text: from numpy.testing import assert_raises
  from numpy.f2py.symbolic import (
      Expr, Op, ArithOp, Language,
      as_symbol, as_number, as_string, as_array, as_complex,
      as_terms, as_factors, eliminate_quotes, insert_quotes,
      fromstring, as_expr, as_apply,
      as_numer_denom, as_ternary, as_ref, as_deref,
      normalize, as_eq, as_ne, as_lt, as_gt, as_le, as_ge
      )
  from . import util
  
  
  class TestSymbolic(util.F2PyTest):
  
      def test_eliminate_quotes(self):
          def worker(s):
              r, d = eliminate_quotes(s)
              s1 = insert_quotes(r, d)
              assert s1 == s
  
          for kind in ['', 'mykind_']:
              worker(kind + '"1234" // "ABCD"')
              worker(kind + '"1234" // ' + kind + '"ABCD"')
              worker(kind + '"1234" // \'ABCD\'')
              worker(kind + '"1234" // ' + kind + '\'ABCD\'')
              worker(kind + '"1\\"2\'AB\'34"')
              worker('a = ' + kind + "'1\\'2\"AB\"34'")
  
      def test_sanity(self):
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
  
          assert x.op == Op.SYMBOL
          assert repr(x) == "Expr(Op.SYMBOL, 'x')"
          assert x == x
          assert x != y
          assert hash(x) is not None
  
          n = as_number(123)
          m = as_number(456)
          assert n.op == Op.INTEGER
          assert repr(n) == "Expr(Op.INTEGER, (123, 4))"
          assert n == n
          assert n != m
          assert hash(n) is not None
  
          fn = as_number(12.3)
          fm = as_number(45.6)
          assert fn.op == Op.REAL
          assert repr(fn) == "Expr(Op.REAL, (12.3, 4))"
          assert fn == fn
          assert fn != fm
          assert hash(fn) is not None
  
          c = as_complex(1, 2)
          c2 = as_complex(3, 4)
          assert c.op == Op.COMPLEX
          assert repr(c) == ("Expr(Op.COMPLEX, (Expr(Op.INTEGER, (1, 4)),"
                             " Expr(Op.INTEGER, (2, 4))))")
          assert c == c
          assert c != c2
          assert hash(c) is not None
  
          s = as_string("'123'")
          s2 = as_string('"ABC"')
          assert s.op == Op.STRING
          assert repr(s) == "Expr(Op.STRING, (\"'123'\", 1))", repr(s)
          assert s == s
          assert s != s2
  
          a = as_array((n, m))
          b = as_array((n,))
          assert a.op == Op.ARRAY
          assert repr(a) == ("Expr(Op.ARRAY, (Expr(Op.INTEGER, (123, 4)),"
                             " Expr(Op.INTEGER, (456, 4))))")
          assert a == a
          assert a != b
  
          t = as_terms(x)
          u = as_terms(y)
          assert t.op == Op.TERMS
          assert repr(t) == "Expr(Op.TERMS, {Expr(Op.SYMBOL, 'x'): 1})"
          assert t == t
          assert t != u
          assert hash(t) is not None
  
          v = as_factors(x)
          w = as_factors(y)
          assert v.op == Op.FACTORS
          assert repr(v) == "Expr(Op.FACTORS, {Expr(Op.SYMBOL, 'x'): 1})"
          assert v == v
          assert w != v
          assert hash(v) is not None
  
          t = as_ternary(x, y, z)
          u = as_ternary(x, z, y)
          assert t.op == Op.TERNARY
          assert t == t
          assert t != u
          assert hash(t) is not None
  
          e = as_eq(x, y)
          f = as_lt(x, y)
          assert e.op == Op.RELATIONAL
          assert e == e
          assert e != f
          assert hash(e) is not None
  
      def test_tostring_fortran(self):
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
          n = as_number(123)
          m = as_number(456)
          a = as_array((n, m))
          c = as_complex(n, m)
  
          assert str(x) == 'x'
          assert str(n) == '123'
          assert str(a) == '[123, 456]'
          assert str(c) == '(123, 456)'
  
