Vehicle-cpp/hkpc/software/sympy/printing/str.py

"""
A Printer for generating readable representation of most SymPy classes.
"""

from __future__ import annotations
from typing import Any

from sympy.core import S, Rational, Pow, Basic, Mul, Number
from sympy.core.mul import _keep_coeff
from sympy.core.relational import Relational
from sympy.core.sorting import default_sort_key
from sympy.core.sympify import SympifyError
from sympy.utilities.iterables import sift
from .precedence import precedence, PRECEDENCE
from .printer import Printer, print_function

from mpmath.libmp import prec_to_dps, to_str as mlib_to_str


class StrPrinter(Printer):
    printmethod = "_sympystr"
    _default_settings: dict[str, Any] = {
        "order": None,
        "full_prec": "auto",
        "sympy_integers": False,
        "abbrev": False,
        "perm_cyclic": True,
        "min": None,
        "max": None,
    }

    _relationals: dict[str, str] = {}

    def parenthesize(self, item, level, strict=False):
        if (precedence(item) < level) or ((not strict) and precedence(item) <= level):
            return "(%s)" % self._print(item)
        else:
            return self._print(item)

    def stringify(self, args, sep, level=0):
        return sep.join([self.parenthesize(item, level) for item in args])

    def emptyPrinter(self, expr):
        if isinstance(expr, str):
            return expr
        elif isinstance(expr, Basic):
            return repr(expr)
        else:
            return str(expr)

    def _print_Add(self, expr, order=None):
        terms = self._as_ordered_terms(expr, order=order)

        prec = precedence(expr)
        l = []
        for term in terms:
            t = self._print(term)
            if t.startswith('-') and not term.is_Add:
                sign = "-"
                t = t[1:]
            else:
                sign = "+"
            if precedence(term) < prec or term.is_Add:
                l.extend([sign, "(%s)" % t])
            else:
                l.extend([sign, t])
        sign = l.pop(0)
        if sign == '+':
            sign = ""
        return sign + ' '.join(l)

    def _print_BooleanTrue(self, expr):
        return "True"

    def _print_BooleanFalse(self, expr):
        return "False"

    def _print_Not(self, expr):
        return '~%s' %(self.parenthesize(expr.args[0],PRECEDENCE["Not"]))

    def _print_And(self, expr):
        args = list(expr.args)
        for j, i in enumerate(args):
            if isinstance(i, Relational) and (
                    i.canonical.rhs is S.NegativeInfinity):
                args.insert(0, args.pop(j))
        return self.stringify(args, " & ", PRECEDENCE["BitwiseAnd"])

    def _print_Or(self, expr):
        return self.stringify(expr.args, " | ", PRECEDENCE["BitwiseOr"])

    def _print_Xor(self, expr):
        return self.stringify(expr.args, " ^ ", PRECEDENCE["BitwiseXor"])

    def _print_AppliedPredicate(self, expr):
        return '%s(%s)' % (
            self._print(expr.function), self.stringify(expr.arguments, ", "))

    def _print_Basic(self, expr):
        l = [self._print(o) for o in expr.args]
        return expr.__class__.__name__ + "(%s)" % ", ".join(l)

    def _print_BlockMatrix(self, B):
        if B.blocks.shape == (1, 1):
            self._print(B.blocks[0, 0])
        return self._print(B.blocks)

    def _print_Catalan(self, expr):
        return 'Catalan'

    def _print_ComplexInfinity(self, expr):
        return 'zoo'

    def _print_ConditionSet(self, s):
        args = tuple([self._print(i) for i in (s.sym, s.condition)])
        if s.base_set is S.UniversalSet:
            return 'ConditionSet(%s, %s)' % args
        args += (self._print(s.base_set),)
        return 'ConditionSet(%s, %s, %s)' % args

    def _print_Derivative(self, expr):
        dexpr = expr.expr
        dvars = [i[0] if i[1] == 1 else i for i in expr.variable_count]
        return 'Derivative(%s)' % ", ".join((self._print(arg) for arg in [dexpr] + dvars))

