"""str() printing tests."""

import pytest

from diofant import (CC, QQ, ZZ, Abs, Add, And, BlockMatrix, Catalan,
                     Complement, Derivative, Dict, Dummy, E, Eq, Equivalent,
                     EulerGamma, Expr, FiniteSet, Float, Function, GoldenRatio,
                     I, Integer, Integral, Interval, Lambda, Limit, Matrix,
                     MatrixSymbol, Mul, Ne, O, Poly, Pow, Rational, Rel,
                     RootOf, RootSum, S, SparseMatrix, StrPrinter, Sum, Symbol,
                     SymmetricDifference, Tuple, Wild, WildFunction, Xor,
                     ZeroMatrix, cbrt, cos, exp, factor, factorial, factorial2,
                     false, field, grlex, groebner, nan, oo, pi, ring, root,
                     sin, sqrt, sstr, sstrrepr, subfactorial, summation,
                     symbols, true, zeta, zoo)
from diofant.abc import w, x, y, z
from diofant.combinatorics import AbelianGroup, Cycle, Permutation
from diofant.core.trace import Tr
from diofant.diffgeom import Differential, LieDerivative, TensorProduct
from diofant.diffgeom.rn import R2
from diofant.geometry import Circle, Point
from diofant.stats import Die, Exponential, Normal, pspace, where
from diofant.tensor.array import ImmutableDenseNDimArray


__all__ = ()

d = Dummy('d')


def test_printmethod():
    class R(Abs):
        def _diofantstr(self, printer):
            return f'foo({printer._print(self.args[0])})'
    assert sstr(R(x)) == 'foo(x)'

    class R2(Abs):
        def _diofantstr(self, printer):
            return 'foo'
    assert sstr(R2(x)) == 'foo'


def test_Abs():
    assert str(abs(x)) == 'Abs(x)'
    assert str(abs(Rational(1, 6))) == '1/6'
    assert str(abs(Rational(-1, 6))) == '1/6'


def test_Add():
    assert str(x + y) == 'x + y'
    assert str(x + 1) == 'x + 1'
    assert str(x + x**2) == 'x**2 + x'
    assert str(5 + x + y + x*y + x**2 + y**2) == 'x**2 + x*y + x + y**2 + y + 5'
    assert str(1 + x + x**2/2 + x**3/3) == 'x**3/3 + x**2/2 + x + 1'
    assert str(2*x - 7*x**2 + 2 + 3*y) == '-7*x**2 + 2*x + 3*y + 2'
    assert str(x - y) == 'x - y'
    assert str(2 - x) == '-x + 2'
    assert str(x - 2) == 'x - 2'
    assert str(x - y - z - w) == '-w + x - y - z'
    assert str(x - z*y**2*z*w) == '-w*y**2*z**2 + x'
    assert str(x - 1*y*x*y) == '-x*y**2 + x'
    assert str(sin(x).series(x, 0, 15)) == 'x - x**3/6 + x**5/120 - x**7/5040 + x**9/362880 - x**11/39916800 + x**13/6227020800 + O(x**15)'
    assert str(Add(0, 0, evaluate=False)) == '0 + 0'
    assert str(Add(And(x, y), z)) == 'z + (x & y)'


def test_Catalan():
    assert str(Catalan) == 'Catalan'


def test_ComplexInfinity():
    assert str(zoo) == 'zoo'


def test_Derivative():
    assert str(Derivative(x, y)) == 'Derivative(x, y)'
    assert str(Derivative(x**2, x, evaluate=False)) == 'Derivative(x**2, x)'
    assert str(Derivative(
        x**2/y, x, y, evaluate=False)) == 'Derivative(x**2/y, x, y)'