          assert str(Expr(Op.TERMS, {x: 1})) == 'x'
          assert str(Expr(Op.TERMS, {x: 2})) == '2 * x'
          assert str(Expr(Op.TERMS, {x: -1})) == '-x'
          assert str(Expr(Op.TERMS, {x: -2})) == '-2 * x'
          assert str(Expr(Op.TERMS, {x: 1, y: 1})) == 'x + y'
          assert str(Expr(Op.TERMS, {x: -1, y: -1})) == '-x - y'
          assert str(Expr(Op.TERMS, {x: 2, y: 3})) == '2 * x + 3 * y'
          assert str(Expr(Op.TERMS, {x: -2, y: 3})) == '-2 * x + 3 * y'
          assert str(Expr(Op.TERMS, {x: 2, y: -3})) == '2 * x - 3 * y'
  
          assert str(Expr(Op.FACTORS, {x: 1})) == 'x'
          assert str(Expr(Op.FACTORS, {x: 2})) == 'x ** 2'
          assert str(Expr(Op.FACTORS, {x: -1})) == 'x ** -1'
          assert str(Expr(Op.FACTORS, {x: -2})) == 'x ** -2'
          assert str(Expr(Op.FACTORS, {x: 1, y: 1})) == 'x * y'
          assert str(Expr(Op.FACTORS, {x: 2, y: 3})) == 'x ** 2 * y ** 3'
  
          v = Expr(Op.FACTORS, {x: 2, Expr(Op.TERMS, {x: 1, y: 1}): 3})
          assert str(v) == 'x ** 2 * (x + y) ** 3', str(v)
          v = Expr(Op.FACTORS, {x: 2, Expr(Op.FACTORS, {x: 1, y: 1}): 3})
          assert str(v) == 'x ** 2 * (x * y) ** 3', str(v)
  
          assert str(Expr(Op.APPLY, ('f', (), {}))) == 'f()'
          assert str(Expr(Op.APPLY, ('f', (x,), {}))) == 'f(x)'
          assert str(Expr(Op.APPLY, ('f', (x, y), {}))) == 'f(x, y)'
          assert str(Expr(Op.INDEXING, ('f', x))) == 'f[x]'
  
          assert str(as_ternary(x, y, z)) == 'merge(y, z, x)'
          assert str(as_eq(x, y)) == 'x .eq. y'
          assert str(as_ne(x, y)) == 'x .ne. y'
          assert str(as_lt(x, y)) == 'x .lt. y'
          assert str(as_le(x, y)) == 'x .le. y'
          assert str(as_gt(x, y)) == 'x .gt. y'
          assert str(as_ge(x, y)) == 'x .ge. y'
  
      def test_tostring_c(self):
          language = Language.C
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
          n = as_number(123)
  
          assert Expr(Op.FACTORS, {x: 2}).tostring(language=language) == 'x * x'
          assert Expr(Op.FACTORS, {x + y: 2}).tostring(
              language=language) == '(x + y) * (x + y)'
          assert Expr(Op.FACTORS, {x: 12}).tostring(
              language=language) == 'pow(x, 12)'
  
          assert as_apply(ArithOp.DIV, x, y).tostring(
              language=language) == 'x / y'
          assert as_apply(ArithOp.DIV, x, x + y).tostring(
              language=language) == 'x / (x + y)'
          assert as_apply(ArithOp.DIV, x - y, x + y).tostring(
              language=language) == '(x - y) / (x + y)'
          assert (x + (x - y) / (x + y) + n).tostring(
              language=language) == '123 + x + (x - y) / (x + y)'
  
          assert as_ternary(x, y, z).tostring(language=language) == '(x ? y : z)'
          assert as_eq(x, y).tostring(language=language) == 'x == y'
          assert as_ne(x, y).tostring(language=language) == 'x != y'
          assert as_lt(x, y).tostring(language=language) == 'x < y'
          assert as_le(x, y).tostring(language=language) == 'x <= y'
          assert as_gt(x, y).tostring(language=language) == 'x > y'
          assert as_ge(x, y).tostring(language=language) == 'x >= y'
  