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

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

        return "{%s}" % ", ".join(items)

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

    def _print_RandomDomain(self, d):
        if hasattr(d, 'as_boolean'):
            return 'Domain: ' + self._print(d.as_boolean())
        elif hasattr(d, 'set'):
            return ('Domain: ' + self._print(d.symbols) + ' in ' +
                    self._print(d.set))
        else:
            return 'Domain on ' + self._print(d.symbols)

    def _print_Dummy(self, expr):
        return '_' + expr.name

    def _print_EulerGamma(self, expr):
        return 'EulerGamma'

    def _print_Exp1(self, expr):
        return 'E'

    def _print_ExprCondPair(self, expr):
        return '(%s, %s)' % (self._print(expr.expr), self._print(expr.cond))

    def _print_Function(self, expr):
        return expr.func.__name__ + "(%s)" % self.stringify(expr.args, ", ")

    def _print_GoldenRatio(self, expr):
        return 'GoldenRatio'

    def _print_Heaviside(self, expr):
        # Same as _print_Function but uses pargs to suppress default 1/2 for
        # 2nd args
        return expr.func.__name__ + "(%s)" % self.stringify(expr.pargs, ", ")

    def _print_TribonacciConstant(self, expr):
        return 'TribonacciConstant'

    def _print_ImaginaryUnit(self, expr):
        return 'I'

    def _print_Infinity(self, expr):
        return 'oo'

    def _print_Integral(self, expr):
        def _xab_tostr(xab):
            if len(xab) == 1:
                return self._print(xab[0])
            else:
                return self._print((xab[0],) + tuple(xab[1:]))
        L = ', '.join([_xab_tostr(l) for l in expr.limits])
        return 'Integral(%s, %s)' % (self._print(expr.function), L)

    def _print_Interval(self, i):
        fin =  'Interval{m}({a}, {b})'
        a, b, l, r = i.args
        if a.is_infinite and b.is_infinite:
            m = ''
        elif a.is_infinite and not r:
            m = ''
        elif b.is_infinite and not l:
            m = ''
        elif not l and not r:
            m = ''
        elif l and r:
            m = '.open'
        elif l:
            m = '.Lopen'
        else:
            m = '.Ropen'
        return fin.format(**{'a': a, 'b': b, 'm': m})

    def _print_AccumulationBounds(self, i):
        return "AccumBounds(%s, %s)" % (self._print(i.min),
                                        self._print(i.max))

    def _print_Inverse(self, I):
        return "%s**(-1)" % self.parenthesize(I.arg, PRECEDENCE["Pow"])

    def _print_Lambda(self, obj):
        expr = obj.expr
        sig = obj.signature
        if len(sig) == 1 and sig[0].is_symbol:
            sig = sig[0]
        return "Lambda(%s, %s)" % (self._print(sig), self._print(expr))

    def _print_LatticeOp(self, expr):
        args = sorted(expr.args, key=default_sort_key)
        return expr.func.__name__ + "(%s)" % ", ".join(self._print(arg) for arg in args)

    def _print_Limit(self, expr):
        e, z, z0, dir = expr.args
        return "Limit(%s, %s, %s, dir='%s')" % tuple(map(self._print, (e, z, z0, dir)))


    def _print_list(self, expr):
        return "[%s]" % self.stringify(expr, ", ")

    def _print_List(self, expr):
        return self._print_list(expr)

    def _print_MatrixBase(self, expr):
        return expr._format_str(self)

    def _print_MatrixElement(self, expr):
        return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) \
            + '[%s, %s]' % (self._print(expr.i), self._print(expr.j))

    def _print_MatrixSlice(self, expr):
        def strslice(x, dim):
            x = list(x)
            if x[2] == 1:
                del x[2]
            if x[0] == 0:
                x[0] = ''
            if x[1] == dim:
                x[1] = ''
            return ':'.join((self._print(arg) for arg in x))
        return (self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) + '[' +
                strslice(expr.rowslice, expr.parent.rows) + ', ' +
                strslice(expr.colslice, expr.parent.cols) + ']')

    def _print_DeferredVector(self, expr):
        return expr.name

    def _print_Mul(self, expr):

        prec = precedence(expr)