def test_dict():
    assert sstr({1: 1 + x}) == '{1: x + 1}'
    assert str({1: 1 + x}) == "{1: Add(Symbol('x'), Integer(1))}"
    assert str({1: x**2, 2: y*x}) in ("{1: Pow(Symbol('x'), Integer(2)), 2: Mul(Symbol('x'), Symbol('y'))}", "{1: Mul(Symbol('x'), Symbol('y')), 2: Pow(Symbol('x'), Integer(2))}")
    assert sstr({1: x**2, 2: y*x}) == '{1: x**2, 2: x*y}'


def test_Dict():
    assert str(Dict({1: 1 + x})) == sstr({1: 1 + x}) == '{1: x + 1}'
    assert str(Dict({1: x**2, 2: y*x})) in (
        '{1: x**2, 2: x*y}', '{2: x*y, 1: x**2}')
    assert sstr(Dict({1: x**2, 2: y*x})) == '{1: x**2, 2: x*y}'


def test_Dummy():
    assert str(d) == '_d'
    assert str(d + x) == 'x + _d'


def test_EulerGamma():
    assert str(EulerGamma) == 'EulerGamma'


def test_Exp():
    assert str(E) == 'E'


def test_factorial():
    n = Symbol('n', integer=True)
    assert str(factorial(-2)) == 'zoo'
    assert str(factorial(0)) == '1'
    assert str(factorial(7)) == '5040'
    assert str(factorial(n)) == 'factorial(n)'
    assert str(factorial(2*n)) == 'factorial(2*n)'
    assert str(factorial(factorial(n))) == 'factorial(factorial(n))'
    assert str(factorial(factorial2(n))) == 'factorial(factorial2(n))'
    assert str(factorial2(factorial(n))) == 'factorial2(factorial(n))'
    assert str(factorial2(factorial2(n))) == 'factorial2(factorial2(n))'
    assert str(subfactorial(3)) == '2'
    assert str(subfactorial(n)) == 'subfactorial(n)'
    assert str(subfactorial(2*n)) == 'subfactorial(2*n)'


def test_Function():
    f = Function('f')
    fx = f(x)
    w = WildFunction('w')
    assert str(f) == 'f'
    assert str(fx) == 'f(x)'
    assert str(w) == 'w_'


def test_Geometry():
    assert sstr(Point(0, 0)) == 'Point(0, 0)'
    assert sstr(Circle(Point(0, 0), 3)) == 'Circle(Point(0, 0), 3)'


def test_GoldenRatio():
    assert str(GoldenRatio) == 'GoldenRatio'


def test_ImaginaryUnit():
    assert str(I) == 'I'


def test_Infinity():
    assert str(oo) == 'oo'
    assert str(oo*I) == 'oo*I'


def test_Integer():
    assert str(Integer(-1)) == '-1'
    assert str(Integer(1)) == '1'
    assert str(Integer(-3)) == '-3'
    assert str(Integer(0)) == '0'
    assert str(Integer(25)) == '25'


def test_Integral():
    assert str(Integral(sin(x), y)) == 'Integral(sin(x), y)'
    assert str(Integral(sin(x), (y, 0, 1))) == 'Integral(sin(x), (y, 0, 1))'


def test_Interval():
    a = Symbol('a', extended_real=True)
    assert str(Interval(0, a)) == '[0, a]'
    assert str(Interval(0, a, False, False)) == '[0, a]'
    assert str(Interval(0, a, True, False)) == '(0, a]'
    assert str(Interval(0, a, False, True)) == '[0, a)'
    assert str(Interval(0, a, True, True)) == '(0, a)'


def test_Lambda():
    assert str(Lambda(d, d**2)) == 'Lambda(_d, _d**2)'
    # issue sympy/sympy#2908
    assert str(Lambda((), 1)) == 'Lambda((), 1)'
    assert str(Lambda((), x)) == 'Lambda((), x)'


def test_Limit():
    assert str(Limit(sin(x)/x, x, y)) == 'Limit(sin(x)/x, x, y)'
    assert str(Limit(1/x, x, 0)) == 'Limit(1/x, x, 0)'
    assert str(
        Limit(sin(x)/x, x, y, dir='-')) == "Limit(sin(x)/x, x, y, dir='-')"


