"""
A Printer which converts an expression into its LaTeX equivalent.
"""

from __future__ import print_function, division

from sympy.core import S, C, Add, Symbol
from sympy.core.function import _coeff_isneg
from sympy.core.sympify import SympifyError
from sympy.core.alphabets import greeks
from sympy.logic.boolalg import true

## sympy.printing imports
from .printer import Printer
from .conventions import split_super_sub, requires_partial
from .precedence import precedence, PRECEDENCE

import sympy.mpmath.libmp as mlib
from sympy.mpmath.libmp import prec_to_dps

from sympy.core.compatibility import default_sort_key, xrange
from sympy.utilities.iterables import has_variety

import re

# Hand-picked functions which can be used directly in both LaTeX and MathJax
# Complete list at http://www.mathjax.org/docs/1.1/tex.html#supported-latex-commands
# This variable only contains those functions which sympy uses.
accepted_latex_functions = ['arcsin', 'arccos', 'arctan', 'sin', 'cos', 'tan',
                    'sinh', 'cosh', 'tanh', 'sqrt', 'ln', 'log', 'sec', 'csc',
                    'cot', 'coth', 're', 'im', 'frac', 'root', 'arg',
                    ]

tex_greek_dictionary = {
    'Alpha': 'A',
    'Beta': 'B',
    'Epsilon': 'E',
    'Zeta': 'Z',
    'Eta': 'H',
    'Iota': 'I',
    'Kappa': 'K',
    'Mu': 'M',
    'Nu': 'N',
    'omicron': 'o',
    'Omicron': 'O',
    'Rho': 'P',
    'Tau': 'T',
    'Chi': 'X',
    'lamda': r'\lambda',
    'Lamda': r'\Lambda',
    'khi': r'\chi',
    'Khi': r'X',
    'varepsilon': r'\varepsilon',
    'varkappa': r'\varkappa',
    'varphi': r'\varphi',
    'varpi': r'\varpi',
    'varrho': r'\varrho',
    'varsigma': r'\varsigma',
    'vartheta': r'\vartheta',
}

other_symbols = set(['aleph', 'beth', 'daleth', 'gimel', 'ell', 'eth', 'hbar',
                     'hslash', 'mho', 'wp', ])

# Variable name modifiers
modifier_dict = {
    # Accents
    'mathring': lambda s: r'\mathring{'+s+r'}',
    'ddddot': lambda s: r'\ddddot{'+s+r'}',
    'dddot': lambda s: r'\dddot{'+s+r'}',
    'ddot': lambda s: r'\ddot{'+s+r'}',
    'dot': lambda s: r'\dot{'+s+r'}',
    'check': lambda s: r'\check{'+s+r'}',
    'breve': lambda s: r'\breve{'+s+r'}',
    'acute': lambda s: r'\acute{'+s+r'}',
    'grave': lambda s: r'\grave{'+s+r'}',
    'tilde': lambda s: r'\tilde{'+s+r'}',
    'hat': lambda s: r'\hat{'+s+r'}',
    'bar': lambda s: r'\bar{'+s+r'}',
    'vec': lambda s: r'\vec{'+s+r'}',
    'prime': lambda s: "{"+s+"}'",
    'prm': lambda s: "{"+s+"}'",
    # Faces
    'bold': lambda s: r'\boldsymbol{'+s+r'}',
    'bm': lambda s: r'\boldsymbol{'+s+r'}',
    'cal': lambda s: r'\mathcal{'+s+r'}',
    'scr': lambda s: r'\mathscr{'+s+r'}',
    'frak': lambda s: r'\mathfrak{'+s+r'}',
    # Brackets
    'norm': lambda s: r'\left\lVert{'+s+r'}\right\rVert',
    'avg': lambda s: r'\left\langle{'+s+r'}\right\rangle',
    'abs': lambda s: r'\left\lvert{'+s+r'}\right\rvert',
    'mag': lambda s: r'\left\lvert{'+s+r'}\right\rvert',
}

greek_letters_set = frozenset(greeks)

class LatexPrinter(Printer):
    printmethod = "_latex"

    _default_settings = {
        "order": None,
        "mode": "plain",
        "itex": False,
        "fold_frac_powers": False,
        "fold_func_brackets": False,
        "fold_short_frac": None,
        "long_frac_ratio": 2,
        "mul_symbol": None,
        "inv_trig_style": "abbreviated",
        "mat_str": None,
        "mat_delim": "[",
        "symbol_names": {},
    }

    def __init__(self, settings=None):
        Printer.__init__(self, settings)

        if 'mode' in self._settings:
            valid_modes = ['inline', 'plain', 'equation',
                           'equation*']
            if self._settings['mode'] not in valid_modes:
                raise ValueError("'mode' must be one of 'inline', 'plain', "
                    "'equation' or 'equation*'")

        if self._settings['fold_short_frac'] is None and \
                self._settings['mode'] == 'inline':
            self._settings['fold_short_frac'] = True

        mul_symbol_table = {
            None: r" ",
            "ldot": r" \,.\, ",
            "dot": r" \cdot ",
            "times": r" \times "
        }

        self._settings['mul_symbol_latex'] = \
            mul_symbol_table[self._settings['mul_symbol']]

        self._settings['mul_symbol_latex_numbers'] = \
            mul_symbol_table[self._settings['mul_symbol'] or 'dot']

        self._delim_dict = {'(': ')', '[': ']'}

    def parenthesize(self, item, level):
        if precedence(item) <= level:
            return r"\left(%s\right)" % self._print(item)
        else:
            return self._print(item)

    def doprint(self, expr):
        tex = Printer.doprint(self, expr)

        if self._settings['mode'] == 'plain':
            return tex
        elif self._settings['mode'] == 'inline':
            return r"$%s$" % tex
        elif self._settings['itex']:
            return r"$$%s$$" % tex
        else:
            env_str = self._settings['mode']
            return r"\begin{%s}%s\end{%s}" % (env_str, tex, env_str)

    def _needs_brackets(self, expr):
        """
        Returns True if the expression needs to be wrapped in brackets when
        printed, False otherwise. For example: a + b => True; a => False;
        10 => False; -10 => True.
        """
        return not ((expr.is_Integer and expr.is_nonnegative)
                or (expr.is_Atom and expr is not S.NegativeOne))

    def _needs_function_brackets(self, expr):
        """
        Returns True if the expression needs to be wrapped in brackets when
        passed as an argument to a function, False otherwise. This is a more
        liberal version of _needs_brackets, in that many expressions which need
        to be wrapped in brackets when added/subtracted/raised to a power do
        not need them when passed to a function. Such an example is a*b.
        """
        if not self._needs_brackets(expr):
            return False
        else:
            # Muls of the form a*b*c... can be folded
            if expr.is_Mul and not self._mul_is_clean(expr):
                return True
            # Pows which don't need brackets can be folded
            elif expr.is_Pow and not self._pow_is_clean(expr):
                return True
            # Add and Function always need brackets
            elif expr.is_Add or expr.is_Function:
                return True
            else:
                return False

    def _needs_mul_brackets(self, expr, last=False):
        """
        Returns True if the expression needs to be wrapped in brackets when
        printed as part of a Mul, False otherwise. This is True for Add,
        but also for some container objects that would not need brackets
        when appearing last in a Mul, e.g. an Integral. ``last=True``
        specifies that this expr is the last to appear in a Mul.
        """
        from sympy import Integral, Piecewise, Product, Sum
        return expr.is_Add or (not last and
            any([expr.has(x) for x in (Integral, Piecewise, Product, Sum)]))

    def _mul_is_clean(self, expr):
        for arg in expr.args:
            if arg.is_Function:
                return False
        return True

    def _pow_is_clean(self, expr):
        return not self._needs_brackets(expr.base)

    def _do_exponent(self, expr, exp):
        if exp is not None:
            return r"\left(%s\right)^{%s}" % (expr, exp)
        else:
            return expr

    def _print_bool(self, e):
        return r"\mathrm{%s}" % e

    _print_BooleanTrue = _print_bool
    _print_BooleanFalse = _print_bool

    def _print_NoneType(self, e):
        return r"\mathrm{%s}" % e

    def _print_Add(self, expr, order=None):
        if self.order == 'none':
            terms = list(expr.args)
        else:
            terms = self._as_ordered_terms(expr, order=order)
        tex = self._print(terms[0])

        for term in terms[1:]:
            if not _coeff_isneg(term):
                tex += " + " + self._print(term)
            else:
                tex += " - " + self._print(-term)

        return tex

    def _print_Float(self, expr):
        # Based off of that in StrPrinter
        dps = prec_to_dps(expr._prec)
        str_real = mlib.to_str(expr._mpf_, dps, strip_zeros=True)

