text: from sympy import (Symbol, exp, Integer, Float, sin, cos, log, Poly, Lambda,
      Function, I, S, sqrt, srepr, Rational, Tuple, Matrix, Interval, Add, Mul,
      Pow, Or, true, false, Abs, pi, Range, Xor)
  from sympy.abc import x, y
  from sympy.core.sympify import (sympify, _sympify, SympifyError, kernS,
      CantSympify)
  from sympy.core.decorators import _sympifyit
  from sympy.external import import_module
  from sympy.testing.pytest import raises, XFAIL, skip
  from sympy.utilities.decorator import conserve_mpmath_dps
  from sympy.geometry import Point, Line
  from sympy.functions.combinatorial.factorials import factorial, factorial2
  from sympy.abc import _clash, _clash1, _clash2
  from sympy.core.compatibility import exec_, HAS_GMPY
  from sympy.sets import FiniteSet, EmptySet
  from sympy.tensor.array.dense_ndim_array import ImmutableDenseNDimArray
  
  import mpmath
  from collections import defaultdict, OrderedDict
  from mpmath.rational import mpq
  
  
  numpy = import_module('numpy')
  
  
  def test_issue_3538():
      v = sympify("exp(x)")
      assert v == exp(x)
      assert type(v) == type(exp(x))
      assert str(type(v)) == str(type(exp(x)))
  
  
  def test_sympify1():
      assert sympify("x") == Symbol("x")
      assert sympify("   x") == Symbol("x")
      assert sympify("   x   ") == Symbol("x")
      # issue 4877
      n1 = S.Half
      assert sympify('--.5') == n1
      assert sympify('-1/2') == -n1
      assert sympify('-+--.5') == -n1
      assert sympify('-.[3]') == Rational(-1, 3)
      assert sympify('.[3]') == Rational(1, 3)
      assert sympify('+.[3]') == Rational(1, 3)
      assert sympify('+0.[3]*10**-2') == Rational(1, 300)
      assert sympify('.[052631578947368421]') == Rational(1, 19)
      assert sympify('.0[526315789473684210]') == Rational(1, 19)
      assert sympify('.034[56]') == Rational(1711, 49500)
      # options to make reals into rationals
      assert sympify('1.22[345]', rational=True) == \
          1 + Rational(22, 100) + Rational(345, 99900)
      assert sympify('2/2.6', rational=True) == Rational(10, 13)
      assert sympify('2.6/2', rational=True) == Rational(13, 10)
      assert sympify('2.6e2/17', rational=True) == Rational(260, 17)
      assert sympify('2.6e+2/17', rational=True) == Rational(260, 17)
      assert sympify('2.6e-2/17', rational=True) == Rational(26, 17000)
      assert sympify('2.1+3/4', rational=True) == \
          Rational(21, 10) + Rational(3, 4)
      assert sympify('2.234456', rational=True) == Rational(279307, 125000)
      assert sympify('2.234456e23', rational=True) == 223445600000000000000000
      assert sympify('2.234456e-23', rational=True) == \
          Rational(279307, 12500000000000000000000000000)
      assert sympify('-2.234456e-23', rational=True) == \
          Rational(-279307, 12500000000000000000000000000)
      assert sympify('12345678901/17', rational=True) == \
          Rational(12345678901, 17)
      assert sympify('1/.3 + x', rational=True) == Rational(10, 3) + x
      # make sure longs in fractions work
      assert sympify('222222222222/11111111111') == \
          Rational(222222222222, 11111111111)
      # ... even if they come from repetend notation
      assert sympify('1/.2[123456789012]') == Rational(333333333333, 70781892967)
      # ... or from high precision reals
      assert sympify('.1234567890123456', rational=True) == \
          Rational(19290123283179, 156250000000000)
  
  
  def test_sympify_Fraction():
      try:
          import fractions
      except ImportError:
          pass
      else:
          value = sympify(fractions.Fraction(101, 127))
          assert value == Rational(101, 127) and type(value) is Rational
  
  
  def test_sympify_gmpy():
      if HAS_GMPY:
          if HAS_GMPY == 2:
              import gmpy2 as gmpy
          elif HAS_GMPY == 1:
              import gmpy
  
          value = sympify(gmpy.mpz(1000001))
          assert value == Integer(1000001) and type(value) is Integer
  
          value = sympify(gmpy.mpq(101, 127))
          assert value == Rational(101, 127) and type(value) is Rational
  
