<reponame>Geektrovert/sympy<filename>sympy/utilities/misc.py
"""Miscellaneous stuff that doesn't really fit anywhere else."""

from __future__ import print_function, division

import sys
import os
import re as _re
import struct
from textwrap import fill, dedent
from sympy.core.compatibility import (get_function_name, range, as_int,
    string_types)



class Undecidable(ValueError):
    # an error to be raised when a decision cannot be made definitively
    # where a definitive answer is needed
    pass


def filldedent(s, w=70):
    """
    Strips leading and trailing empty lines from a copy of `s`, then dedents,
    fills and returns it.

    Empty line stripping serves to deal with docstrings like this one that
    start with a newline after the initial triple quote, inserting an empty
    line at the beginning of the string.

    See Also
    ========
    strlines, rawlines
    """
    return '\n' + fill(dedent(str(s)).strip('\n'), width=w)


def strlines(s, c=64, short=False):
    """Return a cut-and-pastable string that, when printed, is
    equivalent to the input.  The lines will be surrounded by
    parentheses and no line will be longer than c (default 64)
    characters. If the line contains newlines characters, the
    `rawlines` result will be returned.  If ``short`` is True
    (default is False) then if there is one line it will be
    returned without bounding parentheses.

    Examples
    ========

    >>> from sympy.utilities.misc import strlines
    >>> q = 'this is a long string that should be broken into shorter lines'
    >>> print(strlines(q, 40))
    (
    'this is a long string that should be b'
    'roken into shorter lines'
    )
    >>> q == (
    ... 'this is a long string that should be b'
    ... 'roken into shorter lines'
    ... )
    True

    See Also
    ========
    filldedent, rawlines
    """
    if type(s) not in string_types:
        raise ValueError('expecting string input')
    if '\n' in s:
        return rawlines(s)
    q = '"' if repr(s).startswith('"') else "'"
    q = (q,)*2
    if '\\' in s:  # use r-string
        m = '(\nr%s%%s%s\n)' % q
        j = '%s\nr%s' % q
        c -= 3
    else:
        m = '(\n%s%%s%s\n)' % q
        j = '%s\n%s' % q
        c -= 2
    out = []
    while s:
        out.append(s[:c])
        s=s[c:]
    if short and len(out) == 1:
        return (m % out[0]).splitlines()[1]  # strip bounding (\n...\n)
    return m % j.join(out)


def rawlines(s):
    """Return a cut-and-pastable string that, when printed, is equivalent
    to the input. Use this when there is more than one line in the
    string. The string returned is formatted so it can be indented
    nicely within tests; in some cases it is wrapped in the dedent
    function which has to be imported from textwrap.

    Examples
    ========

    Note: because there are characters in the examples below that need
    to be escaped because they are themselves within a triple quoted
    docstring, expressions below look more complicated than they would
    be if they were printed in an interpreter window.

    >>> from sympy.utilities.misc import rawlines
    >>> from sympy import TableForm
    >>> s = str(TableForm([[1, 10]], headings=(None, ['a', 'bee'])))
    >>> print(rawlines(s))
    (
        'a bee\\n'
        '-----\\n'
        '1 10 '
    )
    >>> print(rawlines('''this
    ... that'''))
    dedent('''\\
        this
        that''')

    >>> print(rawlines('''this
    ... that
    ... '''))
    dedent('''\\
        this
        that
        ''')

    >>> s = \"\"\"this
    ... is a triple '''
    ... \"\"\"
    >>> print(rawlines(s))
    dedent(\"\"\"\\
        this
        is a triple '''
        \"\"\")

    >>> print(rawlines('''this
    ... that
    ...     '''))
    (
        'this\\n'
        'that\\n'
        '    '
    )

    See Also
    ========
    filldedent, strlines
    """
    lines = s.split('\n')
    if len(lines) == 1:
        return repr(lines[0])
    triple = ["'''" in s, '"""' in s]
    if any(li.endswith(' ') for li in lines) or '\\' in s or all(triple):
        rv = []
        # add on the newlines
        trailing = s.endswith('\n')
        last = len(lines) - 1
        for i, li in enumerate(lines):
            if i != last or trailing:
                rv.append(repr(li + '\n'))
            else:
                rv.append(repr(li))
        return '(\n    %s\n)' % '\n    '.join(rv)
    else:
        rv = '\n    '.join(lines)
        if triple[0]:
            return 'dedent("""\\\n    %s""")' % rv
        else:
            return "dedent('''\\\n    %s''')" % rv

