro
import string
from sympy.core.random import choice

from .parameters import global_parameters

from sympy.utilities.exceptions import sympy_deprecation_warning
from sympy.utilities.iterables 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 = {}  # type: tDict[Type[Any], Callable[[Any], Basic]]

#holds the conversions defined in SymPy itself, i.e. non-user defined conversions
_sympy_converter = {} # type: tDict[Type[Any], Callable[[Any], Basic]]

#alias for clearer use in the library
_external_converter = converter

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

    Examples
    ========

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

    >>> class Something(dict):
    ...     pass
    ...
    >>> sympify(Something())
    {}

    >>> class Something(dict, CantSympify):
    ...     pass
    ...
    >>> sympify(Something())
    Traceback (most recent call last):
    ...
    SympifyError: SympifyError: {}

    """
    pass


def _is_numpy_instance(a):
    """
    Checks if an object is an instance of a type from the numpy module.
    """
    # This check avoids unnecessarily importing NumPy.  We check the whole
    # __mro__ in case any base type is a numpy type.
    return any(type_.__module__ == 'numpy'
               for type_ in type(a).__mro__)


def _convert_numpy_types(a, **sympify_args):
    """
    Converts a numpy datatype input to an appropriate SymPy type.
    """
    import numpy as np
    if not isinstance(a, np.floating):
        if np.iscomplex(a):
            return _sympy_converter[complex](a.item())
        else:
            return sympify(a.item(), **sympify_args)
    else:
        try:
            from .numbers import Float
            prec = np.finfo(a).nmant + 1
            # E.g. double precision means prec=53 but nmant=52
            # Leading bit of mantissa is always 1, so is not stored
            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)


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.

    Explanation
    ===========

    It will convert Python ints into instances of :class:`~.Integer`, floats
    into instances of :class:`~.Float`, etc. It is also able to coerce
    symbolic expressions which inherit from :class:`~.Basic`. This can be
    useful in cooperation with SAGE.

    .. 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.

    Examples
    ========

    >>> 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 '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 :class:`~.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:

    >>> 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
    >>> set(_clash1)
    {'E', 'I', 'N', 'O', 'Q', '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

    .. deprecated:: 1.6

       ``sympify(obj)`` automatically falls back to ``str(obj)`` when all
       other conversion methods fail, but this is deprecated. ``strict=True``
       will disable this deprecated behavior. See
       :ref:`deprecated-sympify-string-fallback`.

    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. If
    argument a is not a string, the mathematical expression is evaluated
    before being passed to sympify, so adding ``evaluate=False`` will still
    return the evaluated result of expression.

    >>> sympify('2**2 / 3 + 5')
    19/3
    >>> sympify('2**2 / 3 + 5', evaluate=False)
    2**2/3 + 5
    >>> sympify('4/2+7', evaluate=True)
    9
    >>> sympify('4/2+7', evaluate=False)
    4/2 + 7
    >>> sympify(4/2+7, evaluate=False)
    9.00000000000000

    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
    =====

    The keywords ``rational`` and ``convert_xor`` are only used
    when the input is a string.

    convert_xor
    -----------

    >>> sympify('x^y',convert_xor=True)
    x**y
    >>> sympify('x^y',convert_xor=False)
    x ^ y

    rational
    --------

    >>> sympify('0.1',rational=False)
    0.1
    >>> sympify('0.1',rational=True)
    1/10

    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

    Parameters
    ==========

    a :
        - any object defined in SymPy
        - standard numeric Python types: ``int``, ``long``, ``float``, ``Decimal``
        - strings (like ``"0.09"``, ``"2e-19"`` or ``'sin(x)'``)
        - booleans, including ``None`` (will leave ``None`` unchanged)
        - dicts, lists, sets or tuples containing any of the above

    convert_xor : bool, optional
        If true, treats ``^`` as exponentiation.
        If False, treats ``^`` as XOR itself.
        Used only when input is a string.

    locals : any object defined in SymPy, optional
        In order to have strings be recognized it can be imported
        into a namespace dictionary and passed as locals.

    strict : bool, optional
        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.

    rational : bool, optional
        If ``True``, converts floats into :class:`~.Rational`.
        If ``False``, it lets floats remain as it is.
        Used only when input is a string.

    evaluate : bool, optional
        If False, then arithmetic and operators will be converted into
        their SymPy equivalents. If True the expression will be evaluated
        and the result will be returned.