def test_list():
    assert sstr([x]) == '[x]'
    assert str([x]) == "[Symbol('x')]"
    assert sstr([x**2, x*y + 1]) == '[x**2, x*y + 1]'
    assert str([x**2, x*y + 1]) == "[Pow(Symbol('x'), Integer(2)), Add(Mul(Symbol('x'), Symbol('y')), Integer(1))]"
    assert sstr([x**2, [y + x]]) == '[x**2, [x + y]]'
    assert str([x**2, [y + x]]) == "[Pow(Symbol('x'), Integer(2)), [Add(Symbol('x'), Symbol('y'))]]"


def test_Matrix_str():
    M = Matrix([[x**+1, 1], [y, x + y]])
    assert str(M) == 'Matrix([\n[x,     1],\n[y, x + y]])'
    assert sstr(M) == 'Matrix([\n[x,     1],\n[y, x + y]])'
    M = Matrix([[1]])
    assert str(M) == sstr(M) == 'Matrix([[1]])'
    M = Matrix([[1, 2]])
    assert str(M) == sstr(M) == 'Matrix([[1, 2]])'
    M = Matrix()
    assert str(M) == sstr(M) == 'Matrix(0, 0, [])'
    M = Matrix(0, 1, lambda i, j: 0)
    assert str(M) == sstr(M) == 'Matrix(0, 1, [])'


def test_BlockMatrix():
    n, m = symbols('n m', integer=True)
    X = MatrixSymbol('X', n, n)
    Y = MatrixSymbol('Y', m, m)
    Z = MatrixSymbol('Z', n, m)
    B = BlockMatrix([[X, Z], [ZeroMatrix(m, n), Y]])
    assert str(B) == 'Matrix([\n[X, Z],\n[0, Y]])'


def test_Mul():
    assert str(x/y) == 'x/y'
    assert str(y/x) == 'y/x'
    assert str(x/y/z) == 'x/(y*z)'
    assert str((x + 1)/(y + 2)) == '(x + 1)/(y + 2)'
    assert str(2*x/3) == '2*x/3'
    assert str(-2*x/3) == '-2*x/3'
    assert str(-1.0*x) == '-1.0*x'
    assert str(1.0*x) == '1.0*x'

    class CustomClass1(Expr):
        is_commutative = True

    class CustomClass2(Expr):
        is_commutative = True
    cc1 = CustomClass1()
    cc2 = CustomClass2()
    assert str(2*cc1) == '2*CustomClass1()'
    assert str(cc1*2) == '2*CustomClass1()'
    assert str(cc1*Float('1.5')) == '1.5*CustomClass1()'
    assert str(cc2*2) == '2*CustomClass2()'
    assert str(cc2*2*cc1) == '2*CustomClass1()*CustomClass2()'
    assert str(cc1*2*cc2) == '2*CustomClass1()*CustomClass2()'
    assert str(Mul(1, 1, evaluate=False)) == '1*1'


def test_NaN():
    assert str(nan) == 'nan'


def test_NegativeInfinity():
    assert str(-oo) == '-oo'


def test_Order():
    assert str(O(x)) == 'O(x)'
    assert str(O(x**2)) == 'O(x**2)'
    assert str(O(x*y)) == 'O(x*y, x, y)'
    assert str(O(x, x)) == 'O(x)'
    assert str(O(x, (x, 0))) == 'O(x)'
    assert str(O(x, (x, oo))) == 'O(x, (x, oo))'
    assert str(O(x, x, y)) == 'O(x, x, y)'
    assert str(O(x, x, y)) == 'O(x, x, y)'
    assert str(O(x, (x, oo), (y, oo))) == 'O(x, (x, oo), (y, oo))'


def test_Permutation_Cycle():
    # general principle: economically, canonically show all moved elements
    # and the size of the permutation.