  
  @conserve_mpmath_dps
  def test_sympify_mpmath():
      value = sympify(mpmath.mpf(1.0))
      assert value == Float(1.0) and type(value) is Float
  
      mpmath.mp.dps = 12
      assert sympify(
          mpmath.pi).epsilon_eq(Float("3.14159265359"), Float("1e-12")) == True
      assert sympify(
          mpmath.pi).epsilon_eq(Float("3.14159265359"), Float("1e-13")) == False
  
      mpmath.mp.dps = 6
      assert sympify(
          mpmath.pi).epsilon_eq(Float("3.14159"), Float("1e-5")) == True
      assert sympify(
          mpmath.pi).epsilon_eq(Float("3.14159"), Float("1e-6")) == False
  
      assert sympify(mpmath.mpc(1.0 + 2.0j)) == Float(1.0) + Float(2.0)*I
  
      assert sympify(mpq(1, 2)) == S.Half
  
  
  def test_sympify2():
      class A:
          def _sympy_(self):
              return Symbol("x")**3
  
      a = A()
  
      assert _sympify(a) == x**3
      assert sympify(a) == x**3
      assert a == x**3
  
  
  def test_sympify3():
      assert sympify("x**3") == x**3
      assert sympify("x^3") == x**3
      assert sympify("1/2") == Integer(1)/2
  
      raises(SympifyError, lambda: _sympify('x**3'))
      raises(SympifyError, lambda: _sympify('1/2'))
  
  
  def test_sympify_keywords():
      raises(SympifyError, lambda: sympify('if'))
      raises(SympifyError, lambda: sympify('for'))
      raises(SympifyError, lambda: sympify('while'))
      raises(SympifyError, lambda: sympify('lambda'))
  
  
  def test_sympify_float():
      assert sympify("1e-64") != 0
      assert sympify("1e-20000") != 0
  
  
  def test_sympify_bool():
      assert sympify(True) is true
      assert sympify(False) is false
  
  
  def test_sympyify_iterables():
      ans = [Rational(3, 10), Rational(1, 5)]
      assert sympify(['.3', '.2'], rational=True) == ans
      assert sympify(dict(x=0, y=1)) == {x: 0, y: 1}
      assert sympify(['1', '2', ['3', '4']]) == [S(1), S(2), [S(3), S(4)]]
  
  
  @XFAIL
  def test_issue_16772():
      # because there is a converter for tuple, the
      # args are only sympified without the flags being passed
      # along; list, on the other hand, is not converted
      # with a converter so its args are traversed later
      ans = [Rational(3, 10), Rational(1, 5)]
      assert sympify(tuple(['.3', '.2']), rational=True) == Tuple(*ans)
  
  
  def test_issue_16859():
      class no(float, CantSympify):
          pass
      raises(SympifyError, lambda: sympify(no(1.2)))
  
  
  def test_sympify4():
      class A:
          def _sympy_(self):
              return Symbol("x")
  
      a = A()
  
      assert _sympify(a)**3 == x**3
      assert sympify(a)**3 == x**3
      assert a == x
  
  
  def test_sympify_text():
      assert sympify('some') == Symbol('some')
      assert sympify('core') == Symbol('core')
  
      assert sympify('True') is True
      assert sympify('False') is False
  
      assert sympify('Poly') == Poly
      assert sympify('sin') == sin
  
  
  def test_sympify_function():
      assert sympify('factor(x**2-1, x)') == -(1 - x)*(x + 1)
      assert sympify('sin(pi/2)*cos(pi)') == -Integer(1)
  
  
  def test_sympify_poly():
      p = Poly(x**2 + x + 1, x)
  