    """
    # XXX: If a is a Basic subclass rather than instance (e.g. sin rather than
    # sin(x)) then a.__sympy__ will be the property. Only on the instance will
    # a.__sympy__ give the *value* of the property (True). Since sympify(sin)
    # was used for a long time we allow it to pass. However if strict=True as
    # is the case in internal calls to _sympify then we only allow
    # is_sympy=True.
    #
    # https://github.com/sympy/sympy/issues/20124
    is_sympy = getattr(a, '__sympy__', None)
    if is_sympy is True:
        return a
    elif is_sympy is not None:
        if not strict:
            return a
        else:
            raise SympifyError(a)

    if isinstance(a, CantSympify):
        raise SympifyError(a)

    cls = getattr(a, "__class__", None)

    #Check if there exists a converter for any of the types in the mro
    for superclass in getmro(cls):
        #First check for user defined converters
        conv = _external_converter.get(superclass)
        if conv is None:
            #if none exists, check for SymPy defined converters
            conv = _sympy_converter.get(superclass)
        if conv is not None:
            return conv(a)

    if cls is type(None):
        if strict:
            raise SympifyError(a)
        else:
            return a

    if evaluate is None:
        evaluate = global_parameters.evaluate

    # Support for basic numpy datatypes
    if _is_numpy_instance(a):
        import numpy as np
        if np.isscalar(a):
            return _convert_numpy_types(a, locals=locals,
                convert_xor=convert_xor, strict=strict, rational=rational,
                evaluate=evaluate)

    _sympy_ = getattr(a, "_sympy_", None)
    if _sympy_ is not None:
        try:
            return a._sympy_()
        # XXX: Catches AttributeError: 'SymPyConverter' object has no
        # attribute 'tuple'
        # This is probably a bug somewhere but for now we catch it here.
        except AttributeError:
            pass

    if not strict:
        # Put numpy array conversion _before_ float/int, see
        # <https://github.com/sympy/sympy/issues/13924>.
        flat = getattr(a, "flat", None)
        if flat is not None:
            shape = getattr(a, "shape", None)
            if shape is not None:
                from sympy.tensor.array import Array
                return Array(a.flat, a.shape)  # works with e.g. NumPy arrays

    if not isinstance(a, str):
        if _is_numpy_instance(a):
            import numpy as np
            assert not isinstance(a, np.number)
            if isinstance(a, np.ndarray):
                # Scalar arrays (those with zero dimensions) have sympify
                # called on the scalar element.
                if a.ndim == 0:
                    try:
                        return sympify(a.item(),
                                       locals=locals,
                                       convert_xor=convert_xor,
                                       strict=strict,
                                       rational=rational,
                                       evaluate=evaluate)
                    except SympifyError:
                        pass
        else:
            # float and int can coerce size-one numpy arrays to their lone
            # element.  See issue https://github.com/numpy/numpy/issues/10404.
            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, evaluate=evaluate) for x in a])
        except TypeError:
            # Not all iterables are rebuildable with their type.
            pass

    if not isinstance(a, str):
        try:
            a = str(a)
        except Exception as exc:
            raise SympifyError(a, exc)
        sympy_deprecation_warning(
            f"""
The string fallback in sympify() is deprecated.

To explicitly convert the string form of an object, use
sympify(str(obj)). To add define sympify behavior on custom
objects, use sympy.core.sympify.converter or define obj._sympy_
(see the sympify() docstring).

sympify() performed the string fallback resulting in the following string:

{a!r}
            """,
            deprecated_since_version='1.6',
            active_deprecations_target="deprecated-sympify-string-fallback",
        )

    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 :func:`~.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 distributing a
    a number into an Add; 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

    The 2-arg Mul distributes a number (or minus sign) across the terms
    of an expression, but kernS will prevent that:

    >>> 2*(x + y), -(x + 1)
    (2*x + 2*y, -x - 1)
    >>> kernS('2*(x + y)')
    2*(x + y)
    >>> kernS('-(x + 1)')
    -(x + 1)

    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.
    """
    hit = False
    quoted = '"' in s or "'" in s
    if '(' in s and not quoted:
        if s.count('(') != s.count(")"):
            raise SympifyError('unmatched left parenthesis')

        # strip all space from s
        s = ''.join(s.split())
        olds = s
        # now use space to represent a symbol that
        # will
        # step 1. turn potential 2-arg Muls into 3-arg versions
        # 1a. *( -> * *(
        s = s.replace('*(', '* *(')
        # 1b. close up exponentials
        s = s.replace('** *', '**')
        # 2. handle the implied multiplication of a negated
        # parenthesized expression in two steps
        # 2a:  -(...)  -->  -( *(...)
        target = '-( *('
        s = s.replace('-(', target)
        # 2b: double the matching closing parenthesis
        # -( *(...)  -->  -( *(...))
        i = nest = 0
        assert target.endswith('(')  # assumption below
        while True:
            j = s.find(target, i)
            if j == -1:
                break
            j += len(target) - 1
            for j in range(j, len(s)):
                if s[j] == "(":
                    nest += 1
                elif s[j] == ")":
                    nest -= 1
                if nest == 0:
                    break
            s = s[:j] + ")" + s[j:]
            i = j + 2  # the first char after 2nd )
        if ' ' in s:
            # get a unique kern
            kern = '_'
            while kern in s:
                kern += choice(string.ascii_letters + string.digits)
            s = s.replace(' ', kern)
            hit = kern in s
        else:
            hit = False

    for i in range(2):
        try:
            expr = sympify(s)
            break
        except TypeError:  # the kern might cause unknown errors...
            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

    from .symbol import Symbol
    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


# Avoid circular import
from .basic import Basic