    for p, s in [
        (Cycle(),
         'Cycle()'),
        (Cycle(2),
         'Cycle(2)'),
        (Cycle(2, 1),
         'Cycle(1, 2)'),
        (Cycle(1, 2)(5)(6, 7)(10),
         'Cycle(1, 2)(6, 7)(10)'),
        (Cycle(3, 4)(1, 2)(3, 4),
         'Cycle(1, 2)(4)'),
    ]:
        assert str(p) == s

    Permutation.print_cyclic = False
    for p, s in [
        (Permutation([]),
         'Permutation([])'),
        (Permutation([], size=1),
         'Permutation([0])'),
        (Permutation([], size=2),
         'Permutation([0, 1])'),
        (Permutation([], size=10),
         'Permutation([], size=10)'),
        (Permutation([1, 0, 2]),
         'Permutation([1, 0, 2])'),
        (Permutation([1, 0, 2, 3, 4, 5]),
         'Permutation([1, 0], size=6)'),
        (Permutation([1, 0, 2, 3, 4, 5], size=10),
         'Permutation([1, 0], size=10)'),
    ]:
        assert str(p) == s

    Permutation.print_cyclic = True
    for p, s in [
        (Permutation([]),
         'Permutation()'),
        (Permutation([], size=1),
         'Permutation(0)'),
        (Permutation([], size=2),
         'Permutation(1)'),
        (Permutation([], size=10),
         'Permutation(9)'),
        (Permutation([1, 0, 2]),
         'Permutation(2)(0, 1)'),
        (Permutation([1, 0, 2, 3, 4, 5]),
         'Permutation(5)(0, 1)'),
        (Permutation([1, 0, 2, 3, 4, 5], size=10),
         'Permutation(9)(0, 1)'),
        (Permutation([0, 1, 3, 2, 4, 5], size=10),
         'Permutation(9)(2, 3)'),
    ]:
        assert str(p) == s

    assert str(AbelianGroup(3, 4)) == ('PermutationGroup([\n    '
                                       'Permutation(6)(0, 1, 2),\n'
                                       '    Permutation(3, 4, 5, 6)])')
    assert sstr(Cycle(1, 2)) == repr(Cycle(1, 2))


def test_Pi():
    assert str(pi) == 'pi'


def test_Poly():
    assert str(Poly(0, x)) == "Poly(0, x, domain='ZZ')"
    assert str(Poly(1, x)) == "Poly(1, x, domain='ZZ')"
    assert str(Poly(x, x)) == "Poly(x, x, domain='ZZ')"

    assert str(Poly(2*x + 1, x)) == "Poly(2*x + 1, x, domain='ZZ')"
    assert str(Poly(2*x - 1, x)) == "Poly(2*x - 1, x, domain='ZZ')"

    assert str(Poly(-1, x)) == "Poly(-1, x, domain='ZZ')"
    assert str(Poly(-x, x)) == "Poly(-x, x, domain='ZZ')"

    assert str(Poly(-2*x + 1, x)) == "Poly(-2*x + 1, x, domain='ZZ')"
    assert str(Poly(-2*x - 1, x)) == "Poly(-2*x - 1, x, domain='ZZ')"

    assert str(Poly(x - 1, x)) == "Poly(x - 1, x, domain='ZZ')"

    assert str(
        Poly(x**2 + 1 + y, x)) == "Poly(x**2 + y + 1, x, domain='ZZ[y]')"
    assert str(
        Poly(x**2 - 1 + y, x)) == "Poly(x**2 + y - 1, x, domain='ZZ[y]')"

    assert str(Poly(x**2 + I*x, x)) == "Poly(x**2 + I*x, x, domain='QQ<I>')"
    assert str(Poly(x**2 - I*x, x)) == "Poly(x**2 - I*x, x, domain='QQ<I>')"

    assert str(Poly(-x*y*z + x*y - 1, x, y, z)
               ) == "Poly(-x*y*z + x*y - 1, x, y, z, domain='ZZ')"
    assert str(Poly(-w*x**21*y**7*z + (1 + w)*z**3 - 2*x*z + 1, x, y, z)) == \
        "Poly(-w*x**21*y**7*z - 2*x*z + (w + 1)*z**3 + 1, x, y, z, domain='ZZ[w]')"