        # Check for unevaluated Mul. In this case we need to make sure the
        # identities are visible, multiple Rational factors are not combined
        # etc so we display in a straight-forward form that fully preserves all
        # args and their order.
        args = expr.args
        if args[0] is S.One or any(
                isinstance(a, Number) or
                a.is_Pow and all(ai.is_Integer for ai in a.args)
                for a in args[1:]):
            d, n = sift(args, lambda x:
                isinstance(x, Pow) and bool(x.exp.as_coeff_Mul()[0] < 0),
                binary=True)
            for i, di in enumerate(d):
                if di.exp.is_Number:
                    e = -di.exp
                else:
                    dargs = list(di.exp.args)
                    dargs[0] = -dargs[0]
                    e = Mul._from_args(dargs)
                d[i] = Pow(di.base, e, evaluate=False) if e - 1 else di.base

            pre = []
            # don't parenthesize first factor if negative
            if n and not n[0].is_Add and n[0].could_extract_minus_sign():
                pre = [self._print(n.pop(0))]

            nfactors = pre + [self.parenthesize(a, prec, strict=False)
                for a in n]
            if not nfactors:
                nfactors = ['1']

            # don't parenthesize first of denominator unless singleton
            if len(d) > 1 and d[0].could_extract_minus_sign():
                pre = [self._print(d.pop(0))]
            else:
                pre = []
            dfactors = pre + [self.parenthesize(a, prec, strict=False)
                for a in d]

            n = '*'.join(nfactors)
            d = '*'.join(dfactors)
            if len(dfactors) > 1:
                return '%s/(%s)' % (n, d)
            elif dfactors:
                return '%s/%s' % (n, d)
            return n

        c, e = expr.as_coeff_Mul()
        if c < 0:
            expr = _keep_coeff(-c, e)
            sign = "-"
        else:
            sign = ""

        a = []  # items in the numerator
        b = []  # items that are in the denominator (if any)

        pow_paren = []  # Will collect all pow with more than one base element and exp = -1

        if self.order not in ('old', 'none'):
            args = expr.as_ordered_factors()
        else:
            # use make_args in case expr was something like -x -> x
            args = Mul.make_args(expr)

        # Gather args for numerator/denominator
        def apow(i):
            b, e = i.as_base_exp()
            eargs = list(Mul.make_args(e))
            if eargs[0] is S.NegativeOne:
                eargs = eargs[1:]
            else:
                eargs[0] = -eargs[0]
            e = Mul._from_args(eargs)
            if isinstance(i, Pow):
                return i.func(b, e, evaluate=False)
            return i.func(e, evaluate=False)
        for item in args:
            if (item.is_commutative and
                    isinstance(item, Pow) and
                    bool(item.exp.as_coeff_Mul()[0] < 0)):
                if item.exp is not S.NegativeOne:
                    b.append(apow(item))
                else:
                    if (len(item.args[0].args) != 1 and
                            isinstance(item.base, (Mul, Pow))):
                        # To avoid situations like #14160
                        pow_paren.append(item)
                    b.append(item.base)
            elif item.is_Rational and item is not S.Infinity:
                if item.p != 1:
                    a.append(Rational(item.p))
                if item.q != 1:
                    b.append(Rational(item.q))
            else:
                a.append(item)

        a = a or [S.One]

        a_str = [self.parenthesize(x, prec, strict=False) for x in a]
        b_str = [self.parenthesize(x, prec, strict=False) for x in b]