ARCH = str(struct.calcsize('P') * 8) + "-bit"


# XXX: PyPy doesn't support hash randomization
HASH_RANDOMIZATION = getattr(sys.flags, 'hash_randomization', False)

_debug_tmp = []
_debug_iter = 0

def debug_decorator(func):
    """If SYMPY_DEBUG is True, it will print a nice execution tree with
    arguments and results of all decorated functions, else do nothing.
    """
    from sympy import SYMPY_DEBUG

    if not SYMPY_DEBUG:
        return func

    def maketree(f, *args, **kw):
        global _debug_tmp
        global _debug_iter
        oldtmp = _debug_tmp
        _debug_tmp = []
        _debug_iter += 1

        def tree(subtrees):
            def indent(s, type=1):
                x = s.split("\n")
                r = "+-%s\n" % x[0]
                for a in x[1:]:
                    if a == "":
                        continue
                    if type == 1:
                        r += "| %s\n" % a
                    else:
                        r += "  %s\n" % a
                return r
            if len(subtrees) == 0:
                return ""
            f = []
            for a in subtrees[:-1]:
                f.append(indent(a))
            f.append(indent(subtrees[-1], 2))
            return ''.join(f)

        # If there is a bug and the algorithm enters an infinite loop, enable the
        # following lines. It will print the names and parameters of all major functions
        # that are called, *before* they are called
        #from sympy.core.compatibility import reduce
        #print("%s%s %s%s" % (_debug_iter, reduce(lambda x, y: x + y, \
        #    map(lambda x: '-', range(1, 2 + _debug_iter))), get_function_name(f), args))

        r = f(*args, **kw)

        _debug_iter -= 1
        s = "%s%s = %s\n" % (get_function_name(f), args, r)
        if _debug_tmp != []:
            s += tree(_debug_tmp)
        _debug_tmp = oldtmp
        _debug_tmp.append(s)
        if _debug_iter == 0:
            print((_debug_tmp[0]))
            _debug_tmp = []
        return r

    def decorated(*args, **kwargs):
        return maketree(func, *args, **kwargs)

    return decorated


def debug(*args):
    """
    Print ``*args`` if SYMPY_DEBUG is True, else do nothing.
    """
    from sympy import SYMPY_DEBUG
    if SYMPY_DEBUG:
        print(*args, file=sys.stderr)


def find_executable(executable, path=None):
    """Try to find 'executable' in the directories listed in 'path' (a
    string listing directories separated by 'os.pathsep'; defaults to
    os.environ['PATH']).  Returns the complete filename or None if not
    found
    """
    if path is None:
        path = os.environ['PATH']
    paths = path.split(os.pathsep)
    extlist = ['']
    if os.name == 'os2':
        (base, ext) = os.path.splitext(executable)
        # executable files on OS/2 can have an arbitrary extension, but
        # .exe is automatically appended if no dot is present in the name
        if not ext:
            executable = executable + ".exe"
    elif sys.platform == 'win32':
        pathext = os.environ['PATHEXT'].lower().split(os.pathsep)
        (base, ext) = os.path.splitext(executable)
        if ext.lower() not in pathext:
            extlist = pathext
    for ext in extlist:
        execname = executable + ext
        if os.path.isfile(execname):
            return execname
        else:
            for p in paths:
                f = os.path.join(p, execname)
                if os.path.isfile(f):
                    return f

    return None


def func_name(x, short=False):
    """Return function name of `x` (if defined) else the `type(x)`.
    If short is True and there is a shorter alias for the result,
    return the alias.

    Examples
    ========

    >>> from sympy.utilities.misc import func_name
    >>> from sympy import Matrix
    >>> from sympy.abc import x
    >>> func_name(Matrix.eye(3))
    'MutableDenseMatrix'
    >>> func_name(x < 1)
    'StrictLessThan'
    >>> func_name(x < 1, short=True)
    'Lt'

    See Also
    ========
    sympy.core.compatibility get_function_name
    """
    alias = {
    'GreaterThan': 'Ge',
    'StrictGreaterThan': 'Gt',
    'LessThan': 'Le',
    'StrictLessThan': 'Lt',
    'Equality': 'Eq',
    'Unequality': 'Ne',
    }
    typ = type(x)
    if str(typ).startswith("<type '"):
        typ = str(typ).split("'")[1].split("'")[0]
    elif str(typ).startswith("<class '"):
        typ = str(typ).split("'")[1].split("'")[0]
    rv = getattr(getattr(x, 'func', x), '__name__', typ)
    if '.' in rv:
        rv = rv.split('.')[-1]
    if short:
        rv = alias.get(rv, rv)
    return rv


def _replace(reps):
    """Return a function that can make the replacements, given in
    ``reps``, on a string. The replacements should be given as mapping.