        # Must always have a mul symbol (as 2.5 10^{20} just looks odd)
        # thus we use the number separator
        separator = self._settings['mul_symbol_latex_numbers']

        if 'e' in str_real:
            (mant, exp) = str_real.split('e')

            if exp[0] == '+':
                exp = exp[1:]

            return r"%s%s10^{%s}" % (mant, separator, exp)
        elif str_real == "+inf":
            return r"\infty"
        elif str_real == "-inf":
            return r"- \infty"
        else:
            return str_real

    def _print_Mul(self, expr):
        coeff, _ = expr.as_coeff_Mul()

        if not coeff.is_negative:
            tex = ""
        else:
            expr = -expr
            tex = "- "

        from sympy.simplify import fraction
        numer, denom = fraction(expr, exact=True)
        separator = self._settings['mul_symbol_latex']
        numbersep = self._settings['mul_symbol_latex_numbers']

        def convert(expr):
            if not expr.is_Mul:
                return str(self._print(expr))
            else:
                _tex = last_term_tex = ""

                if self.order not in ('old', 'none'):
                    args = expr.as_ordered_factors()
                else:
                    args = expr.args

                for i, term in enumerate(args):
                    term_tex = self._print(term)

                    if self._needs_mul_brackets(term, last=(i == len(args) - 1)):
                        term_tex = r"\left(%s\right)" % term_tex

                    if re.search("[0-9][} ]*$", last_term_tex) and \
                            re.match("[{ ]*[-+0-9]", term_tex):
                        # between two numbers
                        _tex += numbersep
                    elif _tex:
                        _tex += separator

                    _tex += term_tex
                    last_term_tex = term_tex
                return _tex

        if denom is S.One:
            # use the original expression here, since fraction() may have
            # altered it when producing numer and denom
            tex += convert(expr)
        else:
            snumer = convert(numer)
            sdenom = convert(denom)
            ldenom = len(sdenom.split())
            ratio = self._settings['long_frac_ratio']
            if self._settings['fold_short_frac'] \
                    and ldenom <= 2 and not "^" in sdenom:
                # handle short fractions
                if self._needs_mul_brackets(numer, last=False):
                    tex += r"\left(%s\right) / %s" % (snumer, sdenom)
                else:
                    tex += r"%s / %s" % (snumer, sdenom)
            elif len(snumer.split()) > ratio*ldenom:
                # handle long fractions
                if self._needs_mul_brackets(numer, last=True):
                    tex += r"\frac{1}{%s}%s\left(%s\right)" \
                        % (sdenom, separator, snumer)
                elif numer.is_Mul:
                    # split a long numerator
                    a = S.One
                    b = S.One
                    for x in numer.args:
                        if self._needs_mul_brackets(x, last=False) or \
                                len(convert(a*x).split()) > ratio*ldenom or \
                                (b.is_commutative is x.is_commutative is False):
                            b *= x
                        else:
                            a *= x
                    if self._needs_mul_brackets(b, last=True):
                        tex += r"\frac{%s}{%s}%s\left(%s\right)" \
                            % (convert(a), sdenom, separator, convert(b))
                    else:
                        tex += r"\frac{%s}{%s}%s%s" \
                            % (convert(a), sdenom, separator, convert(b))
                else:
                    tex += r"\frac{1}{%s}%s%s" % (sdenom, separator, snumer)
            else:
                tex += r"\frac{%s}{%s}" % (snumer, sdenom)

        return tex

    def _print_Pow(self, expr):
        # Treat x**Rational(1,n) as special case
        if expr.exp.is_Rational and abs(expr.exp.p) == 1 and expr.exp.q != 1:
            base = self._print(expr.base)
            expq = expr.exp.q

            if expq == 2:
                tex = r"\sqrt{%s}" % base
            elif self._settings['itex']:
                tex = r"\root{%d}{%s}" % (expq, base)
            else:
                tex = r"\sqrt[%d]{%s}" % (expq, base)

            if expr.exp.is_negative:
                return r"\frac{1}{%s}" % tex
            else:
                return tex
        elif self._settings['fold_frac_powers'] \
            and expr.exp.is_Rational \
                and expr.exp.q != 1:
            base, p, q = self._print(expr.base), expr.exp.p, expr.exp.q
            if expr.base.is_Function:
                return self._print(expr.base, "%s/%s" % (p, q))
            if self._needs_brackets(expr.base):
                return r"\left(%s\right)^{%s/%s}" % (base, p, q)
            return r"%s^{%s/%s}" % (base, p, q)
        elif expr.exp.is_Rational and expr.exp.is_negative and expr.base.is_commutative:
            # Things like 1/x
            return self._print_Mul(expr)
        else:
            if expr.base.is_Function:
                return self._print(expr.base, self._print(expr.exp))
            else:
                if expr.is_commutative and expr.exp == -1:
                    #solves issue 4129
                    #As Mul always simplify 1/x to x**-1
                    #The objective is achieved with this hack
                    #first we get the latex for -1 * expr,
                    #which is a Mul expression
                    tex = self._print(S.NegativeOne * expr).strip()
                    #the result comes with a minus and a space, so we remove
                    if tex[:1] == "-":
                        return tex[1:].strip()
                if self._needs_brackets(expr.base):
                    tex = r"\left(%s\right)^{%s}"
                else:
                    tex = r"%s^{%s}"

                return tex % (self._print(expr.base),
                              self._print(expr.exp))

    def _print_Sum(self, expr):
        if len(expr.limits) == 1:
            tex = r"\sum_{%s=%s}^{%s} " % \
                tuple([ self._print(i) for i in expr.limits[0] ])
        else:
            def _format_ineq(l):
                return r"%s \leq %s \leq %s" % \
                    tuple([self._print(s) for s in (l[1], l[0], l[2])])

            tex = r"\sum_{\substack{%s}} " % \
                str.join('\\\\', [ _format_ineq(l) for l in expr.limits ])

        if isinstance(expr.function, Add):
            tex += r"\left(%s\right)" % self._print(expr.function)
        else:
            tex += self._print(expr.function)

        return tex

    def _print_Product(self, expr):
        if len(expr.limits) == 1:
            tex = r"\prod_{%s=%s}^{%s} " % \
                tuple([ self._print(i) for i in expr.limits[0] ])
        else:
            def _format_ineq(l):
                return r"%s \leq %s \leq %s" % \
                    tuple([self._print(s) for s in (l[1], l[0], l[2])])

            tex = r"\prod_{\substack{%s}} " % \
                str.join('\\\\', [ _format_ineq(l) for l in expr.limits ])

        if isinstance(expr.function, Add):
            tex += r"\left(%s\right)" % self._print(expr.function)
        else:
            tex += self._print(expr.function)

        return tex

    def _print_BasisDependent(self, expr):
        from sympy.vector import Vector

        o1 = []
        if expr == expr.zero:
            return expr.zero._latex_form
        if isinstance(expr, Vector):
            items = expr.separate().items()
        else:
            items = [(0, expr)]

        for system, vect in items:
            inneritems = list(vect.components.items())
            inneritems.sort(key = lambda x:x[0].__str__())
            for k, v in inneritems:
                if v == 1:
                    o1.append(' + ' + k._latex_form)
                elif v == -1:
                    o1.append(' - ' + k._latex_form)
                else:
                    arg_str = '(' + LatexPrinter().doprint(v) + ')'
                    o1.append(' + ' + arg_str + k._latex_form)