        # To parenthesize Pow with exp = -1 and having more than one Symbol
        for item in pow_paren:
            if item.base in b:
                b_str[b.index(item.base)] = "(%s)" % b_str[b.index(item.base)]

        if not b:
            return sign + '*'.join(a_str)
        elif len(b) == 1:
            return sign + '*'.join(a_str) + "/" + b_str[0]
        else:
            return sign + '*'.join(a_str) + "/(%s)" % '*'.join(b_str)

    def _print_MatMul(self, expr):
        c, m = expr.as_coeff_mmul()

        sign = ""
        if c.is_number:
            re, im = c.as_real_imag()
            if im.is_zero and re.is_negative:
                expr = _keep_coeff(-c, m)
                sign = "-"
            elif re.is_zero and im.is_negative:
                expr = _keep_coeff(-c, m)
                sign = "-"

        return sign + '*'.join(
            [self.parenthesize(arg, precedence(expr)) for arg in expr.args]
        )

    def _print_ElementwiseApplyFunction(self, expr):
        return "{}.({})".format(
            expr.function,
            self._print(expr.expr),
        )

    def _print_NaN(self, expr):
        return 'nan'

    def _print_NegativeInfinity(self, expr):
        return '-oo'

    def _print_Order(self, expr):
        if not expr.variables or all(p is S.Zero for p in expr.point):
            if len(expr.variables) <= 1:
                return 'O(%s)' % self._print(expr.expr)
            else:
                return 'O(%s)' % self.stringify((expr.expr,) + expr.variables, ', ', 0)
        else:
            return 'O(%s)' % self.stringify(expr.args, ', ', 0)

    def _print_Ordinal(self, expr):
        return expr.__str__()

    def _print_Cycle(self, expr):
        return expr.__str__()

    def _print_Permutation(self, expr):
        from sympy.combinatorics.permutations import Permutation, Cycle
        from sympy.utilities.exceptions import sympy_deprecation_warning

        perm_cyclic = Permutation.print_cyclic
        if perm_cyclic is not None:
            sympy_deprecation_warning(
                f"""
                Setting Permutation.print_cyclic is deprecated. Instead use
                init_printing(perm_cyclic={perm_cyclic}).
                """,
                deprecated_since_version="1.6",
                active_deprecations_target="deprecated-permutation-print_cyclic",
                stacklevel=7,
            )
        else:
            perm_cyclic = self._settings.get("perm_cyclic", True)

        if perm_cyclic:
            if not expr.size:
                return '()'
            # before taking Cycle notation, see if the last element is
            # a singleton and move it to the head of the string
            s = Cycle(expr)(expr.size - 1).__repr__()[len('Cycle'):]
            last = s.rfind('(')
            if not last == 0 and ',' not in s[last:]:
                s = s[last:] + s[:last]
            s = s.replace(',', '')
            return s
        else:
            s = expr.support()
            if not s:
                if expr.size < 5:
                    return 'Permutation(%s)' % self._print(expr.array_form)
                return 'Permutation([], size=%s)' % self._print(expr.size)
            trim = self._print(expr.array_form[:s[-1] + 1]) + ', size=%s' % self._print(expr.size)
            use = full = self._print(expr.array_form)
            if len(trim) < len(full):
                use = trim
            return 'Permutation(%s)' % use

    def _print_Subs(self, obj):
        expr, old, new = obj.args
        if len(obj.point) == 1:
            old = old[0]
            new = new[0]
        return "Subs(%s, %s, %s)" % (
            self._print(expr), self._print(old), self._print(new))

    def _print_TensorIndex(self, expr):
        return expr._print()

    def _print_TensorHead(self, expr):
        return expr._print()

    def _print_Tensor(self, expr):
        return expr._print()

    def _print_TensMul(self, expr):
        # prints expressions like "A(a)", "3*A(a)", "(1+x)*A(a)"
        sign, args = expr._get_args_for_traditional_printer()
        return sign + "*".join(
            [self.parenthesize(arg, precedence(expr)) for arg in args]
        )

    def _print_TensAdd(self, expr):
        return expr._print()

    def _print_ArraySymbol(self, expr):
        return self._print(expr.name)

    def _print_ArrayElement(self, expr):
        return "%s[%s]" % (
            self.parenthesize(expr.name, PRECEDENCE["Func"], True), ", ".join([self._print(i) for i in expr.indices]))