    Examples
    ========

    >>> from sympy.utilities.misc import _replace
    >>> f = _replace(dict(foo='bar', d='t'))
    >>> f('food')
    'bart'
    >>> f = _replace({})
    >>> f('food')
    'food'
    """
    if not reps:
        return lambda x: x
    D = lambda match: reps[match.group(0)]
    pattern = _re.compile("|".join(
        [_re.escape(k) for k, v in reps.items()]), _re.M)
    return lambda string: pattern.sub(D, string)


def replace(string, *reps):
    """Return ``string`` with all keys in ``reps`` replaced with
    their corresponding values, longer strings first, irrespective
    of the order they are given.  ``reps`` may be passed as tuples
    or a single mapping.

    Examples
    ========

    >>> from sympy.utilities.misc import replace
    >>> replace('foo', {'oo': 'ar', 'f': 'b'})
    'bar'
    >>> replace("spamham sha", ("spam", "eggs"), ("sha","md5"))
    'eggsham md5'

    There is no guarantee that a unique answer will be
    obtained if keys in a mapping overlap (i.e. are the same
    length and have some identical sequence at the
    beginning/end):

    >>> reps = [
    ...     ('ab', 'x'),
    ...     ('bc', 'y')]
    >>> replace('abc', *reps) in ('xc', 'ay')
    True

    References
    ==========

    .. [1] https://stackoverflow.com/questions/6116978/python-replace-multiple-strings
    """
    if len(reps) == 1:
        kv = reps[0]
        if type(kv) is dict:
            reps = kv
        else:
            return string.replace(*kv)
    else:
        reps = dict(reps)
    return _replace(reps)(string)


def translate(s, a, b=None, c=None):
    """Return ``s`` where characters have been replaced or deleted.

    SYNTAX
    ======

    translate(s, None, deletechars):
        all characters in ``deletechars`` are deleted
    translate(s, map [,deletechars]):
        all characters in ``deletechars`` (if provided) are deleted
        then the replacements defined by map are made; if the keys
        of map are strings then the longer ones are handled first.
        Multicharacter deletions should have a value of ''.
    translate(s, oldchars, newchars, deletechars)
        all characters in ``deletechars`` are deleted
        then each character in ``oldchars`` is replaced with the
        corresponding character in ``newchars``

    Examples
    ========

    >>> from sympy.utilities.misc import translate
    >>> from sympy.core.compatibility import unichr
    >>> abc = 'abc'
    >>> translate(abc, None, 'a')
    'bc'
    >>> translate(abc, {'a': 'x'}, 'c')
    'xb'
    >>> translate(abc, {'abc': 'x', 'a': 'y'})
    'x'

    >>> translate('abcd', 'ac', 'AC', 'd')
    'AbC'

    There is no guarantee that a unique answer will be
    obtained if keys in a mapping overlap are the same
    length and have some identical sequences at the
    beginning/end:

    >>> translate(abc, {'ab': 'x', 'bc': 'y'}) in ('xc', 'ay')
    True
    """
    from sympy.core.compatibility import maketrans, PY3

    mr = {}
    if a is None:
        assert c is None
        if not b:
            return s
        c = b
        a = b = ''
    else:
        if type(a) is dict:
            short = {}
            for k in list(a.keys()):
                if len(k) == 1 and len(a[k]) == 1:
                    short[k] = a.pop(k)
            mr = a
            c = b
            if short:
                a, b = [''.join(i) for i in list(zip(*short.items()))]
            else:
                a = b = ''
        else:
            assert len(a) == len(b)
    if PY3:
        if c:
            s = s.translate(maketrans('', '', c))
        s = replace(s, mr)
        return s.translate(maketrans(a, b))
    else:
        # when support for Python 2 is dropped, this if-else-block
        # can be replaced with the if-clause
        if c:
            c = list(c)
            rem = {}
            for i in range(-1, -1 - len(c), -1):
                if ord(c[i]) > 255:
                    rem[c[i]] = ''
                    c.pop(i)
            s = s.translate(None, ''.join(c))
            s = replace(s, rem)
            if a:
                a = list(a)
                b = list(b)
                for i in range(-1, -1 - len(a), -1):
                    if ord(a[i]) > 255 or ord(b[i]) > 255:
                        mr[a.pop(i)] = b.pop(i)
                a = ''.join(a)
                b = ''.join(b)
        s = replace(s, mr)
        table = maketrans(a, b)
        # s may have become unicode which uses the py3 syntax for translate
        if isinstance(table, str) and isinstance(s, str):
            s = s.translate(table)
        else:
            s = s.translate(dict(
                [(i, ord(c)) for i, c in enumerate(table)]))
        return s


