(names, **args)
Transform strings into instances of :class:`Symbol` class.

    :func:`symbols` function returns a sequence of symbols with names taken
    from ``names`` argument, which can be a comma or whitespace delimited
    string, or a sequence of strings::

        >>> from sympy import symbols, Function

        >>> x, y, z = symbols('x,y,z')
        >>> a, b, c = symbols('a b c')

    The type of output is dependent on the properties of input arguments::

        >>> symbols('x')
        x
        >>> symbols('x,')
        (x,)
        >>> symbols('x,y')
        (x, y)
        >>> symbols(('a', 'b', 'c'))
        (a, b, c)
        >>> symbols(['a', 'b', 'c'])
        [a, b, c]
        >>> symbols(set(['a', 'b', 'c']))
        set([a, b, c])

    If an iterable container is needed for a single symbol, set the ``seq``
    argument to ``True`` or terminate the symbol name with a comma::

        >>> symbols('x', seq=True)
        (x,)

    To reduce typing, range syntax is supported to create indexed symbols.
    Ranges are indicated by a colon and the type of range is determined by
    the character to the right of the colon. If the character is a digit
    then all continguous digits to the left are taken as the nonnegative
    starting value (or 0 if there are no digit of the colon) and all
    contiguous digits to the right are taken as 1 greater than the ending
    value::

        >>> symbols('x:10')
        (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)

        >>> symbols('x5:10')
        (x5, x6, x7, x8, x9)
        >>> symbols('x5(:2)')
        (x50, x51)

        >>> symbols('x5:10,y:5')
        (x5, x6, x7, x8, x9, y0, y1, y2, y3, y4)

        >>> symbols(('x5:10', 'y:5'))
        ((x5, x6, x7, x8, x9), (y0, y1, y2, y3, y4))

    If the character to the right of the colon is a letter, then the single
    letter to the left (or 'a' if there is none) is taken as the start
    and all characters in the lexicographic range *through* the letter to
    the right are used as the range::

        >>> symbols('x:z')
        (x, y, z)
        >>> symbols('x:c')  # null range
        ()
        >>> symbols('x(:c)')
        (xa, xb, xc)

        >>> symbols(':c')
        (a, b, c)

        >>> symbols('a:d, x:z')
        (a, b, c, d, x, y, z)

        >>> symbols(('a:d', 'x:z'))
        ((a, b, c, d), (x, y, z))

    Multiple ranges are supported; contiguous numerical ranges should be
    separated by parentheses to disambiguate the ending number of one
    range from the starting number of the next::

        >>> symbols('x:2(1:3)')
        (x01, x02, x11, x12)
        >>> symbols(':3:2')  # parsing is from left to right
        (00, 01, 10, 11, 20, 21)

    Only one pair of parentheses surrounding ranges are removed, so to
    include parentheses around ranges, double them. And to include spaces,
    commas, or colons, escape them with a backslash::

        >>> symbols('x((a:b))')
        (x(a), x(b))
        >>> symbols('x(:1\,:2)')  # or 'x((:1)\,(:2))'
        (x(0,0), x(0,1))

    All newly created symbols have assumptions set according to ``args``::

        >>> a = symbols('a', integer=True)
        >>> a.is_integer
        True

        >>> x, y, z = symbols('x,y,z', real=True)
        >>> x.is_real and y.is_real and z.is_real
        True

    Despite its name, :func:`symbols` can create symbol-like objects like
    instances of Function or Wild classes. To achieve this, set ``cls``
    keyword argument to the desired type::

        >>> symbols('f,g,h', cls=Function)
        (f, g, h)

        >>> type(_[0])
        <class 'sympy.core.function.UndefinedFunction'>
Transform strings into instances of :class:`Symbol` class.
Transform strings into instances of : class : Symbol class .
def symbols(names, **args):
    """
    Transform strings into instances of :class:`Symbol` class.