    def _print_PermutationGroup(self, expr):
        p = ['    %s' % self._print(a) for a in expr.args]
        return 'PermutationGroup([\n%s])' % ',\n'.join(p)

    def _print_Pi(self, expr):
        return 'pi'

    def _print_PolyRing(self, ring):
        return "Polynomial ring in %s over %s with %s order" % \
            (", ".join((self._print(rs) for rs in ring.symbols)),
            self._print(ring.domain), self._print(ring.order))

    def _print_FracField(self, field):
        return "Rational function field in %s over %s with %s order" % \
            (", ".join((self._print(fs) for fs in field.symbols)),
            self._print(field.domain), self._print(field.order))

    def _print_FreeGroupElement(self, elm):
        return elm.__str__()

    def _print_GaussianElement(self, poly):
        return "(%s + %s*I)" % (poly.x, poly.y)

    def _print_PolyElement(self, poly):
        return poly.str(self, PRECEDENCE, "%s**%s", "*")

    def _print_FracElement(self, frac):
        if frac.denom == 1:
            return self._print(frac.numer)
        else:
            numer = self.parenthesize(frac.numer, PRECEDENCE["Mul"], strict=True)
            denom = self.parenthesize(frac.denom, PRECEDENCE["Atom"], strict=True)
            return numer + "/" + denom

    def _print_Poly(self, expr):
        ATOM_PREC = PRECEDENCE["Atom"] - 1
        terms, gens = [], [ self.parenthesize(s, ATOM_PREC) for s in expr.gens ]

        for monom, coeff in expr.terms():
            s_monom = []

            for i, e in enumerate(monom):
                if e > 0:
                    if e == 1:
                        s_monom.append(gens[i])
                    else:
                        s_monom.append(gens[i] + "**%d" % e)

            s_monom = "*".join(s_monom)

            if coeff.is_Add:
                if s_monom:
                    s_coeff = "(" + self._print(coeff) + ")"
                else:
                    s_coeff = self._print(coeff)
            else:
                if s_monom:
                    if coeff is S.One:
                        terms.extend(['+', s_monom])
                        continue

                    if coeff is S.NegativeOne:
                        terms.extend(['-', s_monom])
                        continue

                s_coeff = self._print(coeff)

            if not s_monom:
                s_term = s_coeff
            else:
                s_term = s_coeff + "*" + s_monom

            if s_term.startswith('-'):
                terms.extend(['-', s_term[1:]])
            else:
                terms.extend(['+', s_term])

        if terms[0] in ('-', '+'):
            modifier = terms.pop(0)

            if modifier == '-':
                terms[0] = '-' + terms[0]

        format = expr.__class__.__name__ + "(%s, %s"

        from sympy.polys.polyerrors import PolynomialError

        try:
            format += ", modulus=%s" % expr.get_modulus()
        except PolynomialError:
            format += ", domain='%s'" % expr.get_domain()

        format += ")"

        for index, item in enumerate(gens):
            if len(item) > 2 and (item[:1] == "(" and item[len(item) - 1:] == ")"):
                gens[index] = item[1:len(item) - 1]

        return format % (' '.join(terms), ', '.join(gens))

    def _print_UniversalSet(self, p):
        return 'UniversalSet'

    def _print_AlgebraicNumber(self, expr):
        if expr.is_aliased:
            return self._print(expr.as_poly().as_expr())
        else:
            return self._print(expr.as_expr())

    def _print_Pow(self, expr, rational=False):
        """Printing helper function for ``Pow``

        Parameters
        ==========

        rational : bool, optional
            If ``True``, it will not attempt printing ``sqrt(x)`` or
            ``x**S.Half`` as ``sqrt``, and will use ``x**(1/2)``
            instead.