    assert str(Poly(x**2 + 1, x, modulus=2)) == 'Poly(x**2 + 1, x, modulus=2)'
    assert str(Poly(2*x**2 + 3*x + 4, x, modulus=17)) == 'Poly(2*x**2 + 3*x + 4, x, modulus=17)'

    assert str(Poly(2**(2*x), 2**x)) == "Poly((2**x)**2, 2**x, domain='ZZ')"
    assert str(Poly((x + 1)**2, x + 1, expand=False)) == "Poly((x + 1)**2, x + 1, domain='ZZ')"

    assert str(Poly(y*x*sqrt(3), x, sqrt(3))) == \
        "Poly(y*x*sqrt(3), x, sqrt(3), domain='ZZ[y]')"


def test_PolynomialRing():
    assert str(ZZ.inject('x')) == 'ZZ[x]'
    assert str(QQ.poly_ring('x', 'y', order=grlex)) == 'QQ[x,y]'
    assert str(ZZ.inject('x', 'y', 'z', 't').eject('t')) == 'ZZ[t][x,y,z]'


def test_FractionField():
    assert str(ZZ.inject('x').field) == 'ZZ(x)'
    assert str(QQ.frac_field('x', 'y', order=grlex)) == 'QQ(x,y)'
    assert str(ZZ.inject('x', 'y', 'z', 't').eject('t').field) == 'ZZ[t](x,y,z)'


def test_PolyElement():
    Ruv,  u, v = ring('u v', ZZ)
    _,  x, y, _ = ring('x y z', Ruv)

    assert str(x - x) == '0'
    assert str(x - 1) == 'x - 1'
    assert str(x + 1) == 'x + 1'

    assert str((u**2 + 3*u*v + 1)*x**2*y + u + 1) == '(u**2 + 3*u*v + 1)*x**2*y + u + 1'
    assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x) == '(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x'
    assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1) == '(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1'
    assert str((-u**2 + 3*u*v - 1)*x**2*y - (u + 1)*x - 1) == '-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1'

    assert str(-(v**2 + v + 1)*x + 3*u*v + 1) == '-(v**2 + v + 1)*x + 3*u*v + 1'
    assert str(-(v**2 + v + 1)*x - 3*u*v + 1) == '-(v**2 + v + 1)*x - 3*u*v + 1'

    K, t = field('t', ZZ)
    _, x = ring('x', K)

    assert str(x/t) == '1/t*x'

    assert str(CC.inject(w).convert(I)) == '(0.0 + 1.0j)'


def test_FracElement():
    Fuv,  u, v = field('u v', ZZ)
    _,  x, y, z, t = field('x y z t', Fuv)

    assert str(x - x) == '0'
    assert str(x - 1) == 'x - 1'
    assert str(x + 1) == 'x + 1'

    assert str(x/3) == 'x/3'
    assert str(x/z) == 'x/z'
    assert str(x*y/z) == 'x*y/z'
    assert str(x/(z*t)) == 'x/(z*t)'
    assert str(x*y/(z*t)) == 'x*y/(z*t)'

    assert str((x - 1)/y) == '(x - 1)/y'
    assert str((x + 1)/y) == '(x + 1)/y'
    assert str((-x - 1)/y) == '(-x - 1)/y'
    assert str((x + 1)/(y*z)) == '(x + 1)/(y*z)'
    assert str(-y/(x + 1)) == '-y/(x + 1)'
    assert str(y*z/(x + 1)) == 'y*z/(x + 1)'

    assert str(((u + 1)*x*y + 1)/((v - 1)*z - 1)) == '((u + 1)*x*y + 1)/((v - 1)*z - 1)'
    assert str(((u + 1)*x*y + 1)/((v - 1)*z - t*u*v - 1)) == '((u + 1)*x*y + 1)/((v - 1)*z - u*v*t - 1)'