      assert _sympify(p) is p
      assert sympify(p) is p
  
  
  def test_sympify_factorial():
      assert sympify('x!') == factorial(x)
      assert sympify('(x+1)!') == factorial(x + 1)
      assert sympify('(1 + y*(x + 1))!') == factorial(1 + y*(x + 1))
      assert sympify('(1 + y*(x + 1)!)^2') == (1 + y*factorial(x + 1))**2
      assert sympify('y*x!') == y*factorial(x)
      assert sympify('x!!') == factorial2(x)
      assert sympify('(x+1)!!') == factorial2(x + 1)
      assert sympify('(1 + y*(x + 1))!!') == factorial2(1 + y*(x + 1))
      assert sympify('(1 + y*(x + 1)!!)^2') == (1 + y*factorial2(x + 1))**2
      assert sympify('y*x!!') == y*factorial2(x)
      assert sympify('factorial2(x)!') == factorial(factorial2(x))
  
      raises(SympifyError, lambda: sympify("+!!"))
      raises(SympifyError, lambda: sympify(")!!"))
      raises(SympifyError, lambda: sympify("!"))
      raises(SympifyError, lambda: sympify("(!)"))
      raises(SympifyError, lambda: sympify("x!!!"))
  
  
  def test_sage():
      # how to effectivelly test for the _sage_() method without having SAGE
      # installed?
      assert hasattr(x, "_sage_")
      assert hasattr(Integer(3), "_sage_")
      assert hasattr(sin(x), "_sage_")
      assert hasattr(cos(x), "_sage_")
      assert hasattr(x**2, "_sage_")
      assert hasattr(x + y, "_sage_")
      assert hasattr(exp(x), "_sage_")
      assert hasattr(log(x), "_sage_")
  
  
  def test_issue_3595():
      assert sympify("a_") == Symbol("a_")
      assert sympify("_a") == Symbol("_a")
  
  
  def test_lambda():
      x = Symbol('x')
      assert sympify('lambda: 1') == Lambda((), 1)
      assert sympify('lambda x: x') == Lambda(x, x)
      assert sympify('lambda x: 2*x') == Lambda(x, 2*x)
      assert sympify('lambda x, y: 2*x+y') == Lambda((x, y), 2*x + y)
  
  
  def test_lambda_raises():
      raises(SympifyError, lambda: sympify("lambda *args: args")) # args argument error
      raises(SympifyError, lambda: sympify("lambda **kwargs: kwargs[0]")) # kwargs argument error
      raises(SympifyError, lambda: sympify("lambda x = 1: x"))    # Keyword argument error
      with raises(SympifyError):
          _sympify('lambda: 1')
  
  
  def test_sympify_raises():
      raises(SympifyError, lambda: sympify("fx)"))
  
  
  def test__sympify():
      x = Symbol('x')
      f = Function('f')
  
      # positive _sympify
      assert _sympify(x) is x
      assert _sympify(f) is f
      assert _sympify(1) == Integer(1)
      assert _sympify(0.5) == Float("0.5")
      assert _sympify(1 + 1j) == 1.0 + I*1.0
  
      class A:
          def _sympy_(self):
              return Integer(5)
  
      a = A()
      assert _sympify(a) == Integer(5)
  
      # negative _sympify
      raises(SympifyError, lambda: _sympify('1'))
      raises(SympifyError, lambda: _sympify([1, 2, 3]))
  
  
  def test_sympifyit():
      x = Symbol('x')
      y = Symbol('y')
  
      @_sympifyit('b', NotImplemented)
      def add(a, b):
          return a + b
  
      assert add(x, 1) == x + 1
      assert add(x, 0.5) == x + Float('0.5')
      assert add(x, y) == x + y
  
      assert add(x, '1') == NotImplemented
  
      @_sympifyit('b')
      def add_raises(a, b):
          return a + b
  
      assert add_raises(x, 1) == x + 1
      assert add_raises(x, 0.5) == x + Float('0.5')
      assert add_raises(x, y) == x + y
  
      raises(SympifyError, lambda: add_raises(x, '1'))
  
  
  def test_int_float():
      class F1_1(object):
          def __float__(self):
              return 1.1
  
      class F1_1b(object):
          """
          This class is still a float, even though it also implements __int__().
          """
          def __float__(self):
              return 1.1
  
          def __int__(self):
              return 1
  
      class F1_1c(object):
          """
          This class is still a float, because it implements _sympy_()
          """
          def __float__(self):
              return 1.1
  