def ordinal(num):
    """Return ordinal number string of num, e.g. 1 becomes 1st.
    """
    # modified from https://codereview.stackexchange.com/questions/41298/producing-ordinal-numbers
    n = as_int(num)
    k = abs(n) % 100
    if 11 <= k <= 13:
        suffix = 'th'
    elif k % 10 == 1:
        suffix = 'st'
    elif k % 10 == 2:
        suffix = 'nd'
    elif k % 10 == 3:
        suffix = 'rd'
    else:
        suffix = 'th'
    return str(n) + suffix

"""Miscellaneous stuff that doesn't really fit anywhere else."""

from __future__ import print_function, division

import sys
import os
import re as _re
import struct
from textwrap import fill, dedent
from sympy.core.compatibility import (get_function_name, range, as_int,
    string_types)



class Undecidable(ValueError):
    # an error to be raised when a decision cannot be made definitively
    # where a definitive answer is needed
    pass


def filldedent(s, w=70):
    """
    Strips leading and trailing empty lines from a copy of `s`, then dedents,
    fills and returns it.

    Empty line stripping serves to deal with docstrings like this one that
    start with a newline after the initial triple quote, inserting an empty
    line at the beginning of the string.

    See Also
    ========
    strlines, rawlines
    """
    return '\n' + fill(dedent(str(s)).strip('\n'), width=w)


def strlines(s, c=64, short=False):
    """Return a cut-and-pastable string that, when printed, is
    equivalent to the input.  The lines will be surrounded by
    parentheses and no line will be longer than c (default 64)
    characters. If the line contains newlines characters, the
    `rawlines` result will be returned.  If ``short`` is True
    (default is False) then if there is one line it will be
    returned without bounding parentheses.

    Examples
    ========

    >>> from sympy.utilities.misc import strlines
    >>> q = 'this is a long string that should be broken into shorter lines'
    >>> print(strlines(q, 40))
    (
    'this is a long string that should be b'
    'roken into shorter lines'
    )
    >>> q == (
    ... 'this is a long string that should be b'
    ... 'roken into shorter lines'
    ... )
    True

    See Also
    ========
    filldedent, rawlines
    """
    if type(s) not in string_types:
        raise ValueError('expecting string input')
    if '\n' in s:
        return rawlines(s)
    q = '"' if repr(s).startswith('"') else "'"
    q = (q,)*2
    if '\\' in s:  # use r-string
        m = '(\nr%s%%s%s\n)' % q
        j = '%s\nr%s' % q
        c -= 3
    else:
        m = '(\n%s%%s%s\n)' % q
        j = '%s\n%s' % q
        c -= 2
    out = []
    while s:
        out.append(s[:c])
        s=s[c:]
    if short and len(out) == 1:
        return (m % out[0]).splitlines()[1]  # strip bounding (\n...\n)
    return m % j.join(out)


def rawlines(s):
    """Return a cut-and-pastable string that, when printed, is equivalent
    to the input. Use this when there is more than one line in the
    string. The string returned is formatted so it can be indented
    nicely within tests; in some cases it is wrapped in the dedent
    function which has to be imported from textwrap.

    Examples
    ========

    Note: because there are characters in the examples below that need
    to be escaped because they are themselves within a triple quoted
    docstring, expressions below look more complicated than they would
    be if they were printed in an interpreter window.