def test_Pow():
    assert str(x**-1) == '1/x'
    assert str(x**-2) == 'x**(-2)'
    assert str(x**2) == 'x**2'
    assert str((x + y)**-1) == '1/(x + y)'
    assert str((x + y)**-2) == '(x + y)**(-2)'
    assert str((x + y)**2) == '(x + y)**2'
    assert str((x + y)**(1 + x)) == '(x + y)**(x + 1)'
    assert str(cbrt(x)) == 'x**(1/3)'
    assert str(1/cbrt(x)) == 'x**(-1/3)'
    assert str(sqrt(sqrt(x))) == 'x**(1/4)'
    # not the same as x**-1
    assert str(x**-1.0) == 'x**(-1.0)'
    # see issue sympy/sympy#2860
    assert str(Pow(Integer(2), -1.0, evaluate=False)) == '2**(-1.0)'


def test_sqrt():
    assert str(sqrt(x)) == 'sqrt(x)'
    assert str(sqrt(x**2)) == 'sqrt(x**2)'
    assert str(1/sqrt(x)) == '1/sqrt(x)'
    assert str(1/sqrt(x**2)) == '1/sqrt(x**2)'
    assert str(y/sqrt(x)) == 'y/sqrt(x)'
    assert str(x**(1/2)) == 'x**0.5'
    assert str(1/x**(1/2)) == 'x**(-0.5)'


def test_Rational():
    n1 = Rational(1, 4)
    n2 = Rational(1, 3)
    n3 = Rational(2, 4)
    n4 = Rational(2, -4)
    n5 = Integer(0)
    n7 = Integer(3)
    n8 = Integer(-3)
    assert str(n1*n2) == '1/12'
    assert str(n1*n2) == '1/12'
    assert str(n3) == '1/2'
    assert str(n1*n3) == '1/8'
    assert str(n1 + n3) == '3/4'
    assert str(n1 + n2) == '7/12'
    assert str(n1 + n4) == '-1/4'
    assert str(n4*n4) == '1/4'
    assert str(n4 + n2) == '-1/6'
    assert str(n4 + n5) == '-1/2'
    assert str(n4*n5) == '0'
    assert str(n3 + n4) == '0'
    assert str(n1**n7) == '1/64'
    assert str(n2**n7) == '1/27'
    assert str(n2**n8) == '27'
    assert str(n7**n8) == '1/27'
    assert str(Rational('-25')) == '-25'
    assert str(Rational('1.25')) == '5/4'
    assert str(Rational('-2.6e-2')) == '-13/500'
    assert str(Rational(25, 7)) == '25/7'
    assert str(Rational(-123, 569)) == '-123/569'

    assert str(sqrt(Rational(1, 4))) == '1/2'
    assert str(sqrt(Rational(1, 36))) == '1/6'

    assert str(root(123**25, 25)) == '123'
    assert str(root(123**25 + 1, 25)) != '123'
    assert str(root(123**25 - 1, 25)) != '123'
    assert str(root(123**25 - 1, 25)) != '122'

    assert str(sqrt(Rational(81, 36))**3) == '27/8'
    assert str(1/sqrt(Rational(81, 36))**3) == '8/27'

    assert str(sqrt(-4)) == str(2*I)
    assert str(root(2, 10**10)) == '2**(1/10000000000)'


def test_Float():
    # NOTE prec is the whole number of decimal digits
    assert str(Float('1.23', dps=1 + 2)) == '1.23'
    assert str(Float('1.23456789', dps=1 + 8)) == '1.23456789'
    assert str(
        Float('1.234567890123456789', dps=1 + 18)) == '1.234567890123456789'
    assert str(pi.evalf(1 + 2)) == '3.14'
    assert str(pi.evalf(1 + 14)) == '3.14159265358979'
    assert str(pi.evalf(1 + 64)) == ('3.141592653589793238462643383279'
                                     '5028841971693993751058209749445923')
    assert str(pi.round(-1)) == '0.'
    assert str((pi**400 - (pi**400).round(1)).evalf(2, strict=False)) == '-0.e+9'
    assert str(Float(+oo)) == 'inf'
    assert str(Float(-oo)) == '-inf'