        outstr = (''.join(o1))
        if outstr[1] != '-':
            outstr = outstr[3:]
        else:
            outstr = outstr[1:]
        return outstr

    def _print_Indexed(self, expr):
        tex = self._print(expr.base)+'_{%s}' % ','.join(
            map(self._print, expr.indices))
        return tex

    def _print_IndexedBase(self, expr):
        return self._print(expr.label)

    def _print_Derivative(self, expr):
        dim = len(expr.variables)
        if requires_partial(expr):
            diff_symbol = r'\partial'
        else:
            diff_symbol = r'd'


        if dim == 1:
            tex = r"\frac{%s}{%s %s}" % (diff_symbol, diff_symbol,
                self._print(expr.variables[0]))
        else:
            multiplicity, i, tex = [], 1, ""
            current = expr.variables[0]

            for symbol in expr.variables[1:]:
                if symbol == current:
                    i = i + 1
                else:
                    multiplicity.append((current, i))
                    current, i = symbol, 1
            else:
                multiplicity.append((current, i))

            for x, i in multiplicity:
                if i == 1:
                    tex += r"%s %s" % (diff_symbol, self._print(x))
                else:
                    tex += r"%s %s^{%s}" % (diff_symbol, self._print(x), i)

            tex = r"\frac{%s^{%s}}{%s} " % (diff_symbol, dim, tex)

        if isinstance(expr.expr, C.AssocOp):
            return r"%s\left(%s\right)" % (tex, self._print(expr.expr))
        else:
            return r"%s %s" % (tex, self._print(expr.expr))

    def _print_Subs(self, subs):
        expr, old, new = subs.args
        latex_expr = self._print(expr)
        latex_old = (self._print(e) for e in old)
        latex_new = (self._print(e) for e in new)
        latex_subs = r'\\ '.join(
            e[0] + '=' + e[1] for e in zip(latex_old, latex_new))
        return r'\left. %s \right|_{\substack{ %s }}' % (latex_expr, latex_subs)

    def _print_Integral(self, expr):
        tex, symbols = "", []

        # Only up to \iiiint exists
        if len(expr.limits) <= 4 and all(len(lim) == 1 for lim in expr.limits):
            # Use len(expr.limits)-1 so that syntax highlighters don't think
            # \" is an escaped quote
            tex = r"\i" + "i"*(len(expr.limits) - 1) + "nt"
            symbols = [r"\, d%s" % self._print(symbol[0])
                       for symbol in expr.limits]

        else:
            for lim in reversed(expr.limits):
                symbol = lim[0]
                tex += r"\int"

                if len(lim) > 1:
                    if self._settings['mode'] in ['equation', 'equation*'] \
                            and not self._settings['itex']:
                        tex += r"\limits"

                    if len(lim) == 3:
                        tex += "_{%s}^{%s}" % (self._print(lim[1]),
                                               self._print(lim[2]))
                    if len(lim) == 2:
                        tex += "^{%s}" % (self._print(lim[1]))

                symbols.insert(0, r"\, d%s" % self._print(symbol))

        return r"%s %s%s" % (tex,
            str(self._print(expr.function)), "".join(symbols))

    def _print_Limit(self, expr):
        e, z, z0, dir = expr.args

        tex = r"\lim_{%s \to " % self._print(z)
        if z0 in (S.Infinity, S.NegativeInfinity):
            tex += r"%s}" % self._print(z0)
        else:
            tex += r"%s^%s}" % (self._print(z0), self._print(dir))

        if isinstance(e, C.AssocOp):
            return r"%s\left(%s\right)" % (tex, self._print(e))
        else:
            return r"%s %s" % (tex, self._print(e))

    def _hprint_Function(self, func):
        '''
        Logic to decide how to render a function to latex
          - if it is a recognized latex name, use the appropriate latex command
          - if it is a single letter, just use that letter
          - if it is a longer name, then put \operatorname{} around it and be
            mindful of undercores in the name
        '''
        func = self._deal_with_super_sub(func)

        if func in accepted_latex_functions:
            name = r"\%s" % func
        elif len(func) == 1 or func.startswith('\\'):
            name = func
        else:
            name = r"\operatorname{%s}" % func
        return name

    def _print_Function(self, expr, exp=None):
        '''
        Render functions to LaTeX, handling functions that LaTeX knows about
        e.g., sin, cos, ... by using the proper LaTeX command (\sin, \cos, ...).
        For single-letter function names, render them as regular LaTeX math
        symbols. For multi-letter function names that LaTeX does not know
        about, (e.g., Li, sech) use \operatorname{} so that the function name
        is rendered in Roman font and LaTeX handles spacing properly.

        expr is the expression involving the function
        exp is an exponent
        '''
        func = expr.func.__name__

        if hasattr(self, '_print_' + func):
            return getattr(self, '_print_' + func)(expr, exp)
        else:
            args = [ str(self._print(arg)) for arg in expr.args ]
            # How inverse trig functions should be displayed, formats are:
            # abbreviated: asin, full: arcsin, power: sin^-1
            inv_trig_style = self._settings['inv_trig_style']
            # If we are dealing with a power-style inverse trig function
            inv_trig_power_case = False
            # If it is applicable to fold the argument brackets
            can_fold_brackets = self._settings['fold_func_brackets'] and \
                len(args) == 1 and \
                not self._needs_function_brackets(expr.args[0])

            inv_trig_table = ["asin", "acos", "atan", "acot"]

            # If the function is an inverse trig function, handle the style
            if func in inv_trig_table:
                if inv_trig_style == "abbreviated":
                    func = func
                elif inv_trig_style == "full":
                    func = "arc" + func[1:]
                elif inv_trig_style == "power":
                    func = func[1:]
                    inv_trig_power_case = True

                    # Can never fold brackets if we're raised to a power
                    if exp is not None:
                        can_fold_brackets = False

            if inv_trig_power_case:
                if func in accepted_latex_functions:
                    name = r"\%s^{-1}" % func
                else:
                    name = r"\operatorname{%s}^{-1}" % func
            elif exp is not None:
                name = r'%s^{%s}' % (self._hprint_Function(func), exp)
            else:
                name = self._hprint_Function(func)

            if can_fold_brackets:
                if func in accepted_latex_functions:
                    # Wrap argument safely to avoid parse-time conflicts
                    # with the function name itself
                    name += r" {%s}"
                else:
                    name += r"%s"
            else:
                name += r"{\left (%s \right )}"

            if inv_trig_power_case and exp is not None:
                name += r"^{%s}" % exp

            return name % ",".join(args)

    def _print_UndefinedFunction(self, expr):
        return self._hprint_Function(str(expr))

    def _print_FunctionClass(self, expr):
        if hasattr(expr, '_latex_no_arg'):
            return expr._latex_no_arg(self)

        return self._hprint_Function(str(expr))

    def _print_Lambda(self, expr):
        symbols, expr = expr.args

        if len(symbols) == 1:
            symbols = self._print(symbols[0])
        else:
            symbols = self._print(tuple(symbols))

        args = (symbols, self._print(expr))
        tex = r"\left( %s \mapsto %s \right)" % (symbols, self._print(expr))

        return tex

    def _print_Min(self, expr, exp=None):
        args = sorted(expr.args, key=default_sort_key)
        texargs = [r"%s" % self._print(symbol) for symbol in args]
        tex = r"\min\left(%s\right)" % ", ".join(texargs)

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_Max(self, expr, exp=None):
        args = sorted(expr.args, key=default_sort_key)
        texargs = [r"%s" % self._print(symbol) for symbol in args]
        tex = r"\max\left(%s\right)" % ", ".join(texargs)

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_floor(self, expr, exp=None):
        tex = r"\lfloor{%s}\rfloor" % self._print(expr.args[0])

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_ceiling(self, expr, exp=None):
        tex = r"\lceil{%s}\rceil" % self._print(expr.args[0])

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_Abs(self, expr, exp=None):
        tex = r"\left\lvert{%s}\right\rvert" % self._print(expr.args[0])

