python-sympy 0.7.1.rc1-3 / usr / share / pyshared / sympy / printing / str.py

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

from sympy.core import S, Rational, Pow, Basic
from printer import Printer
from sympy.printing.precedence import precedence, PRECEDENCE

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

from sympy.polys.polyerrors import PolynomialError

from sympy.core.compatibility import cmp_to_key

class StrPrinter(Printer):
    printmethod = "_sympystr"
    _default_settings = {
        "order": None,
        "full_prec": "auto",
    }

    def parenthesize(self, item, level):
        if 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):
            if hasattr(expr, "args"):
                return repr(expr)
            else:
                raise
        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('-'):
                sign = "-"
                t = t[1:]
            else:
                sign = "+"
            if precedence(term) < PREC:
                l.extend([sign, "(%s)"%t])
            else:
                l.extend([sign, t])
        sign = l.pop(0)
        if sign=='+':
            sign = ""
        return sign + ' '.join(l)

    def _print_AppliedPredicate(self, expr):
        return '%s(%s)' % (expr.func, expr.arg)

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

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

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

    def _print_Derivative(self, expr):
        return 'Derivative(%s)'%", ".join(map(self._print, expr.args))

    def _print_dict(self, expr):
        keys = expr.keys()
        keys.sort( key=cmp_to_key(Basic.compare_pretty) )

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

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

    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)' % (expr.expr, expr.cond)

    def _print_factorial(self, expr):
        return "%s!" % self.parenthesize(expr.args[0], PRECEDENCE["Pow"])

    def _print_FiniteSet(self, s):
        if len(s) > 10:
            #take ten elements from the set at random
            q = iter(s)
            printset = [q.next() for i in xrange(10)]
        else:
            printset = s
        try:
            printset = sorted(printset)
        except:  pass
        return '{' + ', '.join(self._print(el) for el in printset) + '}'

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

    def _print_GeometryEntity(self, expr):
        # GeometryEntity is special -- it's base is tuple
        return str(expr)

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

    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_FiniteSet(self, s):
        if len(s) > 10:
            #take ten elements from the set at random
            q = iter(s)
            printset = [q.next() for i in xrange(10)]
        else:
            printset = s
        try:
            printset = sorted(printset)
        except:  pass
        return '{' + ', '.join(self._print(el) for el in printset) + '}'

    def _print_Interval(self, i):
        if i.left_open:
            left = '('
        else:
            left = '['

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

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

    def _print_Lambda(self, obj):
        args, expr = obj.args
        if len(args) == 1:
            return "Lambda(%s, %s)" % (args.args[0], expr)
        else:
            arg_string = ", ".join(self._print(arg) for arg in args)
            return "Lambda((%s), %s" % (arg_string, expr)

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

    def _print_Limit(self, expr):
        e, z, z0, dir = expr.args
        if dir == "+":
            return "Limit(%s, %s, %s)" % (e, z, z0)
        else:
            return "Limit(%s, %s, %s, dir='%s')" % (e, z, z0, dir)

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

    def _print_Matrix(self, expr):
        return expr._format_str(lambda elem: self._print(elem))

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

    def _print_Mul(self, expr):
        coeff, terms = expr.as_coeff_mul()
        if coeff.is_negative:
            coeff = -coeff
            if coeff is not S.One:
                terms = (coeff,) + terms
            sign = "-"
        else:
            terms = (coeff,) + terms
            sign = ""

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

        if self.order != 'old':
            args = expr._new_rawargs(*terms).as_ordered_factors()
        else:
            args = terms

        # Gather args for numerator/denominator
        for item in args:
            if item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
                b.append(Pow(item.base, -item.exp))
            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)

        if len(a)==0:
            a = [S.One]

        a_str = map(lambda x:self.parenthesize(x, precedence(expr)), a)
        b_str = map(lambda x:self.parenthesize(x, precedence(expr)), b)

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

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

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

    def _print_Normal(self, expr):
        return "Normal(%s, %s)"%(expr.mu, expr.sigma)

    def _print_Order(self, expr):
        if len(expr.variables) <= 1:
            return 'O(%s)'%self._print(expr.expr)
        else:
            return 'O(%s)'%self.stringify(expr.args, ', ', 0)

    def _print_PDF(self, expr):
        return 'PDF(%s, (%s, %s, %s))' % \
            (self._print(expr.pdf.args[1]), self._print(expr.pdf.args[0]), \
            self._print(expr.domain[0]), self._print(expr.domain[1]))

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

    def _print_Poly(self, expr):
        terms, gens = [], [ self._print(s) for s in expr.gens ]

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

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

            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"

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

        format += ")"

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

    def _print_ProductSet(self, p):
        return ' x '.join(self._print(set) for set in p.sets)


    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):
        PREC = precedence(expr)
        if expr.exp is S.NegativeOne:
            return '1/%s'%(self.parenthesize(expr.base, PREC))
        else:
            return '%s**%s'%(self.parenthesize(expr.base, PREC),
                             self.parenthesize(expr.exp, PREC))

    def _print_Integer(self, expr):
        return str(expr.p)

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

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

    def _print_Rational(self, expr):
        return '%s/%s' % (expr.p, expr.q)

    def _print_Fraction(self, expr):
        return '%s/%s' % (expr.numerator, expr.denominator)

    def _print_mpq(self, expr):
        return '%s/%s' % (expr.numer(), expr.denom())

    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"] == True:
            strip = False
        elif self._settings["full_prec"] == False:
            strip = True
        elif self._settings["full_prec"] == "auto":
            strip = self._print_level > 1
        return mlib.to_str(expr._mpf_, dps, strip_zeros=strip)

    def _print_Relational(self, expr):
        return '%s %s %s'%(self.parenthesize(expr.lhs, precedence(expr)),
                           expr.rel_op,
                           self.parenthesize(expr.rhs, precedence(expr)))

    def _print_DMP(self, expr):
        cls = expr.__class__.__name__
        rep = self._print(expr.rep)
        dom = self._print(expr.dom)

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

    def _print_DMF(self, expr):
        cls = expr.__class__.__name__
        num = self._print(expr.num)
        den = self._print(expr.den)
        dom = self._print(expr.dom)

        return "%s((%s, %s), %s)" % (cls, num, den, dom)

    def _print_RootOf(self, expr):
        return "RootOf(%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_Sample(self, expr):
        return "Sample([%s])"%self.stringify(expr, ", ", 0)

    def __print_set(self, expr):
        items = list(expr)
        items.sort( key=cmp_to_key(Basic.compare_pretty) )

        args = ', '.join(self._print(item) for item in items)
        if args:
            args = '[%s]' % args
        return '%s(%s)' % (type(expr).__name__, args)

    _print_set       = __print_set
    _print_frozenset = __print_set

    def _print_SparseMatrix(self, expr):
        return self._print(expr.toMatrix())

    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

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

    def _print_str(self, expr):
        return 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_Uniform(self, expr):
        return "Uniform(%s, %s)"%(expr.a, expr.b)

    def _print_Union(self, expr):
        return ' U '.join(self._print(set) for set in expr.args)

    def _print_Unit(self, expr):
        return expr.abbrev

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

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

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


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

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