          def __int__(self):
              return 1
  
          def _sympy_(self):
              return Float(1.1)
  
      class I5(object):
          def __int__(self):
              return 5
  
      class I5b(object):
          """
          This class implements both __int__() and __float__(), so it will be
          treated as Float in SymPy. One could change this behavior, by using
          float(a) == int(a), but deciding that integer-valued floats represent
          exact numbers is arbitrary and often not correct, so we do not do it.
          If, in the future, we decide to do it anyway, the tests for I5b need to
          be changed.
          """
          def __float__(self):
              return 5.0
  
          def __int__(self):
              return 5
  
      class I5c(object):
          """
          This class implements both __int__() and __float__(), but also
          a _sympy_() method, so it will be Integer.
          """
          def __float__(self):
              return 5.0
  
          def __int__(self):
              return 5
  
          def _sympy_(self):
              return Integer(5)
  
      i5 = I5()
      i5b = I5b()
      i5c = I5c()
      f1_1 = F1_1()
      f1_1b = F1_1b()
      f1_1c = F1_1c()
      assert sympify(i5) == 5
      assert isinstance(sympify(i5), Integer)
      assert sympify(i5b) == 5
      assert isinstance(sympify(i5b), Float)
      assert sympify(i5c) == 5
      assert isinstance(sympify(i5c), Integer)
      assert abs(sympify(f1_1) - 1.1) < 1e-5
      assert abs(sympify(f1_1b) - 1.1) < 1e-5
      assert abs(sympify(f1_1c) - 1.1) < 1e-5
  
      assert _sympify(i5) == 5
      assert isinstance(_sympify(i5), Integer)
      assert _sympify(i5b) == 5
      assert isinstance(_sympify(i5b), Float)
      assert _sympify(i5c) == 5
      assert isinstance(_sympify(i5c), Integer)
      assert abs(_sympify(f1_1) - 1.1) < 1e-5
      assert abs(_sympify(f1_1b) - 1.1) < 1e-5
      assert abs(_sympify(f1_1c) - 1.1) < 1e-5
  
  
  def test_evaluate_false():
      cases = {
          '2 + 3': Add(2, 3, evaluate=False),
          '2**2 / 3': Mul(Pow(2, 2, evaluate=False), Pow(3, -1, evaluate=False), evaluate=False),
          '2 + 3 * 5': Add(2, Mul(3, 5, evaluate=False), evaluate=False),
          '2 - 3 * 5': Add(2, Mul(-1, Mul(3, 5,evaluate=False), evaluate=False), evaluate=False),
          '1 / 3': Mul(1, Pow(3, -1, evaluate=False), evaluate=False),
          'True | False': Or(True, False, evaluate=False),
          '1 + 2 + 3 + 5*3 + integrate(x)': Add(1, 2, 3, Mul(5, 3, evaluate=False), x**2/2, evaluate=False),
          '2 * 4 * 6 + 8': Add(Mul(2, 4, 6, evaluate=False), 8, evaluate=False),
          '2 - 8 / 4': Add(2, Mul(-1, Mul(8, Pow(4, -1, evaluate=False), evaluate=False), evaluate=False), evaluate=False),
          '2 - 2**2': Add(2, Mul(-1, Pow(2, 2, evaluate=False), evaluate=False), evaluate=False),
      }
      for case, result in cases.items():
          assert sympify(case, evaluate=False) == result
  
  
  def test_issue_4133():
      a = sympify('Integer(4)')
  
      assert a == Integer(4)
      assert a.is_Integer
  
  
  def test_issue_3982():
      a = [3, 2.0]
      assert sympify(a) == [Integer(3), Float(2.0)]
      assert sympify(tuple(a)) == Tuple(Integer(3), Float(2.0))
      assert sympify(set(a)) == FiniteSet(Integer(3), Float(2.0))
  
  
  def test_S_sympify():
      assert S(1)/2 == sympify(1)/2
      assert (-2)**(S(1)/2) == sqrt(2)*I
  
  
  def test_issue_4788():
      assert srepr(S(1.0 + 0J)) == srepr(S(1.0)) == srepr(Float(1.0))
  