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex
    _print_Determinant = _print_Abs

    def _print_re(self, expr, exp=None):
        if self._needs_brackets(expr.args[0]):
            tex = r"\Re {\left (%s \right )}" % self._print(expr.args[0])
        else:
            tex = r"\Re{%s}" % self._print(expr.args[0])

        return self._do_exponent(tex, exp)

    def _print_im(self, expr, exp=None):
        if self._needs_brackets(expr.args[0]):
            tex = r"\Im {\left ( %s \right )}" % self._print(expr.args[0])
        else:
            tex = r"\Im{%s}" % self._print(expr.args[0])

        return self._do_exponent(tex, exp)

    def _print_Not(self, e):
        from sympy import Equivalent, Implies
        if isinstance(e.args[0], Equivalent):
            return self._print_Equivalent(e.args[0], r"\not\equiv")
        if isinstance(e.args[0], Implies):
            return self._print_Implies(e.args[0], r"\not\Rightarrow")
        if (e.args[0].is_Boolean):
            return r"\neg (%s)" % self._print(e.args[0])
        else:
            return r"\neg %s" % self._print(e.args[0])

    def _print_LogOp(self, args, char):
        arg = args[0]
        if arg.is_Boolean and not arg.is_Not:
            tex = r"\left(%s\right)" % self._print(arg)
        else:
            tex = r"%s" % self._print(arg)

        for arg in args[1:]:
            if arg.is_Boolean and not arg.is_Not:
                tex += r" %s \left(%s\right)" % (char, self._print(arg))
            else:
                tex += r" %s %s" % (char, self._print(arg))

        return tex

    def _print_And(self, e):
        args = sorted(e.args, key=default_sort_key)
        return self._print_LogOp(args, r"\wedge")

    def _print_Or(self, e):
        args = sorted(e.args, key=default_sort_key)
        return self._print_LogOp(args, r"\vee")

    def _print_Xor(self, e):
        args = sorted(e.args, key=default_sort_key)
        return self._print_LogOp(args, r"\veebar")

    def _print_Implies(self, e, altchar=None):
        return self._print_LogOp(e.args, altchar or r"\Rightarrow")

    def _print_Equivalent(self, e, altchar=None):
        args = sorted(e.args, key=default_sort_key)
        return self._print_LogOp(args, altchar or r"\equiv")

    def _print_conjugate(self, expr, exp=None):
        tex = r"\overline{%s}" % self._print(expr.args[0])

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_polar_lift(self, expr, exp=None):
        func = r"\operatorname{polar\_lift}"
        arg = r"{\left (%s \right )}" % self._print(expr.args[0])

        if exp is not None:
            return r"%s^{%s}%s" % (func, exp, arg)
        else:
            return r"%s%s" % (func, arg)

    def _print_ExpBase(self, expr, exp=None):
        # TODO should exp_polar be printed differently?
        #      what about exp_polar(0), exp_polar(1)?
        tex = r"e^{%s}" % self._print(expr.args[0])
        return self._do_exponent(tex, exp)

    def _print_elliptic_k(self, expr, exp=None):
        tex = r"\left(%s\right)" % self._print(expr.args[0])
        if exp is not None:
            return r"K^{%s}%s" % (exp, tex)
        else:
            return r"K%s" % tex

    def _print_elliptic_f(self, expr, exp=None):
        tex = r"\left(%s\middle| %s\right)" % \
            (self._print(expr.args[0]), self._print(expr.args[1]))
        if exp is not None:
            return r"F^{%s}%s" % (exp, tex)
        else:
            return r"F%s" % tex

    def _print_elliptic_e(self, expr, exp=None):
        if len(expr.args) == 2:
            tex = r"\left(%s\middle| %s\right)" % \
                (self._print(expr.args[0]), self._print(expr.args[1]))
        else:
            tex = r"\left(%s\right)" % self._print(expr.args[0])
        if exp is not None:
            return r"E^{%s}%s" % (exp, tex)
        else:
            return r"E%s" % tex

    def _print_elliptic_pi(self, expr, exp=None):
        if len(expr.args) == 3:
            tex = r"\left(%s; %s\middle| %s\right)" % \
                (self._print(expr.args[0]), self._print(expr.args[1]), \
                 self._print(expr.args[2]))
        else:
            tex = r"\left(%s\middle| %s\right)" % \
                (self._print(expr.args[0]), self._print(expr.args[1]))
        if exp is not None:
            return r"\Pi^{%s}%s" % (exp, tex)
        else:
            return r"\Pi%s" % tex

    def _print_gamma(self, expr, exp=None):
        tex = r"\left(%s\right)" % self._print(expr.args[0])

        if exp is not None:
            return r"\Gamma^{%s}%s" % (exp, tex)
        else:
            return r"\Gamma%s" % tex

    def _print_uppergamma(self, expr, exp=None):
        tex = r"\left(%s, %s\right)" % (self._print(expr.args[0]),
                                        self._print(expr.args[1]))

        if exp is not None:
            return r"\Gamma^{%s}%s" % (exp, tex)
        else:
            return r"\Gamma%s" % tex

    def _print_lowergamma(self, expr, exp=None):
        tex = r"\left(%s, %s\right)" % (self._print(expr.args[0]),
                                        self._print(expr.args[1]))

        if exp is not None:
            return r"\gamma^{%s}%s" % (exp, tex)
        else:
            return r"\gamma%s" % tex

    def _print_expint(self, expr, exp=None):
        tex = r"\left(%s\right)" % self._print(expr.args[1])
        nu = self._print(expr.args[0])

        if exp is not None:
            return r"\operatorname{E}_{%s}^{%s}%s" % (nu, exp, tex)
        else:
            return r"\operatorname{E}_{%s}%s" % (nu, tex)

    def _print_fresnels(self, expr, exp=None):
        tex = r"\left(%s\right)" % self._print(expr.args[0])

        if exp is not None:
            return r"S^{%s}%s" % (exp, tex)
        else:
            return r"S%s" % tex

    def _print_fresnelc(self, expr, exp=None):
        tex = r"\left(%s\right)" % self._print(expr.args[0])

        if exp is not None:
            return r"C^{%s}%s" % (exp, tex)
        else:
            return r"C%s" % tex

    def _print_subfactorial(self, expr, exp=None):
        x = expr.args[0]
        if self._needs_brackets(x):
            tex = r"!\left(%s\right)" % self._print(x)
        else:
            tex = "!" + self._print(x)

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_factorial(self, expr, exp=None):
        x = expr.args[0]
        if self._needs_brackets(x):
            tex = r"\left(%s\right)!" % self._print(x)
        else:
            tex = self._print(x) + "!"

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_factorial2(self, expr, exp=None):
        x = expr.args[0]
        if self._needs_brackets(x):
            tex = r"\left(%s\right)!!" % self._print(x)
        else:
            tex = self._print(x) + "!!"

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_binomial(self, expr, exp=None):
        tex = r"{\binom{%s}{%s}}" % (self._print(expr.args[0]),
                                     self._print(expr.args[1]))

        if exp is not None:
            return r"%s^{%s}" % (tex, exp)
        else:
            return tex

    def _print_RisingFactorial(self, expr, exp=None):
        tex = r"{\left(%s\right)}^{\left(%s\right)}" % \
            (self._print(expr.args[0]), self._print(expr.args[1]))

        return self._do_exponent(tex, exp)

    def _print_FallingFactorial(self, expr, exp=None):
        tex = r"{\left(%s\right)}_{\left(%s\right)}" % \
            (self._print(expr.args[0]), self._print(expr.args[1]))

        return self._do_exponent(tex, exp)

    def _hprint_BesselBase(self, expr, exp, sym):
        tex = r"%s" % (sym)

        need_exp = False
        if exp is not None:
            if tex.find('^') == -1:
                tex = r"%s^{%s}" % (tex, self._print(exp))
            else:
                need_exp = True

        tex = r"%s_{%s}\left(%s\right)" % (tex, self._print(expr.order),
                                           self._print(expr.argument))