            See examples for additional details

        Examples
        ========

        >>> from sympy import sqrt, StrPrinter
        >>> from sympy.abc import x

        How ``rational`` keyword works with ``sqrt``:

        >>> printer = StrPrinter()
        >>> printer._print_Pow(sqrt(x), rational=True)
        'x**(1/2)'
        >>> printer._print_Pow(sqrt(x), rational=False)
        'sqrt(x)'
        >>> printer._print_Pow(1/sqrt(x), rational=True)
        'x**(-1/2)'
        >>> printer._print_Pow(1/sqrt(x), rational=False)
        '1/sqrt(x)'

        Notes
        =====

        ``sqrt(x)`` is canonicalized as ``Pow(x, S.Half)`` in SymPy,
        so there is no need of defining a separate printer for ``sqrt``.
        Instead, it should be handled here as well.
        """
        PREC = precedence(expr)

        if expr.exp is S.Half and not rational:
            return "sqrt(%s)" % self._print(expr.base)

        if expr.is_commutative:
            if -expr.exp is S.Half and not rational:
                # Note: Don't test "expr.exp == -S.Half" here, because that will
                # match -0.5, which we don't want.
                return "%s/sqrt(%s)" % tuple((self._print(arg) for arg in (S.One, expr.base)))
            if expr.exp is -S.One:
                # Similarly to the S.Half case, don't test with "==" here.
                return '%s/%s' % (self._print(S.One),
                                  self.parenthesize(expr.base, PREC, strict=False))

        e = self.parenthesize(expr.exp, PREC, strict=False)
        if self.printmethod == '_sympyrepr' and expr.exp.is_Rational and expr.exp.q != 1:
            # the parenthesized exp should be '(Rational(a, b))' so strip parens,
            # but just check to be sure.
            if e.startswith('(Rational'):
                return '%s**%s' % (self.parenthesize(expr.base, PREC, strict=False), e[1:-1])
        return '%s**%s' % (self.parenthesize(expr.base, PREC, strict=False), e)

    def _print_UnevaluatedExpr(self, expr):
        return self._print(expr.args[0])

    def _print_MatPow(self, expr):
        PREC = precedence(expr)
        return '%s**%s' % (self.parenthesize(expr.base, PREC, strict=False),
                         self.parenthesize(expr.exp, PREC, strict=False))

    def _print_Integer(self, expr):
        if self._settings.get("sympy_integers", False):
            return "S(%s)" % (expr)
        return str(expr.p)

    def _print_Integers(self, expr):
        return 'Integers'

    def _print_Naturals(self, expr):
        return 'Naturals'

    def _print_Naturals0(self, expr):
        return 'Naturals0'

    def _print_Rationals(self, expr):
        return 'Rationals'

    def _print_Reals(self, expr):
        return 'Reals'

    def _print_Complexes(self, expr):
        return 'Complexes'

    def _print_EmptySet(self, expr):
        return 'EmptySet'

    def _print_EmptySequence(self, expr):
        return 'EmptySequence'

    def _print_int(self, expr):
        return str(expr)

    def _print_mpz(self, expr):
        return str(expr)

    def _print_Rational(self, expr):
        if expr.q == 1:
            return str(expr.p)
        else:
            if self._settings.get("sympy_integers", False):
                return "S(%s)/%s" % (expr.p, expr.q)
            return "%s/%s" % (expr.p, expr.q)

    def _print_PythonRational(self, expr):
        if expr.q == 1:
            return str(expr.p)
        else:
            return "%d/%d" % (expr.p, expr.q)

    def _print_Fraction(self, expr):
        if expr.denominator == 1:
            return str(expr.numerator)
        else:
            return "%s/%s" % (expr.numerator, expr.denominator)

    def _print_mpq(self, expr):
        if expr.denominator == 1:
            return str(expr.numerator)
        else:
            return "%s/%s" % (expr.numerator, expr.denominator)