  
  def test_issue_4798_None():
      assert S(None) is None
  
  
  def test_issue_3218():
      assert sympify("x+\ny") == x + y
  
  
  def test_issue_4988_builtins():
      C = Symbol('C')
      vars = {'C': C}
      exp1 = sympify('C')
      assert exp1 == C  # Make sure it did not get mixed up with sympy.C
  
      exp2 = sympify('C', vars)
      assert exp2 == C  # Make sure it did not get mixed up with sympy.C
  
  
  def test_geometry():
      p = sympify(Point(0, 1))
      assert p == Point(0, 1) and isinstance(p, Point)
      L = sympify(Line(p, (1, 0)))
      assert L == Line((0, 1), (1, 0)) and isinstance(L, Line)
  
  
  def test_kernS():
      s =   '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'
      # when 1497 is fixed, this no longer should pass: the expression
      # should be unchanged
      assert -1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) == -1
      # sympification should not allow the constant to enter a Mul
      # or else the structure can change dramatically
      ss = kernS(s)
      assert ss != -1 and ss.simplify() == -1
      s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'.replace(
          'x', '_kern')
      ss = kernS(s)
      assert ss != -1 and ss.simplify() == -1
      # issue 6687
      assert kernS('Interval(-1,-2 - 4*(-3))') == Interval(-1, 10)
      assert kernS('_kern') == Symbol('_kern')
      assert kernS('E**-(x)') == exp(-x)
      e = 2*(x + y)*y
      assert kernS(['2*(x + y)*y', ('2*(x + y)*y',)]) == [e, (e,)]
      assert kernS('-(2*sin(x)**2 + 2*sin(x)*cos(x))*y/2') == \
          -y*(2*sin(x)**2 + 2*sin(x)*cos(x))/2
      # issue 15132
      assert kernS('(1 - x)/(1 - x*(1-y))') == kernS('(1-x)/(1-(1-y)*x)')
      assert kernS('(1-2**-(4+1)*(1-y)*x)') == (1 - x*(1 - y)/32)
      assert kernS('(1-2**(4+1)*(1-y)*x)') == (1 - 32*x*(1 - y))
      assert kernS('(1-2.*(1-y)*x)') == 1 - 2.*x*(1 - y)
      one = kernS('x - (x - 1)')
      assert one != 1 and one.expand() == 1
  
  
  def test_issue_6540_6552():
      assert S('[[1/3,2], (2/5,)]') == [[Rational(1, 3), 2], (Rational(2, 5),)]
      assert S('[[2/6,2], (2/4,)]') == [[Rational(1, 3), 2], (S.Half,)]
      assert S('[[[2*(1)]]]') == [[[2]]]
      assert S('Matrix([2*(1)])') == Matrix([2])
  
  
  def test_issue_6046():
      assert str(S("Q & C", locals=_clash1)) == 'C & Q'
      assert str(S('pi(x)', locals=_clash2)) == 'pi(x)'
      assert str(S('pi(C, Q)', locals=_clash)) == 'pi(C, Q)'
      locals = {}
      exec_("from sympy.abc import Q, C", locals)
      assert str(S('C&Q', locals)) == 'C & Q'
  
  
  def test_issue_8821_highprec_from_str():
      s = str(pi.evalf(128))
      p = sympify(s)
      assert Abs(sin(p)) < 1e-127
  
  
  def test_issue_10295():
      if not numpy:
          skip("numpy not installed.")
  
      A = numpy.array([[1, 3, -1],
                       [0, 1, 7]])
      sA = S(A)
      assert sA.shape == (2, 3)
      for (ri, ci), val in numpy.ndenumerate(A):
          assert sA[ri, ci] == val
  
      B = numpy.array([-7, x, 3*y**2])
      sB = S(B)
      assert sB.shape == (3,)
      assert B[0] == sB[0] == -7
      assert B[1] == sB[1] == x
      assert B[2] == sB[2] == 3*y**2
  