        if need_exp:
            tex = self._do_exponent(tex, exp)
        return tex

    def _hprint_vec(self, vec):
        if len(vec) == 0:
            return ""
        s = ""
        for i in vec[:-1]:
            s += "%s, " % self._print(i)
        s += self._print(vec[-1])
        return s

    def _print_besselj(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'J')

    def _print_besseli(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'I')

    def _print_besselk(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'K')

    def _print_bessely(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'Y')

    def _print_yn(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'y')

    def _print_jn(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'j')

    def _print_hankel1(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'H^{(1)}')

    def _print_hankel2(self, expr, exp=None):
        return self._hprint_BesselBase(expr, exp, 'H^{(2)}')

    def _hprint_airy(self, expr, exp=None, notation=""):
        tex = r"\left(%s\right)" % self._print(expr.args[0])

        if exp is not None:
            return r"%s^{%s}%s" % (notation, exp, tex)
        else:
            return r"%s%s" % (notation, tex)

    def _hprint_airy_prime(self, expr, exp=None, notation=""):
        tex = r"\left(%s\right)" % self._print(expr.args[0])

        if exp is not None:
            return r"{%s^\prime}^{%s}%s" % (notation, exp, tex)
        else:
            return r"%s^\prime%s" % (notation, tex)

    def _print_airyai(self, expr, exp=None):
        return self._hprint_airy(expr, exp, 'Ai')

    def _print_airybi(self, expr, exp=None):
        return self._hprint_airy(expr, exp, 'Bi')

    def _print_airyaiprime(self, expr, exp=None):
        return self._hprint_airy_prime(expr, exp, 'Ai')

    def _print_airybiprime(self, expr, exp=None):
        return self._hprint_airy_prime(expr, exp, 'Bi')

    def _print_hyper(self, expr, exp=None):
        tex = r"{{}_{%s}F_{%s}\left(\begin{matrix} %s \\ %s \end{matrix}" \
              r"\middle| {%s} \right)}" % \
            (self._print(len(expr.ap)), self._print(len(expr.bq)),
              self._hprint_vec(expr.ap), self._hprint_vec(expr.bq),
              self._print(expr.argument))

        if exp is not None:
            tex = r"{%s}^{%s}" % (tex, self._print(exp))
        return tex

    def _print_meijerg(self, expr, exp=None):
        tex = r"{G_{%s, %s}^{%s, %s}\left(\begin{matrix} %s & %s \\" \
              r"%s & %s \end{matrix} \middle| {%s} \right)}" % \
            (self._print(len(expr.ap)), self._print(len(expr.bq)),
              self._print(len(expr.bm)), self._print(len(expr.an)),
              self._hprint_vec(expr.an), self._hprint_vec(expr.aother),
              self._hprint_vec(expr.bm), self._hprint_vec(expr.bother),
              self._print(expr.argument))

        if exp is not None:
            tex = r"{%s}^{%s}" % (tex, self._print(exp))
        return tex

    def _print_dirichlet_eta(self, expr, exp=None):
        tex = r"\left(%s\right)" % self._print(expr.args[0])
        if exp is not None:
            return r"\eta^{%s}%s" % (self._print(exp), tex)
        return r"\eta%s" % tex

    def _print_zeta(self, expr, exp=None):
        if len(expr.args) == 2:
            tex = r"\left(%s, %s\right)" % tuple(map(self._print, expr.args))
        else:
            tex = r"\left(%s\right)" % self._print(expr.args[0])
        if exp is not None:
            return r"\zeta^{%s}%s" % (self._print(exp), tex)
        return r"\zeta%s" % tex

    def _print_lerchphi(self, expr, exp=None):
        tex = r"\left(%s, %s, %s\right)" % tuple(map(self._print, expr.args))
        if exp is None:
            return r"\Phi%s" % tex
        return r"\Phi^{%s}%s" % (self._print(exp), tex)

    def _print_polylog(self, expr, exp=None):
        s, z = map(self._print, expr.args)
        tex = r"\left(%s\right)" % z
        if exp is None:
            return r"\operatorname{Li}_{%s}%s" % (s, tex)
        return r"\operatorname{Li}_{%s}^{%s}%s" % (s, self._print(exp), tex)

    def _print_jacobi(self, expr, exp=None):
        n, a, b, x = map(self._print, expr.args)
        tex = r"P_{%s}^{\left(%s,%s\right)}\left(%s\right)" % (n, a, b, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_gegenbauer(self, expr, exp=None):
        n, a, x = map(self._print, expr.args)
        tex = r"C_{%s}^{\left(%s\right)}\left(%s\right)" % (n, a, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_chebyshevt(self, expr, exp=None):
        n, x = map(self._print, expr.args)
        tex = r"T_{%s}\left(%s\right)" % (n, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_chebyshevu(self, expr, exp=None):
        n, x = map(self._print, expr.args)
        tex = r"U_{%s}\left(%s\right)" % (n, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_legendre(self, expr, exp=None):
        n, x = map(self._print, expr.args)
        tex = r"P_{%s}\left(%s\right)" % (n, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_assoc_legendre(self, expr, exp=None):
        n, a, x = map(self._print, expr.args)
        tex = r"P_{%s}^{\left(%s\right)}\left(%s\right)" % (n, a, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_hermite(self, expr, exp=None):
        n, x = map(self._print, expr.args)
        tex = r"H_{%s}\left(%s\right)" % (n, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_laguerre(self, expr, exp=None):
        n, x = map(self._print, expr.args)
        tex = r"L_{%s}\left(%s\right)" % (n, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_assoc_laguerre(self, expr, exp=None):
        n, a, x = map(self._print, expr.args)
        tex = r"L_{%s}^{\left(%s\right)}\left(%s\right)" % (n, a, x)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_Ynm(self, expr, exp=None):
        n, m, theta, phi = map(self._print, expr.args)
        tex = r"Y_{%s}^{%s}\left(%s,%s\right)" % (n, m, theta, phi)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_Znm(self, expr, exp=None):
        n, m, theta, phi = map(self._print, expr.args)
        tex = r"Z_{%s}^{%s}\left(%s,%s\right)" % (n, m, theta, phi)
        if exp is not None:
            tex = r"\left(" + tex + r"\right)^{%s}" % (self._print(exp))
        return tex

    def _print_Rational(self, expr):
        if expr.q != 1:
            sign = ""
            p = expr.p
            if expr.p < 0:
                sign = "- "
                p = -p
            return r"%s\frac{%d}{%d}" % (sign, p, expr.q)
        else:
            return self._print(expr.p)

    def _print_Order(self, expr):
        s = self._print(expr.expr)
        if expr.point and any(p != S.Zero for p in expr.point) or \
           len(expr.variables) > 1:
            s += '; '
            if len(expr.variables) > 1:
                s += self._print(expr.variables)
            elif len(expr.variables):
                s += self._print(expr.variables[0])
            s += r'\rightarrow'
            if len(expr.point) > 1:
                s += self._print(expr.point)
            else:
                s += self._print(expr.point[0])
        return r"\mathcal{O}\left(%s\right)" % s

    def _print_Symbol(self, expr):
        if expr in self._settings['symbol_names']:
            return self._settings['symbol_names'][expr]

        return self._deal_with_super_sub(expr.name)

    _print_RandomSymbol = _print_Symbol
    _print_MatrixSymbol = _print_Symbol

    def _deal_with_super_sub(self, string):

        name, supers, subs = split_super_sub(string)

        name = translate(name)
        supers = [translate(sup) for sup in supers]
        subs = [translate(sub) for sub in subs]