      def test_operations(self):
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
  
          assert x + x == Expr(Op.TERMS, {x: 2})
          assert x - x == Expr(Op.INTEGER, (0, 4))
          assert x + y == Expr(Op.TERMS, {x: 1, y: 1})
          assert x - y == Expr(Op.TERMS, {x: 1, y: -1})
          assert x * x == Expr(Op.FACTORS, {x: 2})
          assert x * y == Expr(Op.FACTORS, {x: 1, y: 1})
  
          assert +x == x
          assert -x == Expr(Op.TERMS, {x: -1}), repr(-x)
          assert 2 * x == Expr(Op.TERMS, {x: 2})
          assert 2 + x == Expr(Op.TERMS, {x: 1, as_number(1): 2})
          assert 2 * x + 3 * y == Expr(Op.TERMS, {x: 2, y: 3})
          assert (x + y) * 2 == Expr(Op.TERMS, {x: 2, y: 2})
  
          assert x ** 2 == Expr(Op.FACTORS, {x: 2})
          assert (x + y) ** 2 == Expr(Op.TERMS,
                                      {Expr(Op.FACTORS, {x: 2}): 1,
                                       Expr(Op.FACTORS, {y: 2}): 1,
                                       Expr(Op.FACTORS, {x: 1, y: 1}): 2})
          assert (x + y) * x == x ** 2 + x * y
          assert (x + y) ** 2 == x ** 2 + 2 * x * y + y ** 2
          assert (x + y) ** 2 + (x - y) ** 2 == 2 * x ** 2 + 2 * y ** 2
          assert (x + y) * z == x * z + y * z
          assert z * (x + y) == x * z + y * z
  
          assert (x / 2) == as_apply(ArithOp.DIV, x, as_number(2))
          assert (2 * x / 2) == x
          assert (3 * x / 2) == as_apply(ArithOp.DIV, 3*x, as_number(2))
          assert (4 * x / 2) == 2 * x
          assert (5 * x / 2) == as_apply(ArithOp.DIV, 5*x, as_number(2))
          assert (6 * x / 2) == 3 * x
          assert ((3*5) * x / 6) == as_apply(ArithOp.DIV, 5*x, as_number(2))
          assert (30*x**2*y**4 / (24*x**3*y**3)) == as_apply(ArithOp.DIV,
                                                             5*y, 4*x)
          assert ((15 * x / 6) / 5) == as_apply(
              ArithOp.DIV, x, as_number(2)), ((15 * x / 6) / 5)
          assert (x / (5 / x)) == as_apply(ArithOp.DIV, x**2, as_number(5))
  
          assert (x / 2.0) == Expr(Op.TERMS, {x: 0.5})
  
          s = as_string('"ABC"')
          t = as_string('"123"')
  
          assert s // t == Expr(Op.STRING, ('"ABC123"', 1))
          assert s // x == Expr(Op.CONCAT, (s, x))
          assert x // s == Expr(Op.CONCAT, (x, s))
  
          c = as_complex(1., 2.)
          assert -c == as_complex(-1., -2.)
          assert c + c == as_expr((1+2j)*2)
          assert c * c == as_expr((1+2j)**2)
  
      def test_substitute(self):
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
          a = as_array((x, y))
  
          assert x.substitute({x: y}) == y
          assert (x + y).substitute({x: z}) == y + z
          assert (x * y).substitute({x: z}) == y * z
          assert (x ** 4).substitute({x: z}) == z ** 4
          assert (x / y).substitute({x: z}) == z / y
          assert x.substitute({x: y + z}) == y + z
          assert a.substitute({x: y + z}) == as_array((y + z, y))
  
          assert as_ternary(x, y, z).substitute(
              {x: y + z}) == as_ternary(y + z, y, z)
          assert as_eq(x, y).substitute(
              {x: y + z}) == as_eq(y + z, y)
  
      def test_fromstring(self):
  