      C = numpy.arange(0, 24)
      C.resize(2,3,4)
      sC = S(C)
      assert sC[0, 0, 0].is_integer
      assert sC[0, 0, 0] == 0
  
      a1 = numpy.array([1, 2, 3])
      a2 = numpy.array([i for i in range(24)])
      a2.resize(2, 4, 3)
      assert sympify(a1) == ImmutableDenseNDimArray([1, 2, 3])
      assert sympify(a2) == ImmutableDenseNDimArray([i for i in range(24)], (2, 4, 3))
  
  
  def test_Range():
      # Only works in Python 3 where range returns a range type
      assert sympify(range(10)) == Range(10)
      assert _sympify(range(10)) == Range(10)
  
  
  def test_sympify_set():
      n = Symbol('n')
      assert sympify({n}) == FiniteSet(n)
      assert sympify(set()) == EmptySet
  
  
  def test_sympify_numpy():
      if not numpy:
          skip('numpy not installed. Abort numpy tests.')
      np = numpy
  
      def equal(x, y):
          return x == y and type(x) == type(y)
  
      assert sympify(np.bool_(1)) is S(True)
      try:
          assert equal(
              sympify(np.int_(1234567891234567891)), S(1234567891234567891))
          assert equal(
              sympify(np.intp(1234567891234567891)), S(1234567891234567891))
      except OverflowError:
          # May fail on 32-bit systems: Python int too large to convert to C long
          pass
      assert equal(sympify(np.intc(1234567891)), S(1234567891))
      assert equal(sympify(np.int8(-123)), S(-123))
      assert equal(sympify(np.int16(-12345)), S(-12345))
      assert equal(sympify(np.int32(-1234567891)), S(-1234567891))
      assert equal(
          sympify(np.int64(-1234567891234567891)), S(-1234567891234567891))
      assert equal(sympify(np.uint8(123)), S(123))
      assert equal(sympify(np.uint16(12345)), S(12345))
      assert equal(sympify(np.uint32(1234567891)), S(1234567891))
      assert equal(
          sympify(np.uint64(1234567891234567891)), S(1234567891234567891))
      assert equal(sympify(np.float32(1.123456)), Float(1.123456, precision=24))
      assert equal(sympify(np.float64(1.1234567891234)),
                  Float(1.1234567891234, precision=53))
      assert equal(sympify(np.longdouble(1.123456789)),
                   Float(1.123456789, precision=80))
      assert equal(sympify(np.complex64(1 + 2j)), S(1.0 + 2.0*I))
      assert equal(sympify(np.complex128(1 + 2j)), S(1.0 + 2.0*I))
      assert equal(sympify(np.longcomplex(1 + 2j)), S(1.0 + 2.0*I))
  
      #float96 does not exist on all platforms
      if hasattr(np, 'float96'):
          assert equal(sympify(np.float96(1.123456789)),
                      Float(1.123456789, precision=80))
      #float128 does not exist on all platforms
      if hasattr(np, 'float128'):
          assert equal(sympify(np.float128(1.123456789123)),
                      Float(1.123456789123, precision=80))
  
  
  @XFAIL
  def test_sympify_rational_numbers_set():
      ans = [Rational(3, 10), Rational(1, 5)]
      assert sympify({'.3', '.2'}, rational=True) == FiniteSet(*ans)
  
  
  def test_issue_13924():
      if not numpy:
          skip("numpy not installed.")
  
      a = sympify(numpy.array([1]))
      assert isinstance(a, ImmutableDenseNDimArray)
      assert a[0] == 1
  
  
  def test_numpy_sympify_args():
      # Issue 15098. Make sure sympify args work with numpy types (like numpy.str_)
      if not numpy:
          skip("numpy not installed.")
  
      a = sympify(numpy.str_('a'))
      assert type(a) is Symbol
      assert a == Symbol('a')
  
      class CustomSymbol(Symbol):
          pass
  
      a = sympify(numpy.str_('a'), {"Symbol": CustomSymbol})
      assert isinstance(a, CustomSymbol)
  
      a = sympify(numpy.str_('x^y'))
      assert a == x**y
      a = sympify(numpy.str_('x^y'), convert_xor=False)
      assert a == Xor(x, y)
  
      raises(SympifyError, lambda: sympify(numpy.str_('x'), strict=True))
  
      a = sympify(numpy.str_('1.1'))
      assert isinstance(a, Float)
      assert a == 1.1
  