        # glue all items together:
        if len(supers) > 0:
            name += "^{%s}" % " ".join(supers)
        if len(subs) > 0:
            name += "_{%s}" % " ".join(subs)

        return name

    def _print_Relational(self, expr):
        if self._settings['itex']:
            gt = r"\gt"
            lt = r"\lt"
        else:
            gt = ">"
            lt = "<"

        charmap = {
            "==": "=",
            ">": gt,
            "<": lt,
            ">=": r"\geq",
            "<=": r"\leq",
            "!=": r"\neq",
        }

        return "%s %s %s" % (self._print(expr.lhs),
            charmap[expr.rel_op], self._print(expr.rhs))

    def _print_Piecewise(self, expr):
        ecpairs = [r"%s & \text{for}\: %s" % (self._print(e), self._print(c))
                   for e, c in expr.args[:-1]]
        if expr.args[-1].cond == true:
            ecpairs.append(r"%s & \text{otherwise}" %
                           self._print(expr.args[-1].expr))
        else:
            ecpairs.append(r"%s & \text{for}\: %s" %
                           (self._print(expr.args[-1].expr),
                            self._print(expr.args[-1].cond)))
        tex = r"\begin{cases} %s \end{cases}"
        return tex % r" \\".join(ecpairs)

    def _print_MatrixBase(self, expr):
        lines = []

        for line in range(expr.rows):  # horrible, should be 'rows'
            lines.append(" & ".join([ self._print(i) for i in expr[line, :] ]))

        mat_str = self._settings['mat_str']
        if mat_str is None:
            if self._settings['mode'] == 'inline':
                mat_str = 'smallmatrix'
            else:
                if (expr.cols <= 10) is True:
                    mat_str = 'matrix'
                else:
                    mat_str = 'array'

        out_str = r'\begin{%MATSTR%}%s\end{%MATSTR%}'
        out_str = out_str.replace('%MATSTR%', mat_str)
        if mat_str == 'array':
            out_str = out_str.replace('%s', '{' + 'c'*expr.cols + '}%s')
        if self._settings['mat_delim']:
            left_delim = self._settings['mat_delim']
            right_delim = self._delim_dict[left_delim]
            out_str = r'\left' + left_delim + out_str + \
                      r'\right' + right_delim
        return out_str % r"\\".join(lines)
    _print_ImmutableMatrix = _print_MatrixBase
    _print_Matrix = _print_MatrixBase

    def _print_MatrixElement(self, expr):
        return self._print(expr.parent) + '_{%s, %s}'%(expr.i, expr.j)

    def _print_MatrixSlice(self, expr):
        def latexslice(x):
            x = list(x)
            if x[2] == 1:
                del x[2]
            if x[1] == x[0] + 1:
                del x[1]
            if x[0] == 0:
                x[0] = ''
            return ':'.join(map(self._print, x))
        return (self._print(expr.parent) + r'\left[' +
                latexslice(expr.rowslice) + ', ' +
                latexslice(expr.colslice) + r'\right]')

    def _print_BlockMatrix(self, expr):
        return self._print(expr.blocks)

    def _print_Transpose(self, expr):
        mat = expr.arg
        from sympy.matrices import MatrixSymbol
        if not isinstance(mat, MatrixSymbol):
            return r"\left(%s\right)^T" % self._print(mat)
        else:
            return "%s^T" % self._print(mat)

    def _print_Adjoint(self, expr):
        mat = expr.arg
        from sympy.matrices import MatrixSymbol
        if not isinstance(mat, MatrixSymbol):
            return r"\left(%s\right)^\dag" % self._print(mat)
        else:
            return "%s^\dag" % self._print(mat)

    def _print_MatAdd(self, expr):
        terms = list(expr.args)
        tex = " + ".join(map(self._print, terms))
        return tex

    def _print_MatMul(self, expr):
        from sympy import Add, MatAdd, HadamardProduct

        def parens(x):
            if isinstance(x, (Add, MatAdd, HadamardProduct)):
                return r"\left(%s\right)" % self._print(x)
            return self._print(x)
        return ' '.join(map(parens, expr.args))

    def _print_HadamardProduct(self, expr):
        from sympy import Add, MatAdd, MatMul

        def parens(x):
            if isinstance(x, (Add, MatAdd, MatMul)):
                return r"\left(%s\right)" % self._print(x)
            return self._print(x)
        return ' \circ '.join(map(parens, expr.args))

    def _print_MatPow(self, expr):
        base, exp = expr.base, expr.exp
        from sympy.matrices import MatrixSymbol
        if not isinstance(base, MatrixSymbol):
            return r"\left(%s\right)^{%s}" % (self._print(base), self._print(exp))
        else:
            return "%s^{%s}" % (self._print(base), self._print(exp))

    def _print_ZeroMatrix(self, Z):
        return r"\bold{0}"

    def _print_Identity(self, I):
        return r"\mathbb{I}"

    def _print_tuple(self, expr):
        return r"\left ( %s\right )" % \
            r", \quad ".join([ self._print(i) for i in expr ])

    def _print_Tuple(self, expr):
        return self._print_tuple(expr)

    def _print_list(self, expr):
        return r"\left [ %s\right ]" % \
            r", \quad ".join([ self._print(i) for i in expr ])

    def _print_dict(self, d):
        keys = sorted(d.keys(), key=default_sort_key)
        items = []

        for key in keys:
            val = d[key]
            items.append("%s : %s" % (self._print(key), self._print(val)))

        return r"\left \{ %s\right \}" % r", \quad ".join(items)

    def _print_Dict(self, expr):
        return self._print_dict(expr)

    def _print_DiracDelta(self, expr, exp=None):
        if len(expr.args) == 1 or expr.args[1] == 0:
            tex = r"\delta\left(%s\right)" % self._print(expr.args[0])
        else:
            tex = r"\delta^{\left( %s \right)}\left( %s \right)" % (
                self._print(expr.args[1]), self._print(expr.args[0]))
        if exp:
            tex = r"\left(%s\right)^{%s}" % (tex, exp)
        return tex

    def _print_Heaviside(self, expr, exp=None):
        tex = r"\theta\left(%s\right)" % self._print(expr.args[0])
        if exp:
            tex = r"\left(%s\right)^{%s}" % (tex, exp)
        return tex

    def _print_KroneckerDelta(self, expr, exp=None):
        i = self._print(expr.args[0])
        j = self._print(expr.args[1])
        if expr.args[0].is_Atom and expr.args[1].is_Atom:
            tex = r'\delta_{%s %s}' % (i, j)
        else:
            tex = r'\delta_{%s, %s}' % (i, j)
        if exp:
            tex = r'\left(%s\right)^{%s}' % (tex, exp)
        return tex

    def _print_LeviCivita(self, expr, exp=None):
        indices = map(self._print, expr.args)
        if all(map(lambda x: x.is_Atom, expr.args)):
            tex = r'\varepsilon_{%s}' % " ".join(indices)
        else:
            tex = r'\varepsilon_{%s}' % ", ".join(indices)
        if exp:
            tex = r'\left(%s\right)^{%s}' % (tex, exp)
        return tex

    def _print_ProductSet(self, p):
        if len(p.sets) > 1 and not has_variety(p.sets):
            return self._print(p.sets[0]) + "^%d" % len(p.sets)
        else:
            return r" \times ".join(self._print(set) for set in p.sets)

    def _print_RandomDomain(self, d):
        try:
            return 'Domain: ' + self._print(d.as_boolean())
        except Exception:
            try:
                return ('Domain: ' + self._print(d.symbols) + ' in ' +
                        self._print(d.set))
            except:
                return 'Domain on ' + self._print(d.symbols)

    def _print_FiniteSet(self, s):
        items = sorted(s.args, key=default_sort_key)
        return self._print_set(items)

    def _print_set(self, s):
        items = sorted(s, key=default_sort_key)
        items = ", ".join(map(self._print, items))
        return r"\left\{%s\right\}" % items