    >>> from sympy.utilities.misc import rawlines
    >>> from sympy import TableForm
    >>> s = str(TableForm([[1, 10]], headings=(None, ['a', 'bee'])))
    >>> print(rawlines(s))
    (
        'a bee\\n'
        '-----\\n'
        '1 10 '
    )
    >>> print(rawlines('''this
    ... that'''))
    dedent('''\\
        this
        that''')

    >>> print(rawlines('''this
    ... that
    ... '''))
    dedent('''\\
        this
        that
        ''')

    >>> s = \"\"\"this
    ... is a triple '''
    ... \"\"\"
    >>> print(rawlines(s))
    dedent(\"\"\"\\
        this
        is a triple '''
        \"\"\")

    >>> print(rawlines('''this
    ... that
    ...     '''))
    (
        'this\\n'
        'that\\n'
        '    '
    )

    See Also
    ========
    filldedent, strlines
    """
    lines = s.split('\n')
    if len(lines) == 1:
        return repr(lines[0])
    triple = ["'''" in s, '"""' in s]
    if any(li.endswith(' ') for li in lines) or '\\' in s or all(triple):
        rv = []
        # add on the newlines
        trailing = s.endswith('\n')
        last = len(lines) - 1
        for i, li in enumerate(lines):
            if i != last or trailing:
                rv.append(repr(li + '\n'))
            else:
                rv.append(repr(li))
        return '(\n    %s\n)' % '\n    '.join(rv)
    else:
        rv = '\n    '.join(lines)
        if triple[0]:
            return 'dedent("""\\\n    %s""")' % rv
        else:
            return "dedent('''\\\n    %s''')" % rv

ARCH = str(struct.calcsize('P') * 8) + "-bit"


# XXX: PyPy doesn't support hash randomization
HASH_RANDOMIZATION = getattr(sys.flags, 'hash_randomization', False)

_debug_tmp = []
_debug_iter = 0

def debug_decorator(func):
    """If SYMPY_DEBUG is True, it will print a nice execution tree with
    arguments and results of all decorated functions, else do nothing.
    """
    from sympy import SYMPY_DEBUG

    if not SYMPY_DEBUG:
        return func

    def maketree(f, *args, **kw):
        global _debug_tmp
        global _debug_iter
        oldtmp = _debug_tmp
        _debug_tmp = []
        _debug_iter += 1

        def tree(subtrees):
            def indent(s, type=1):
                x = s.split("\n")
                r = "+-%s\n" % x[0]
                for a in x[1:]:
                    if a == "":
                        continue
                    if type == 1:
                        r += "| %s\n" % a
                    else:
                        r += "  %s\n" % a
                return r
            if len(subtrees) == 0:
                return ""
            f = []
            for a in subtrees[:-1]:
                f.append(indent(a))
            f.append(indent(subtrees[-1], 2))
            return ''.join(f)

        # If there is a bug and the algorithm enters an infinite loop, enable the
        # following lines. It will print the names and parameters of all major functions
        # that are called, *before* they are called
        #from sympy.core.compatibility import reduce
        #print("%s%s %s%s" % (_debug_iter, reduce(lambda x, y: x + y, \
        #    map(lambda x: '-', range(1, 2 + _debug_iter))), get_function_name(f), args))

        r = f(*args, **kw)

        _debug_iter -= 1
        s = "%s%s = %s\n" % (get_function_name(f), args, r)
        if _debug_tmp != []:
            s += tree(_debug_tmp)
        _debug_tmp = oldtmp
        _debug_tmp.append(s)
        if _debug_iter == 0:
            print((_debug_tmp[0]))
            _debug_tmp = []
        return r

    def decorated(*args, **kwargs):
        return maketree(func, *args, **kwargs)

    return decorated


def debug(*args):
    """
    Print ``*args`` if SYMPY_DEBUG is True, else do nothing.
    """
    from sympy import SYMPY_DEBUG
    if SYMPY_DEBUG:
        print(*args, file=sys.stderr)


def find_executable(executable, path=None):
    """Try to find 'executable' in the directories listed in 'path' (a
    string listing directories separated by 'os.pathsep'; defaults to
    os.environ['PATH']).  Returns the complete filename or None if not
    found
    """
    if path is None:
        path = os.environ['PATH']
    paths = path.split(os.pathsep)
    extlist = ['']
    if os.name == 'os2':
        (base, ext) = os.path.splitext(executable)
        # executable files on OS/2 can have an arbitrary extension, but
        # .exe is automatically appended if no dot is present in the name
        if not ext:
            executable = executable + ".exe"
    elif sys.platform == 'win32':
        pathext = os.environ['PATHEXT'].lower().split(os.pathsep)
        (base, ext) = os.path.splitext(executable)
        if ext.lower() not in pathext:
            extlist = pathext
    for ext in extlist:
        execname = executable + ext
        if os.path.isfile(execname):
            return execname
        else:
            for p in paths:
                f = os.path.join(p, execname)
                if os.path.isfile(f):
                    return f

    return None


def func_name(x, short=False):
    """Return function name of `x` (if defined) else the `type(x)`.
    If short is True and there is a shorter alias for the result,
    return the alias.