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
          f = as_symbol('f')
          s = as_string('"ABC"')
          t = as_string('"123"')
          a = as_array((x, y))
  
          assert fromstring('x') == x
          assert fromstring('+ x') == x
          assert fromstring('-  x') == -x
          assert fromstring('x + y') == x + y
          assert fromstring('x + 1') == x + 1
          assert fromstring('x * y') == x * y
          assert fromstring('x * 2') == x * 2
          assert fromstring('x / y') == x / y
          assert fromstring('x ** 2',
                            language=Language.Python) == x ** 2
          assert fromstring('x ** 2 ** 3',
                            language=Language.Python) == x ** 2 ** 3
          assert fromstring('(x + y) * z') == (x + y) * z
  
          assert fromstring('f(x)') == f(x)
          assert fromstring('f(x,y)') == f(x, y)
          assert fromstring('f[x]') == f[x]
          assert fromstring('f[x][y]') == f[x][y]
  
          assert fromstring('"ABC"') == s
          assert normalize(fromstring('"ABC" // "123" ',
                                      language=Language.Fortran)) == s // t
          assert fromstring('f("ABC")') == f(s)
          assert fromstring('MYSTRKIND_"ABC"') == as_string('"ABC"', 'MYSTRKIND')
  
          assert fromstring('(/x, y/)') == a, fromstring('(/x, y/)')
          assert fromstring('f((/x, y/))') == f(a)
          assert fromstring('(/(x+y)*z/)') == as_array(((x+y)*z,))
  
          assert fromstring('123') == as_number(123)
          assert fromstring('123_2') == as_number(123, 2)
          assert fromstring('123_myintkind') == as_number(123, 'myintkind')
  
          assert fromstring('123.0') == as_number(123.0, 4)
          assert fromstring('123.0_4') == as_number(123.0, 4)
          assert fromstring('123.0_8') == as_number(123.0, 8)
          assert fromstring('123.0e0') == as_number(123.0, 4)
          assert fromstring('123.0d0') == as_number(123.0, 8)
          assert fromstring('123d0') == as_number(123.0, 8)
          assert fromstring('123e-0') == as_number(123.0, 4)
          assert fromstring('123d+0') == as_number(123.0, 8)
          assert fromstring('123.0_myrealkind') == as_number(123.0, 'myrealkind')
          assert fromstring('3E4') == as_number(30000.0, 4)
  
          assert fromstring('(1, 2)') == as_complex(1, 2)
          assert fromstring('(1e2, PI)') == as_complex(
              as_number(100.0), as_symbol('PI'))
  
          assert fromstring('[1, 2]') == as_array((as_number(1), as_number(2)))
  
          assert fromstring('POINT(x, y=1)') == as_apply(
              as_symbol('POINT'), x, y=as_number(1))
          assert (fromstring('PERSON(name="John", age=50, shape=(/34, 23/))')
                  == as_apply(as_symbol('PERSON'),
                              name=as_string('"John"'),
                              age=as_number(50),
                              shape=as_array((as_number(34), as_number(23)))))
  
          assert fromstring('x?y:z') == as_ternary(x, y, z)
  
          assert fromstring('*x') == as_deref(x)
          assert fromstring('**x') == as_deref(as_deref(x))
          assert fromstring('&x') == as_ref(x)
          assert fromstring('(*x) * (*y)') == as_deref(x) * as_deref(y)
          assert fromstring('(*x) * *y') == as_deref(x) * as_deref(y)
          assert fromstring('*x * *y') == as_deref(x) * as_deref(y)
          assert fromstring('*x**y') == as_deref(x) * as_deref(y)
  
          assert fromstring('x == y') == as_eq(x, y)
          assert fromstring('x != y') == as_ne(x, y)
          assert fromstring('x < y') == as_lt(x, y)
          assert fromstring('x > y') == as_gt(x, y)
          assert fromstring('x <= y') == as_le(x, y)
          assert fromstring('x >= y') == as_ge(x, y)
  
          assert fromstring('x .eq. y', language=Language.Fortran) == as_eq(x, y)
          assert fromstring('x .ne. y', language=Language.Fortran) == as_ne(x, y)
          assert fromstring('x .lt. y', language=Language.Fortran) == as_lt(x, y)
          assert fromstring('x .gt. y', language=Language.Fortran) == as_gt(x, y)
          assert fromstring('x .le. y', language=Language.Fortran) == as_le(x, y)
          assert fromstring('x .ge. y', language=Language.Fortran) == as_ge(x, y)
  
      def test_traverse(self):
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
          f = as_symbol('f')
  