    def _print_Float(self, expr):
        prec = expr._prec
        if prec < 5:
            dps = 0
        else:
            dps = prec_to_dps(expr._prec)
        if self._settings["full_prec"] is True:
            strip = False
        elif self._settings["full_prec"] is False:
            strip = True
        elif self._settings["full_prec"] == "auto":
            strip = self._print_level > 1
        low = self._settings["min"] if "min" in self._settings else None
        high = self._settings["max"] if "max" in self._settings else None
        rv = mlib_to_str(expr._mpf_, dps, strip_zeros=strip, min_fixed=low, max_fixed=high)
        if rv.startswith('-.0'):
            rv = '-0.' + rv[3:]
        elif rv.startswith('.0'):
            rv = '0.' + rv[2:]
        if rv.startswith('+'):
            # e.g., +inf -> inf
            rv = rv[1:]
        return rv

    def _print_Relational(self, expr):

        charmap = {
            "==": "Eq",
            "!=": "Ne",
            ":=": "Assignment",
            '+=': "AddAugmentedAssignment",
            "-=": "SubAugmentedAssignment",
            "*=": "MulAugmentedAssignment",
            "/=": "DivAugmentedAssignment",
            "%=": "ModAugmentedAssignment",
        }

        if expr.rel_op in charmap:
            return '%s(%s, %s)' % (charmap[expr.rel_op], self._print(expr.lhs),
                                   self._print(expr.rhs))

        return '%s %s %s' % (self.parenthesize(expr.lhs, precedence(expr)),
                           self._relationals.get(expr.rel_op) or expr.rel_op,
                           self.parenthesize(expr.rhs, precedence(expr)))

    def _print_ComplexRootOf(self, expr):
        return "CRootOf(%s, %d)" % (self._print_Add(expr.expr,  order='lex'),
                                    expr.index)

    def _print_RootSum(self, expr):
        args = [self._print_Add(expr.expr, order='lex')]

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

        return "RootSum(%s)" % ", ".join(args)

    def _print_GroebnerBasis(self, basis):
        cls = basis.__class__.__name__

        exprs = [self._print_Add(arg, order=basis.order) for arg in basis.exprs]
        exprs = "[%s]" % ", ".join(exprs)

        gens = [ self._print(gen) for gen in basis.gens ]
        domain = "domain='%s'" % self._print(basis.domain)
        order = "order='%s'" % self._print(basis.order)

        args = [exprs] + gens + [domain, order]

        return "%s(%s)" % (cls, ", ".join(args))

    def _print_set(self, s):
        items = sorted(s, key=default_sort_key)

        args = ', '.join(self._print(item) for item in items)
        if not args:
            return "set()"
        return '{%s}' % args

    def _print_FiniteSet(self, s):
        from sympy.sets.sets import FiniteSet
        items = sorted(s, key=default_sort_key)

        args = ', '.join(self._print(item) for item in items)
        if any(item.has(FiniteSet) for item in items):
            return 'FiniteSet({})'.format(args)
        return '{{{}}}'.format(args)

    def _print_Partition(self, s):
        items = sorted(s, key=default_sort_key)

        args = ', '.join(self._print(arg) for arg in items)
        return 'Partition({})'.format(args)

    def _print_frozenset(self, s):
        if not s:
            return "frozenset()"
        return "frozenset(%s)" % self._print_set(s)

    def _print_Sum(self, expr):
        def _xab_tostr(xab):
            if len(xab) == 1:
                return self._print(xab[0])
            else:
                return self._print((xab[0],) + tuple(xab[1:]))
        L = ', '.join([_xab_tostr(l) for l in expr.limits])
        return 'Sum(%s, %s)' % (self._print(expr.function), L)

    def _print_Symbol(self, expr):
        return expr.name
    _print_MatrixSymbol = _print_Symbol
    _print_RandomSymbol = _print_Symbol

    def _print_Identity(self, expr):
        return "I"

    def _print_ZeroMatrix(self, expr):
        return "0"

    def _print_OneMatrix(self, expr):
        return "1"

    def _print_Predicate(self, expr):
        return "Q.%s" % expr.name

    def _print_str(self, expr):
        return str(expr)

    def _print_tuple(self, expr):
        if len(expr) == 1:
            return "(%s,)" % self._print(expr[0])
        else:
            return "(%s)" % self.stringify(expr, ", ")