    _print_frozenset = _print_set

    def _print_Range(self, s):
        if len(s) > 4:
            it = iter(s)
            printset = next(it), next(it), '\ldots', s._last_element
        else:
            printset = tuple(s)

        return (r"\left\{"
              + r", ".join(self._print(el) for el in printset)
              + r"\right\}")

    def _print_Interval(self, i):
        if i.start == i.end:
            return r"\left\{%s\right\}" % self._print(i.start)

        else:
            if i.left_open:
                left = '('
            else:
                left = '['

            if i.right_open:
                right = ')'
            else:
                right = ']'

            return r"\left%s%s, %s\right%s" % \
                   (left, self._print(i.start), self._print(i.end), right)

    def _print_Union(self, u):
        return r" \cup ".join([self._print(i) for i in u.args])

    def _print_Complement(self, u):
        return r" \setminus ".join([self._print(i) for i in u.args])

    def _print_Intersection(self, u):
        return r" \cap ".join([self._print(i) for i in u.args])

    def _print_EmptySet(self, e):
        return r"\emptyset"

    def _print_Naturals(self, n):
        return r"\mathbb{N}"

    def _print_Integers(self, i):
        return r"\mathbb{Z}"

    def _print_Reals(self, i):
        return r"\mathbb{R}"

    def _print_ImageSet(self, s):
        return r"\left\{%s\; |\; %s \in %s\right\}" % (
            self._print(s.lamda.expr),
            ', '.join([self._print(var) for var in s.lamda.variables]),
            self._print(s.base_set))

    def _print_Contains(self, e):
        return r"%s \in %s" % tuple(self._print(a) for a in e.args)

    def _print_FiniteField(self, expr):
        return r"\mathbb{F}_{%s}" % expr.mod

    def _print_IntegerRing(self, expr):
        return r"\mathbb{Z}"

    def _print_RationalField(self, expr):
        return r"\mathbb{Q}"

    def _print_RealField(self, expr):
        return r"\mathbb{R}"

    def _print_ComplexField(self, expr):
        return r"\mathbb{C}"

    def _print_PolynomialRing(self, expr):
        domain = self._print(expr.domain)
        symbols = ", ".join(map(self._print, expr.symbols))
        return r"%s\left[%s\right]" % (domain, symbols)

    def _print_FractionField(self, expr):
        domain = self._print(expr.domain)
        symbols = ", ".join(map(self._print, expr.symbols))
        return r"%s\left(%s\right)" % (domain, symbols)

    def _print_PolynomialRingBase(self, expr):
        domain = self._print(expr.domain)
        symbols = ", ".join(map(self._print, expr.symbols))
        inv = ""
        if not expr.is_Poly:
            inv = r"S_<^{-1}"
        return r"%s%s\left[%s\right]" % (inv, domain, symbols)

    def _print_Poly(self, poly):
        cls = poly.__class__.__name__
        expr = self._print(poly.as_expr())
        gens = list(map(self._print, poly.gens))
        domain = "domain=%s" % self._print(poly.get_domain())

        args = ", ".join([expr] + gens + [domain])
        if cls in accepted_latex_functions:
            tex = r"\%s {\left (%s \right )}" % (cls, args)
        else:
            tex = r"\operatorname{%s}{\left( %s \right)}" % (cls, args)

        return tex

    def _print_RootOf(self, root):
        cls = root.__class__.__name__
        expr = self._print(root.expr)
        index = root.index
        if cls in accepted_latex_functions:
            return r"\%s {\left(%s, %d\right)}" % (cls, expr, index)
        else:
            return r"\operatorname{%s} {\left(%s, %d\right)}" % (cls, expr, index)

    def _print_RootSum(self, expr):
        cls = expr.__class__.__name__
        args = [self._print(expr.expr)]

        if expr.fun is not S.IdentityFunction:
            args.append(self._print(expr.fun))

        if cls in accepted_latex_functions:
            return r"\%s {\left(%s\right)}" % (cls, ", ".join(args))
        else:
            return r"\operatorname{%s} {\left(%s\right)}" % (cls, ", ".join(args))

    def _print_PolyElement(self, poly):
        mul_symbol = self._settings['mul_symbol_latex']
        return poly.str(self, PRECEDENCE, "{%s}^{%d}", mul_symbol)

    def _print_FracElement(self, frac):
        if frac.denom == 1:
            return self._print(frac.numer)
        else:
            numer = self._print(frac.numer)
            denom = self._print(frac.denom)
            return r"\frac{%s}{%s}" % (numer, denom)

    def _print_euler(self, expr):
        return r"E_{%s}" % self._print(expr.args[0])

    def _print_catalan(self, expr):
        return r"C_{%s}" % self._print(expr.args[0])

    def _print_MellinTransform(self, expr):
        return r"\mathcal{M}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_InverseMellinTransform(self, expr):
        return r"\mathcal{M}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_LaplaceTransform(self, expr):
        return r"\mathcal{L}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_InverseLaplaceTransform(self, expr):
        return r"\mathcal{L}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_FourierTransform(self, expr):
        return r"\mathcal{F}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_InverseFourierTransform(self, expr):
        return r"\mathcal{F}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_SineTransform(self, expr):
        return r"\mathcal{SIN}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_InverseSineTransform(self, expr):
        return r"\mathcal{SIN}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_CosineTransform(self, expr):
        return r"\mathcal{COS}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_InverseCosineTransform(self, expr):
        return r"\mathcal{COS}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))

    def _print_DMP(self, p):
        try:
            if p.ring is not None:
                # TODO incorporate order
                return self._print(p.ring.to_sympy(p))
        except SympifyError:
            pass
        return self._print(repr(p))

    def _print_DMF(self, p):
        return self._print_DMP(p)

    def _print_Object(self, object):
        return self._print(Symbol(object.name))

    def _print_Morphism(self, morphism):
        domain = self._print(morphism.domain)
        codomain = self._print(morphism.codomain)
        return "%s\\rightarrow %s" % (domain, codomain)

    def _print_NamedMorphism(self, morphism):
        pretty_name = self._print(Symbol(morphism.name))
        pretty_morphism = self._print_Morphism(morphism)
        return "%s:%s" % (pretty_name, pretty_morphism)

    def _print_IdentityMorphism(self, morphism):
        from sympy.categories import NamedMorphism
        return self._print_NamedMorphism(NamedMorphism(
            morphism.domain, morphism.codomain, "id"))

    def _print_CompositeMorphism(self, morphism):
        # All components of the morphism have names and it is thus
        # possible to build the name of the composite.
        component_names_list = [self._print(Symbol(component.name)) for
                                component in morphism.components]
        component_names_list.reverse()
        component_names = "\\circ ".join(component_names_list) + ":"

        pretty_morphism = self._print_Morphism(morphism)
        return component_names + pretty_morphism

    def _print_Category(self, morphism):
        return "\\mathbf{%s}" % self._print(Symbol(morphism.name))

    def _print_Diagram(self, diagram):
        if not diagram.premises:
            # This is an empty diagram.
            return self._print(S.EmptySet)

        latex_result = self._print(diagram.premises)
        if diagram.conclusions:
            latex_result += "\\Longrightarrow %s" % \
                            self._print(diagram.conclusions)

        return latex_result

    def _print_DiagramGrid(self, grid):
        latex_result = "\\begin{array}{%s}\n" % ("c" * grid.width)

        for i in xrange(grid.height):
            for j in xrange(grid.width):
                if grid[i, j]:
                    latex_result += latex(grid[i, j])
                latex_result += " "
                if j != grid.width - 1:
                    latex_result += "& "

            if i != grid.height - 1:
                latex_result += "\\\\"
            latex_result += "\n"

        latex_result += "\\end{array}\n"
        return latex_result

    def _print_FreeModule(self, M):
        return '{%s}^{%s}' % (self._print(M.ring), self._print(M.rank))

    def _print_FreeModuleElement(self, m):
        # Print as row vector for convenience, for now.
        return r"\left[ %s \right]" % ",".join(
            '{' + self._print(x) + '}' for x in m)

    def _print_SubModule(self, m):
        return r"\left< %s \right>" % ",".join(
            '{' + self._print(x) + '}' for x in m.gens)

    def _print_ModuleImplementedIdeal(self, m):
        return r"\left< %s \right>" % ",".join(
            '{' + self._print(x) + '}' for [x] in m._module.gens)

    def _print_QuotientRing(self, R):
        # TODO nicer fractions for few generators...
        return r"\frac{%s}{%s}" % (self._print(R.ring), self._print(R.base_ideal))

    def _print_QuotientRingElement(self, x):
        return r"{%s} + {%s}" % (self._print(x.data), self._print(x.ring.base_ideal))