      a = sympify(numpy.str_('1.1'), rational=True)
      assert isinstance(a, Rational)
      assert a == Rational(11, 10)
  
      a = sympify(numpy.str_('x + x'))
      assert isinstance(a, Mul)
      assert a == 2*x
  
      a = sympify(numpy.str_('x + x'), evaluate=False)
      assert isinstance(a, Add)
      assert a == Add(x, x, evaluate=False)
  
  
  def test_issue_5939():
       a = Symbol('a')
       b = Symbol('b')
       assert sympify('''a+\nb''') == a + b
  
  
  def test_issue_16759():
      d = sympify({.5: 1})
      assert S.Half not in d
      assert Float(.5) in d
      assert d[.5] is S.One
      d = sympify(OrderedDict({.5: 1}))
      assert S.Half not in d
      assert Float(.5) in d
      assert d[.5] is S.One
      d = sympify(defaultdict(int, {.5: 1}))
      assert S.Half not in d
      assert Float(.5) in d
      assert d[.5] is S.One
  
  
  def test_issue_17811():
      a = Function('a')
      assert sympify('a(x)*5', evaluate=False) == Mul(a(x), 5, evaluate=False)
  
  
  def test_issue_14706():
      if not numpy:
          skip("numpy not installed.")
  
      z1 = numpy.zeros((1, 1), dtype=numpy.float)
      z2 = numpy.zeros((2, 2), dtype=numpy.float)
      z3 = numpy.zeros((), dtype=numpy.float)
  
      y1 = numpy.ones((1, 1), dtype=numpy.float)
      y2 = numpy.ones((2, 2), dtype=numpy.float)
      y3 = numpy.ones((), dtype=numpy.float)
  
      assert numpy.all(x + z1 == numpy.full((1, 1), x))
      assert numpy.all(x + z2 == numpy.full((2, 2), x))
      assert numpy.all(z1 + x == numpy.full((1, 1), x))
      assert numpy.all(z2 + x == numpy.full((2, 2), x))
      for z in [z3,
                numpy.int(0),
                numpy.float(0),
                numpy.complex(0)]:
          assert x + z == x
          assert z + x == x
          assert isinstance(x + z, Symbol)
          assert isinstance(z + x, Symbol)
  
      # If these tests fail, then it means that numpy has finally
      # fixed the issue of scalar conversion for rank>0 arrays
      # which is mentioned in numpy/numpy#10404. In that case,
      # some changes have to be made in sympify.py.
      # Note: For future reference, for anyone who takes up this
      # issue when numpy has finally fixed their side of the problem,
      # the changes for this temporary fix were introduced in PR 18651
      assert numpy.all(x + y1 == numpy.full((1, 1), x + 1.0))
      assert numpy.all(x + y2 == numpy.full((2, 2), x + 1.0))
      assert numpy.all(y1 + x == numpy.full((1, 1), x + 1.0))
      assert numpy.all(y2 + x == numpy.full((2, 2), x + 1.0))
      for y_ in [y3,
                numpy.int(1),
                numpy.float(1),
                numpy.complex(1)]:
          assert x + y_ == y_ + x
          assert isinstance(x + y_, Add)
          assert isinstance(y_ + x, Add)
  
      assert x + numpy.array(x) == 2 * x
      assert x + numpy.array([x]) == numpy.array([2*x], dtype=object)
  
      assert sympify(numpy.array([1])) == ImmutableDenseNDimArray([1], 1)
      assert sympify(numpy.array([[[1]]])) == ImmutableDenseNDimArray([1], (1, 1, 1))
      assert sympify(z1) == ImmutableDenseNDimArray([0], (1, 1))
      assert sympify(z2) == ImmutableDenseNDimArray([0, 0, 0, 0], (2, 2))
      assert sympify(z3) == ImmutableDenseNDimArray([0], ())
      assert sympify(z3, strict=True) == 0.0
  
      raises(SympifyError, lambda: sympify(numpy.array([1]), strict=True))
      raises(SympifyError, lambda: sympify(z1, strict=True))
      raises(SympifyError, lambda: sympify(z2, strict=True))
  