    Examples
    ========

    >>> from sympy.utilities.misc import func_name
    >>> from sympy import Matrix
    >>> from sympy.abc import x
    >>> func_name(Matrix.eye(3))
    'MutableDenseMatrix'
    >>> func_name(x < 1)
    'StrictLessThan'
    >>> func_name(x < 1, short=True)
    'Lt'

    See Also
    ========
    sympy.core.compatibility get_function_name
    """
    alias = {
    'GreaterThan': 'Ge',
    'StrictGreaterThan': 'Gt',
    'LessThan': 'Le',
    'StrictLessThan': 'Lt',
    'Equality': 'Eq',
    'Unequality': 'Ne',
    }
    typ = type(x)
    if str(typ).startswith("<type '"):
        typ = str(typ).split("'")[1].split("'")[0]
    elif str(typ).startswith("<class '"):
        typ = str(typ).split("'")[1].split("'")[0]
    rv = getattr(getattr(x, 'func', x), '__name__', typ)
    if '.' in rv:
        rv = rv.split('.')[-1]
    if short:
        rv = alias.get(rv, rv)
    return rv


def _replace(reps):
    """Return a function that can make the replacements, given in
    ``reps``, on a string. The replacements should be given as mapping.

    Examples
    ========

    >>> from sympy.utilities.misc import _replace
    >>> f = _replace(dict(foo='bar', d='t'))
    >>> f('food')
    'bart'
    >>> f = _replace({})
    >>> f('food')
    'food'
    """
    if not reps:
        return lambda x: x
    D = lambda match: reps[match.group(0)]
    pattern = _re.compile("|".join(
        [_re.escape(k) for k, v in reps.items()]), _re.M)
    return lambda string: pattern.sub(D, string)


def replace(string, *reps):
    """Return ``string`` with all keys in ``reps`` replaced with
    their corresponding values, longer strings first, irrespective
    of the order they are given.  ``reps`` may be passed as tuples
    or a single mapping.

    Examples
    ========

    >>> from sympy.utilities.misc import replace
    >>> replace('foo', {'oo': 'ar', 'f': 'b'})
    'bar'
    >>> replace("spamham sha", ("spam", "eggs"), ("sha","md5"))
    'eggsham md5'

    There is no guarantee that a unique answer will be
    obtained if keys in a mapping overlap (i.e. are the same
    length and have some identical sequence at the
    beginning/end):

    >>> reps = [
    ...     ('ab', 'x'),
    ...     ('bc', 'y')]
    >>> replace('abc', *reps) in ('xc', 'ay')
    True

    References
    ==========

    .. [1] https://stackoverflow.com/questions/6116978/python-replace-multiple-strings
    """
    if len(reps) == 1:
        kv = reps[0]
        if type(kv) is dict:
            reps = kv
        else:
            return string.replace(*kv)
    else:
        reps = dict(reps)
    return _replace(reps)(string)


def translate(s, a, b=None, c=None):
    """Return ``s`` where characters have been replaced or deleted.

    SYNTAX
    ======

    translate(s, None, deletechars):
        all characters in ``deletechars`` are deleted
    translate(s, map [,deletechars]):
        all characters in ``deletechars`` (if provided) are deleted
        then the replacements defined by map are made; if the keys
        of map are strings then the longer ones are handled first.
        Multicharacter deletions should have a value of ''.
    translate(s, oldchars, newchars, deletechars)
        all characters in ``deletechars`` are deleted
        then each character in ``oldchars`` is replaced with the
        corresponding character in ``newchars``

    Examples
    ========

    >>> from sympy.utilities.misc import translate
    >>> from sympy.core.compatibility import unichr
    >>> abc = 'abc'
    >>> translate(abc, None, 'a')
    'bc'
    >>> translate(abc, {'a': 'x'}, 'c')
    'xb'
    >>> translate(abc, {'abc': 'x', 'a': 'y'})
    'x'

    >>> translate('abcd', 'ac', 'AC', 'd')
    'AbC'

    There is no guarantee that a unique answer will be
    obtained if keys in a mapping overlap are the same
    length and have some identical sequences at the
    beginning/end:

    >>> translate(abc, {'ab': 'x', 'bc': 'y'}) in ('xc', 'ay')
    True
    """
    from sympy.core.compatibility import maketrans, PY3

    mr = {}
    if a is None:
        assert c is None
        if not b:
            return s
        c = b
        a = b = ''
    else:
        if type(a) is dict:
            short = {}
            for k in list(a.keys()):
                if len(k) == 1 and len(a[k]) == 1:
                    short[k] = a.pop(k)
            mr = a
            c = b
            if short:
                a, b = [''.join(i) for i in list(zip(*short.items()))]
            else:
                a = b = ''
        else:
            assert len(a) == len(b)
    if PY3:
        if c:
            s = s.translate(maketrans('', '', c))
        s = replace(s, mr)
        return s.translate(maketrans(a, b))
    else:
        # when support for Python 2 is dropped, this if-else-block
        # can be replaced with the if-clause
        if c:
            c = list(c)
            rem = {}
            for i in range(-1, -1 - len(c), -1):
                if ord(c[i]) > 255:
                    rem[c[i]] = ''
                    c.pop(i)
            s = s.translate(None, ''.join(c))
            s = replace(s, rem)
            if a:
                a = list(a)
                b = list(b)
                for i in range(-1, -1 - len(a), -1):
                    if ord(a[i]) > 255 or ord(b[i]) > 255:
                        mr[a.pop(i)] = b.pop(i)
                a = ''.join(a)
                b = ''.join(b)
        s = replace(s, mr)
        table = maketrans(a, b)
        # s may have become unicode which uses the py3 syntax for translate
        if isinstance(table, str) and isinstance(s, str):
            s = s.translate(table)
        else:
            s = s.translate(dict(
                [(i, ord(c)) for i, c in enumerate(table)]))
        return s