          # Use traverse to substitute a symbol
          def replace_visit(s, r=z):
              if s == x:
                  return r
  
          assert x.traverse(replace_visit) == z
          assert y.traverse(replace_visit) == y
          assert z.traverse(replace_visit) == z
          assert (f(y)).traverse(replace_visit) == f(y)
          assert (f(x)).traverse(replace_visit) == f(z)
          assert (f[y]).traverse(replace_visit) == f[y]
          assert (f[z]).traverse(replace_visit) == f[z]
          assert (x + y + z).traverse(replace_visit) == (2 * z + y)
          assert (x + f(y, x - z)).traverse(
              replace_visit) == (z + f(y, as_number(0)))
          assert as_eq(x, y).traverse(replace_visit) == as_eq(z, y)
  
          # Use traverse to collect symbols, method 1
          function_symbols = set()
          symbols = set()
  
          def collect_symbols(s):
              if s.op is Op.APPLY:
                  oper = s.data[0]
                  function_symbols.add(oper)
                  if oper in symbols:
                      symbols.remove(oper)
              elif s.op is Op.SYMBOL and s not in function_symbols:
                  symbols.add(s)
  
          (x + f(y, x - z)).traverse(collect_symbols)
          assert function_symbols == {f}
          assert symbols == {x, y, z}
  
          # Use traverse to collect symbols, method 2
          def collect_symbols2(expr, symbols):
              if expr.op is Op.SYMBOL:
                  symbols.add(expr)
  
          symbols = set()
          (x + f(y, x - z)).traverse(collect_symbols2, symbols)
          assert symbols == {x, y, z, f}
  
          # Use traverse to partially collect symbols
          def collect_symbols3(expr, symbols):
              if expr.op is Op.APPLY:
                  # skip traversing function calls
                  return expr
              if expr.op is Op.SYMBOL:
                  symbols.add(expr)
  
          symbols = set()
          (x + f(y, x - z)).traverse(collect_symbols3, symbols)
          assert symbols == {x}
  
      def test_linear_solve(self):
          x = as_symbol('x')
          y = as_symbol('y')
          z = as_symbol('z')
  
          assert x.linear_solve(x) == (as_number(1), as_number(0))
          assert (x+1).linear_solve(x) == (as_number(1), as_number(1))
          assert (2*x).linear_solve(x) == (as_number(2), as_number(0))
          assert (2*x+3).linear_solve(x) == (as_number(2), as_number(3))
          assert as_number(3).linear_solve(x) == (as_number(0), as_number(3))
          assert y.linear_solve(x) == (as_number(0), y)
          assert (y*z).linear_solve(x) == (as_number(0), y * z)
  
          assert (x+y).linear_solve(x) == (as_number(1), y)
          assert (z*x+y).linear_solve(x) == (z, y)
          assert ((z+y)*x+y).linear_solve(x) == (z + y, y)
          assert (z*y*x+y).linear_solve(x) == (z * y, y)
  
          assert_raises(RuntimeError, lambda: (x*x).linear_solve(x))
  
      def test_as_numer_denom(self):
          x = as_symbol('x')
          y = as_symbol('y')
          n = as_number(123)
  
          assert as_numer_denom(x) == (x, as_number(1))
          assert as_numer_denom(x / n) == (x, n)
          assert as_numer_denom(n / x) == (n, x)
          assert as_numer_denom(x / y) == (x, y)
          assert as_numer_denom(x * y) == (x * y, as_number(1))
          assert as_numer_denom(n + x / y) == (x + n * y, y)
          assert as_numer_denom(n + x / (y - x / n)) == (y * n ** 2, y * n - x)
  
      def test_polynomial_atoms(self):
          x = as_symbol('x')
          y = as_symbol('y')
          n = as_number(123)
  
          assert x.polynomial_atoms() == {x}
          assert n.polynomial_atoms() == set()
          assert (y[x]).polynomial_atoms() == {y[x]}
          assert (y(x)).polynomial_atoms() == {y(x)}
          assert (y(x) + x).polynomial_atoms() == {y(x), x}
          assert (y(x) * x[y]).polynomial_atoms() == {y(x), x[y]}
          assert (y(x) ** x).polynomial_atoms() == {y(x)}
  