    def _print_QuotientModuleElement(self, m):
        return r"{%s} + {%s}" % (self._print(m.data),
                                 self._print(m.module.killed_module))

    def _print_QuotientModule(self, M):
        # TODO nicer fractions for few generators...
        return r"\frac{%s}{%s}" % (self._print(M.base),
                                   self._print(M.killed_module))

    def _print_MatrixHomomorphism(self, h):
        return r"{%s} : {%s} \to {%s}" % (self._print(h._sympy_matrix()),
            self._print(h.domain), self._print(h.codomain))

    def _print_BaseScalarField(self, field):
        string = field._coord_sys._names[field._index]
        return r'\boldsymbol{\mathrm{%s}}' % self._print(Symbol(string))

    def _print_BaseVectorField(self, field):
        string = field._coord_sys._names[field._index]
        return r'\partial_{%s}' % self._print(Symbol(string))

    def _print_Differential(self, diff):
        field = diff._form_field
        if hasattr(field, '_coord_sys'):
            string = field._coord_sys._names[field._index]
            return r'\mathrm{d}%s' % self._print(Symbol(string))
        else:
            return 'd(%s)' % self._print(field)
            string = self._print(field)
            return r'\mathrm{d}\left(%s\right)' % string

    def _print_Tr(self, p):
        #Todo: Handle indices
        contents = self._print(p.args[0])
        return r'\mbox{Tr}\left(%s\right)' % (contents)

    def _print_totient(self, expr):
        return r'\phi\left( %s \right)' %  self._print(expr.args[0])

    def _print_divisor_sigma(self, expr, exp=None):
        if len(expr.args) == 2:
            tex = r"_%s\left(%s\right)" % tuple(map(self._print,
                                                (expr.args[1], expr.args[0])))
        else:
            tex = r"\left(%s\right)" % self._print(expr.args[0])
        if exp is not None:
            return r"\sigma^{%s}%s" % (self._print(exp), tex)
        return r"\sigma%s" % tex


def translate(s):
    r'''
    Check for a modifier ending the string.  If present, convert the
    modifier to latex and translate the rest recursively.

    Given a description of a Greek letter or other special character,
    return the appropriate latex.

    Let everything else pass as given.

    >>> from sympy.printing.latex import translate
    >>> translate('alphahatdotprime')
    "{\\dot{\\hat{\\alpha}}}'"
    '''
    # Process the rest
    tex = tex_greek_dictionary.get(s)
    if tex:
        return tex
    elif s.lower() in greek_letters_set or s in other_symbols:
        return "\\" + s
    else:
        # Process modifiers, if any, and recurse
        for key in sorted(modifier_dict.keys(), key=lambda k:len(k), reverse=True):
            if s.lower().endswith(key) and len(s)>len(key):
                return modifier_dict[key](translate(s[:-len(key)]))
        return s

def latex(expr, **settings):
    r"""
    Convert the given expression to LaTeX representation.

    >>> from sympy import latex, pi, sin, asin, Integral, Matrix, Rational
    >>> from sympy.abc import x, y, mu, r, tau

    >>> print(latex((2*tau)**Rational(7,2)))
    8 \sqrt{2} \tau^{\frac{7}{2}}

    order: Any of the supported monomial orderings (currently "lex", "grlex", or
    "grevlex"), "old", and "none". This parameter does nothing for Mul objects.
    Setting order to "old" uses the compatibility ordering for Add defined in
    Printer. For very large expressions, set the 'order' keyword to 'none' if
    speed is a concern.

    mode: Specifies how the generated code will be delimited. 'mode' can be one
    of 'plain', 'inline', 'equation' or 'equation*'.  If 'mode' is set to
    'plain', then the resulting code will not be delimited at all (this is the
    default). If 'mode' is set to 'inline' then inline LaTeX $ $ will be used.
    If 'mode' is set to 'equation' or 'equation*', the resulting code will be
    enclosed in the 'equation' or 'equation*' environment (remember to import
    'amsmath' for 'equation*'), unless the 'itex' option is set. In the latter
    case, the ``$$ $$`` syntax is used.

    >>> print(latex((2*mu)**Rational(7,2), mode='plain'))
    8 \sqrt{2} \mu^{\frac{7}{2}}

    >>> print(latex((2*tau)**Rational(7,2), mode='inline'))
    $8 \sqrt{2} \tau^{\frac{7}{2}}$

    >>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
    \begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}

    >>> print(latex((2*mu)**Rational(7,2), mode='equation'))
    \begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}

    itex: Specifies if itex-specific syntax is used, including emitting ``$$ $$``.

    >>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
    $$8 \sqrt{2} \mu^{\frac{7}{2}}$$

    fold_frac_powers: Emit "^{p/q}" instead of "^{\frac{p}{q}}" for fractional
    powers.

    >>> print(latex((2*tau)**Rational(7,2), fold_frac_powers=True))
    8 \sqrt{2} \tau^{7/2}

    fold_func_brackets: Fold function brackets where applicable.

    >>> print(latex((2*tau)**sin(Rational(7,2))))
    \left(2 \tau\right)^{\sin{\left (\frac{7}{2} \right )}}
    >>> print(latex((2*tau)**sin(Rational(7,2)), fold_func_brackets = True))
    \left(2 \tau\right)^{\sin {\frac{7}{2}}}

    fold_short_frac: Emit "p / q" instead of "\frac{p}{q}" when the
    denominator is simple enough (at most two terms and no powers).
    The default value is `True` for inline mode, False otherwise.

    >>> print(latex(3*x**2/y))
    \frac{3 x^{2}}{y}
    >>> print(latex(3*x**2/y, fold_short_frac=True))
    3 x^{2} / y

    long_frac_ratio: The allowed ratio of the width of the numerator to the
    width of the denominator before we start breaking off long fractions.
    The default value is 2.

    >>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=2))
    \frac{\int r\, dr}{2 \pi}
    >>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=0))
    \frac{1}{2 \pi} \int r\, dr

    mul_symbol: The symbol to use for multiplication. Can be one of None,
    "ldot", "dot", or "times".

    >>> print(latex((2*tau)**sin(Rational(7,2)), mul_symbol="times"))
    \left(2 \times \tau\right)^{\sin{\left (\frac{7}{2} \right )}}

    inv_trig_style: How inverse trig functions should be displayed. Can be one
    of "abbreviated", "full", or "power". Defaults to "abbreviated".

    >>> print(latex(asin(Rational(7,2))))
    \operatorname{asin}{\left (\frac{7}{2} \right )}
    >>> print(latex(asin(Rational(7,2)), inv_trig_style="full"))
    \arcsin{\left (\frac{7}{2} \right )}
    >>> print(latex(asin(Rational(7,2)), inv_trig_style="power"))
    \sin^{-1}{\left (\frac{7}{2} \right )}

    mat_str: Which matrix environment string to emit. "smallmatrix", "matrix",
    "array", etc. Defaults to "smallmatrix" for inline mode, "matrix" for
    matrices of no more than 10 columns, and "array" otherwise.

    >>> print(latex(Matrix(2, 1, [x, y])))
    \left[\begin{matrix}x\\y\end{matrix}\right]

    >>> print(latex(Matrix(2, 1, [x, y]), mat_str = "array"))
    \left[\begin{array}{c}x\\y\end{array}\right]

    mat_delim: The delimiter to wrap around matrices. Can be one of "[", "(",
    or the empty string. Defaults to "[".

    >>> print(latex(Matrix(2, 1, [x, y]), mat_delim="("))
    \left(\begin{matrix}x\\y\end{matrix}\right)

    symbol_names: Dictionary of symbols and the custom strings they should be
    emitted as.

    >>> print(latex(x**2, symbol_names={x:'x_i'}))
    x_i^{2}

    ``latex`` also supports the builtin container types list, tuple, and
    dictionary.

    >>> print(latex([2/x, y], mode='inline'))
    $\left [ 2 / x, \quad y\right ]$

    """

    return LatexPrinter(settings).doprint(expr)


def print_latex(expr, **settings):
    """Prints LaTeX representation of the given expression."""
    print(latex(expr, **settings))