def ordinal(num):
    """Return ordinal number string of num, e.g. 1 becomes 1st.
    """
    # modified from https://codereview.stackexchange.com/questions/41298/producing-ordinal-numbers
    n = as_int(num)
    k = abs(n) % 100
    if 11 <= k <= 13:
        suffix = 'th'
    elif k % 10 == 1:
        suffix = 'st'
    elif k % 10 == 2:
        suffix = 'nd'
    elif k % 10 == 3:
        suffix = 'rd'
    else:
        suffix = 'th'
    return str(n) + suffix
Miscellaneous stuff that doesn't really fit anywhere else. # an error to be raised when a decision cannot be made definitively # where a definitive answer is needed Strips leading and trailing empty lines from a copy of `s`, then dedents,     fills and returns it.      Empty line stripping serves to deal with docstrings like this one that     start with a newline after the initial triple quote, inserting an empty     line at the beginning of the string.      See Also     ========     strlines, rawlines Return a cut-and-pastable string that, when printed, is     equivalent to the input.  The lines will be surrounded by     parentheses and no line will be longer than c (default 64)     characters. If the line contains newlines characters, the     `rawlines` result will be returned.  If ``short`` is True     (default is False) then if there is one line it will be     returned without bounding parentheses.      Examples     ========      >>> from sympy.utilities.misc import strlines     >>> q = 'this is a long string that should be broken into shorter lines'     >>> print(strlines(q, 40))     (     'this is a long string that should be b'     'roken into shorter lines'     )     >>> q == (     ... 'this is a long string that should be b'     ... 'roken into shorter lines'     ... )     True      See Also     ========     filldedent, rawlines # use r-string # strip bounding (\n...\n) Return a cut-and-pastable string that, when printed, is equivalent     to the input. Use this when there is more than one line in the     string. The string returned is formatted so it can be indented     nicely within tests; in some cases it is wrapped in the dedent     function which has to be imported from textwrap.      Examples     ========      Note: because there are characters in the examples below that need     to be escaped because they are themselves within a triple quoted     docstring, expressions below look more complicated than they would     be if they were printed in an interpreter window.      >>> from sympy.utilities.misc import rawlines     >>> from sympy import TableForm     >>> s = str(TableForm([[1, 10]], headings=(None, ['a', 'bee'])))     >>> print(rawlines(s))     (         'a bee\\n'         '-----\\n'         '1 10 '     )     >>> print(rawlines('''this     ... that'''))     dedent('''\\         this         that''')      >>> print(rawlines('''this     ... that     ... '''))     dedent('''\\         this         that         ''')      >>> s = \"\"\"this     ... is a triple '''     ... \"\"\"     >>> print(rawlines(s))     dedent(\"\"\"\\         this         is a triple '''         \"\"\")      >>> print(rawlines('''this     ... that     ...     '''))     (         'this\\n'         'that\\n'         '    '     )      See Also     ========     filldedent, strlines " in s, '"""' in s]     if any(li.endswith(' ') for li in lines) or '\\' in s or all(triple):         rv = []         # add on the newlines         trailing = s.endswith('\n')         last = len(lines) - 1         for i, li in enumerate(lines):             if i != last or trailing:                 rv.append(repr(li + '\n'))             else:                 rv.append(repr(li))         return '(\n    %s\n)' % '\n    '.join(rv)     else:         rv = '\n    '.join(lines)         if triple[0]:             return 'dedent("""\\\n    %s""")' % rv         else:             return "dedent( # XXX: PyPy doesn't support hash randomization If SYMPY_DEBUG is True, it will print a nice execution tree with     arguments and results of all decorated functions, else do nothing. # If there is a bug and the algorithm enters an infinite loop, enable the # following lines. It will print the names and parameters of all major functions # that are called, *before* they are called #from sympy.core.compatibility import reduce #print("%s%s %s%s" % (_debug_iter, reduce(lambda x, y: x + y, \ #    map(lambda x: '-', range(1, 2 + _debug_iter))), get_function_name(f), args)) Print ``*args`` if SYMPY_DEBUG is True, else do nothing. Try to find 'executable' in the directories listed in 'path' (a     string listing directories separated by 'os.pathsep'; defaults to     os.environ['PATH']).  Returns the complete filename or None if not     found # executable files on OS/2 can have an arbitrary extension, but # .exe is automatically appended if no dot is present in the name Return function name of `x` (if defined) else the `type(x)`.     If short is True and there is a shorter alias for the result,     return the alias.      Examples     ========      >>> from sympy.utilities.misc import func_name     >>> from sympy import Matrix     >>> from sympy.abc import x     >>> func_name(Matrix.eye(3))     'MutableDenseMatrix'     >>> func_name(x < 1)     'StrictLessThan'     >>> func_name(x < 1, short=True)     'Lt'      See Also     ========     sympy.core.compatibility get_function_name Return a function that can make the replacements, given in     ``reps``, on a string. The replacements should be given as mapping.      Examples     ========      >>> from sympy.utilities.misc import _replace     >>> f = _replace(dict(foo='bar', d='t'))     >>> f('food')     'bart'     >>> f = _replace({})     >>> f('food')     'food' Return ``string`` with all keys in ``reps`` replaced with     their corresponding values, longer strings first, irrespective     of the order they are given.  ``reps`` may be passed as tuples     or a single mapping.      Examples     ========      >>> from sympy.utilities.misc import replace     >>> replace('foo', {'oo': 'ar', 'f': 'b'})     'bar'     >>> replace("spamham sha", ("spam", "eggs"), ("sha","md5"))     'eggsham md5'      There is no guarantee that a unique answer will be     obtained if keys in a mapping overlap (i.e. are the same     length and have some identical sequence at the     beginning/end):      >>> reps = [     ...     ('ab', 'x'),     ...     ('bc', 'y')]     >>> replace('abc', *reps) in ('xc', 'ay')     True      References     ==========      .. [1] https://stackoverflow.com/questions/6116978/python-replace-multiple-strings Return ``s`` where characters have been replaced or deleted.      SYNTAX     ======      translate(s, None, deletechars):         all characters in ``deletechars`` are deleted     translate(s, map [,deletechars]):         all characters in ``deletechars`` (if provided) are deleted         then the replacements defined by map are made; if the keys         of map are strings then the longer ones are handled first.         Multicharacter deletions should have a value of ''.     translate(s, oldchars, newchars, deletechars)         all characters in ``deletechars`` are deleted         then each character in ``oldchars`` is replaced with the         corresponding character in ``newchars``      Examples     ========      >>> from sympy.utilities.misc import translate     >>> from sympy.core.compatibility import unichr     >>> abc = 'abc'     >>> translate(abc, None, 'a')     'bc'     >>> translate(abc, {'a': 'x'}, 'c')     'xb'     >>> translate(abc, {'abc': 'x', 'a': 'y'})     'x'      >>> translate('abcd', 'ac', 'AC', 'd')     'AbC'      There is no guarantee that a unique answer will be     obtained if keys in a mapping overlap are the same     length and have some identical sequences at the     beginning/end:      >>> translate(abc, {'ab': 'x', 'bc': 'y'}) in ('xc', 'ay')     True # when support for Python 2 is dropped, this if-else-block # can be replaced with the if-clause # s may have become unicode which uses the py3 syntax for translate Return ordinal number string of num, e.g. 1 becomes 1st. # modified from https://codereview.stackexchange.com/questions/41298/producing-ordinal-numbers