    :func:`symbols` function returns a sequence of symbols with names taken
    from ``names`` argument, which can be a comma or whitespace delimited
    string, or a sequence of strings::

        >>> from sympy import symbols, Function

        >>> x, y, z = symbols('x,y,z')
        >>> a, b, c = symbols('a b c')

    The type of output is dependent on the properties of input arguments::

        >>> symbols('x')
        x
        >>> symbols('x,')
        (x,)
        >>> symbols('x,y')
        (x, y)
        >>> symbols(('a', 'b', 'c'))
        (a, b, c)
        >>> symbols(['a', 'b', 'c'])
        [a, b, c]
        >>> symbols(set(['a', 'b', 'c']))
        set([a, b, c])

    If an iterable container is needed for a single symbol, set the ``seq``
    argument to ``True`` or terminate the symbol name with a comma::

        >>> symbols('x', seq=True)
        (x,)

    To reduce typing, range syntax is supported to create indexed symbols.
    Ranges are indicated by a colon and the type of range is determined by
    the character to the right of the colon. If the character is a digit
    then all continguous digits to the left are taken as the nonnegative
    starting value (or 0 if there are no digit of the colon) and all
    contiguous digits to the right are taken as 1 greater than the ending
    value::

        >>> symbols('x:10')
        (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)

        >>> symbols('x5:10')
        (x5, x6, x7, x8, x9)
        >>> symbols('x5(:2)')
        (x50, x51)

        >>> symbols('x5:10,y:5')
        (x5, x6, x7, x8, x9, y0, y1, y2, y3, y4)

        >>> symbols(('x5:10', 'y:5'))
        ((x5, x6, x7, x8, x9), (y0, y1, y2, y3, y4))

    If the character to the right of the colon is a letter, then the single
    letter to the left (or 'a' if there is none) is taken as the start
    and all characters in the lexicographic range *through* the letter to
    the right are used as the range::

        >>> symbols('x:z')
        (x, y, z)
        >>> symbols('x:c')  # null range
        ()
        >>> symbols('x(:c)')
        (xa, xb, xc)

        >>> symbols(':c')
        (a, b, c)

        >>> symbols('a:d, x:z')
        (a, b, c, d, x, y, z)

        >>> symbols(('a:d', 'x:z'))
        ((a, b, c, d), (x, y, z))

    Multiple ranges are supported; contiguous numerical ranges should be
    separated by parentheses to disambiguate the ending number of one
    range from the starting number of the next::

        >>> symbols('x:2(1:3)')
        (x01, x02, x11, x12)
        >>> symbols(':3:2')  # parsing is from left to right
        (00, 01, 10, 11, 20, 21)

    Only one pair of parentheses surrounding ranges are removed, so to
    include parentheses around ranges, double them. And to include spaces,
    commas, or colons, escape them with a backslash::

        >>> symbols('x((a:b))')
        (x(a), x(b))
        >>> symbols('x(:1\,:2)')  # or 'x((:1)\,(:2))'
        (x(0,0), x(0,1))

    All newly created symbols have assumptions set according to ``args``::

        >>> a = symbols('a', integer=True)
        >>> a.is_integer
        True

        >>> x, y, z = symbols('x,y,z', real=True)
        >>> x.is_real and y.is_real and z.is_real
        True

    Despite its name, :func:`symbols` can create symbol-like objects like
    instances of Function or Wild classes. To achieve this, set ``cls``
    keyword argument to the desired type::

        >>> symbols('f,g,h', cls=Function)
        (f, g, h)

        >>> type(_[0])
        <class 'sympy.core.function.UndefinedFunction'>

    """
    result = []

    if isinstance(names, string_types):
        marker = 0
        literals = ['\,', '\:', '\ ']
        for i in range(len(literals)):
            lit = literals.pop(0)
            if lit in names:
                while chr(marker) in names:
                    marker += 1
                lit_char = chr(marker)
                marker += 1
                names = names.replace(lit, lit_char)
                literals.append((lit_char, lit[1:]))
        def literal(s):
            if literals:
                for c, l in literals:
                    s = s.replace(c, l)
            return s

        names = names.strip()
        as_seq = names.endswith(',')
        if as_seq:
            names = names[:-1].rstrip()
        if not names:
            raise ValueError('no symbols given')