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

    def _print_Transpose(self, T):
        return "%s.T" % self.parenthesize(T.arg, PRECEDENCE["Pow"])

    def _print_Uniform(self, expr):
        return "Uniform(%s, %s)" % (self._print(expr.a), self._print(expr.b))

    def _print_Quantity(self, expr):
        if self._settings.get("abbrev", False):
            return "%s" % expr.abbrev
        return "%s" % expr.name

    def _print_Quaternion(self, expr):
        s = [self.parenthesize(i, PRECEDENCE["Mul"], strict=True) for i in expr.args]
        a = [s[0]] + [i+"*"+j for i, j in zip(s[1:], "ijk")]
        return " + ".join(a)

    def _print_Dimension(self, expr):
        return str(expr)

    def _print_Wild(self, expr):
        return expr.name + '_'

    def _print_WildFunction(self, expr):
        return expr.name + '_'

    def _print_WildDot(self, expr):
        return expr.name

    def _print_WildPlus(self, expr):
        return expr.name

    def _print_WildStar(self, expr):
        return expr.name

    def _print_Zero(self, expr):
        if self._settings.get("sympy_integers", False):
            return "S(0)"
        return "0"

    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

        cls = p.__class__.__name__
        rep = self._print(p.rep)
        dom = self._print(p.dom)
        ring = self._print(p.ring)

        return "%s(%s, %s, %s)" % (cls, rep, dom, ring)

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

    def _print_Object(self, obj):
        return 'Object("%s")' % obj.name

    def _print_IdentityMorphism(self, morphism):
        return 'IdentityMorphism(%s)' % morphism.domain

    def _print_NamedMorphism(self, morphism):
        return 'NamedMorphism(%s, %s, "%s")' % \
               (morphism.domain, morphism.codomain, morphism.name)

    def _print_Category(self, category):
        return 'Category("%s")' % category.name

    def _print_Manifold(self, manifold):
        return manifold.name.name

    def _print_Patch(self, patch):
        return patch.name.name

    def _print_CoordSystem(self, coords):
        return coords.name.name

    def _print_BaseScalarField(self, field):
        return field._coord_sys.symbols[field._index].name

    def _print_BaseVectorField(self, field):
        return 'e_%s' % field._coord_sys.symbols[field._index].name

    def _print_Differential(self, diff):
        field = diff._form_field
        if hasattr(field, '_coord_sys'):
            return 'd%s' % field._coord_sys.symbols[field._index].name
        else:
            return 'd(%s)' % self._print(field)

    def _print_Tr(self, expr):
        #TODO : Handle indices
        return "%s(%s)" % ("Tr", self._print(expr.args[0]))

    def _print_Str(self, s):
        return self._print(s.name)

    def _print_AppliedBinaryRelation(self, expr):
        rel = expr.function
        return '%s(%s, %s)' % (self._print(rel),
                               self._print(expr.lhs),
                               self._print(expr.rhs))


@print_function(StrPrinter)
def sstr(expr, **settings):
    """Returns the expression as a string.

    For large expressions where speed is a concern, use the setting
    order='none'. If abbrev=True setting is used then units are printed in
    abbreviated form.

    Examples
    ========

    >>> from sympy import symbols, Eq, sstr
    >>> a, b = symbols('a b')
    >>> sstr(Eq(a + b, 0))
    'Eq(a + b, 0)'
    """

    p = StrPrinter(settings)
    s = p.doprint(expr)

    return s


class StrReprPrinter(StrPrinter):
    """(internal) -- see sstrrepr"""

    def _print_str(self, s):
        return repr(s)

    def _print_Str(self, s):
        # Str does not to be printed same as str here
        return "%s(%s)" % (s.__class__.__name__, self._print(s.name))


@print_function(StrReprPrinter)
def sstrrepr(expr, **settings):
    """return expr in mixed str/repr form

       i.e. strings are returned in repr form with quotes, and everything else
       is returned in str form.

       This function could be useful for hooking into sys.displayhook
    """

    p = StrReprPrinter(settings)
    s = p.doprint(expr)

    return s