        # split on commas
        names = [n.strip() for n in names.split(',')]
        if not all(n for n in names):
            raise ValueError('missing symbol between commas')
        # split on spaces
        for i in range(len(names) - 1, -1, -1):
            names[i: i + 1] = names[i].split()

        cls = args.pop('cls', Symbol)
        seq = args.pop('seq', as_seq)

        for name in names:
            if not name:
                raise ValueError('missing symbol')

            if ':' not in name:
                symbol = cls(literal(name), **args)
                result.append(symbol)
                continue

            split = _range.split(name)
            # remove 1 layer of bounding parentheses around ranges
            for i in range(len(split) - 1):
                if i and ':' in split[i] and split[i] != ':' and \
                        split[i - 1].endswith('(') and \
                        split[i + 1].startswith(')'):
                    split[i - 1] = split[i - 1][:-1]
                    split[i + 1] = split[i + 1][1:]
            for i, s in enumerate(split):
                if ':' in s:
                    if s[-1].endswith(':'):
                        raise ValueError('missing end range')
                    a, b = s.split(':')
                    if b[-1] in string.digits:
                        a = 0 if not a else int(a)
                        b = int(b)
                        split[i] = [str(c) for c in range(a, b)]
                    else:
                        a = a or 'a'
                        split[i] = [string.ascii_letters[c] for c in range(
                            string.ascii_letters.index(a),
                            string.ascii_letters.index(b) + 1)]  # inclusive
                    if not split[i]:
                        break
                else:
                    split[i] = [s]
            else:
                seq = True
                if len(split) == 1:
                    names = split[0]
                else:
                    names = [''.join(s) for s in cartes(*split)]
                if literals:
                    result.extend([cls(literal(s), **args) for s in names])
                else:
                    result.extend([cls(s, **args) for s in names])

        if not seq and len(result) <= 1:
            if not result:
                return ()
            return result[0]

        return tuple(result)
    else:
        for name in names:
            result.append(symbols(name, **args))

        return type(names)(result)
def symbols ( names , * * args ) : result = [ ] if isinstance ( names , string_types ) : marker = 0 literals = [ '\,' , '\:' , '\ ' ] for i in range ( len ( literals ) ) : lit = literals . pop ( 0 ) if lit in names : while chr ( marker ) in names : marker += 1 lit_char = chr ( marker ) marker += 1 names = names . replace ( lit , lit_char ) literals . append ( ( lit_char , lit [ 1 : ] ) ) def literal ( s ) : if literals : for c , l in literals : s = s . replace ( c , l ) return s names = names . strip ( ) as_seq = names . endswith ( ',' ) if as_seq : names = names [ : - 1 ] . rstrip ( ) if not names : raise ValueError ( 'no symbols given' ) # split on commas names = [ n . strip ( ) for n in names . split ( ',' ) ] if not all ( n for n in names ) : raise ValueError ( 'missing symbol between commas' ) # split on spaces for i in range ( len ( names ) - 1 , - 1 , - 1 ) : names [ i : i + 1 ] = names [ i ] . split ( ) cls = args . pop ( 'cls' , Symbol ) seq = args . pop ( 'seq' , as_seq ) for name in names : if not name : raise ValueError ( 'missing symbol' ) if ':' not in name : symbol = cls ( literal ( name ) , * * args ) result . append ( symbol ) continue split = _range . split ( name ) # remove 1 layer of bounding parentheses around ranges for i in range ( len ( split ) - 1 ) : if i and ':' in split [ i ] and split [ i ] != ':' and split [ i - 1 ] . endswith ( '(' ) and split [ i + 1 ] . startswith ( ')' ) : split [ i - 1 ] = split [ i - 1 ] [ : - 1 ] split [ i + 1 ] = split [ i + 1 ] [ 1 : ] for i , s in enumerate ( split ) : if ':' in s : if s [ - 1 ] . endswith ( ':' ) : raise ValueError ( 'missing end range' ) a , b = s . split ( ':' ) if b [ - 1 ] in string . digits : a = 0 if not a else int ( a ) b = int ( b ) split [ i ] = [ str ( c ) for c in range ( a , b ) ] else : a = a or 'a' split [ i ] = [ string . ascii_letters [ c ] for c in range ( string . ascii_letters . index ( a ) , string . ascii_letters . index ( b ) + 1 ) ] # inclusive if not split [ i ] : break else : split [ i ] = [ s ] else : seq = True if len ( split ) == 1 : names = split [ 0 ] else : names = [ '' . join ( s ) for s in cartes ( * split ) ] if literals : result . extend ( [ cls ( literal ( s ) , * * args ) for s in names ] ) else : result . extend ( [ cls ( s , * * args ) for s in names ] ) if not seq and len ( result ) <= 1 : if not result : return ( ) return result [ 0 ] return tuple ( result ) else : for name in names : result . append ( symbols ( name , * * args ) ) return type ( names ) ( result )