def test_Relational():
    assert str(Rel(x, y, '<')) == 'x < y'
    assert str(Rel(x + y, y, '==')) == 'Eq(x + y, y)'
    assert str(Rel(x, y, '!=')) == 'Ne(x, y)'
    assert str(Eq(x, 1) | Eq(x, 2)) == 'Eq(x, 1) | Eq(x, 2)'
    assert str(Ne(x, 1) & Ne(x, 2)) == 'Ne(x, 1) & Ne(x, 2)'


def test_RootOf():
    assert str(RootOf(x**5 + 2*x - 1, 0)) == 'RootOf(x**5 + 2*x - 1, 0)'
    assert str(RootOf(x**3 + y*x + 1, x, 0)) == 'RootOf(x**3 + x*y + 1, x, 0)'


def test_RootSum():
    f = x**5 + 2*x - 1

    assert str(
        RootSum(f, Lambda(z, z), auto=False)) == 'RootSum(x**5 + 2*x - 1)'
    assert str(RootSum(f, Lambda(
        z, z**2), auto=False)) == 'RootSum(x**5 + 2*x - 1, Lambda(z, z**2))'


def test_GroebnerBasis():
    assert str(groebner(
        [], x, y)) == "GroebnerBasis([], x, y, domain='ZZ', order='lex')"

    F = [x**2 - 3*y - x + 1, y**2 - 2*x + y - 1]

    assert str(groebner(F, order='grlex')) == \
        "GroebnerBasis([x**2 - x - 3*y + 1, y**2 - 2*x + y - 1], x, y, domain='ZZ', order='grlex')"
    assert str(groebner(F, order='lex')) == \
        "GroebnerBasis([2*x - y**2 - y + 1, y**4 + 2*y**3 - 3*y**2 - 16*y + 7], x, y, domain='ZZ', order='lex')"


def test_set():
    assert sstr(set()) == 'set()'
    assert sstr(frozenset()) == 'frozenset()'

    assert sstr({1, 2, 3}) == '{1, 2, 3}'
    assert sstr(frozenset({1, 2, 3})) == 'frozenset({1, 2, 3})'
    assert sstr(
        {1, x, x**2, x**3, x**4}) == '{1, x, x**2, x**3, x**4}'


def test_SparseMatrix():
    M = SparseMatrix([[x**+1, 1], [y, x + y]])
    assert str(M) == 'Matrix([\n[x,     1],\n[y, x + y]])'
    assert sstr(M) == 'Matrix([\n[x,     1],\n[y, x + y]])'


def test_Sum():
    assert str(summation(cos(3*z), (z, x, y))) == 'Sum(cos(3*z), (z, x, y))'
    assert str(Sum(x*y**2, (x, -2, 2), (y, -5, 5))) == \
        'Sum(x*y**2, (x, -2, 2), (y, -5, 5))'


def test_Symbol():
    assert str(y) == 'y'
    assert str(x) == 'x'
    e = x
    assert str(e) == 'x'


def test_tuple():
    assert sstr((x,)) == '(x,)'
    assert str((x,)) == "(Symbol('x'),)"
    assert sstr((x + y, 1 + x)) == '(x + y, x + 1)'
    assert str((x + y, 1 + x)) == "(Add(Symbol('x'), Symbol('y')), Add(Symbol('x'), Integer(1)))"
    assert sstr((x + y, (1 + x, x**2))) == '(x + y, (x + 1, x**2))'
    assert str((x + y, (1 + x, x**2))) == "(Add(Symbol('x'), Symbol('y')), (Add(Symbol('x'), Integer(1)), Pow(Symbol('x'), Integer(2))))"


def test_wild_str():
    # Check expressions containing Wild not causing infinite recursion
    w = Wild('x')
    assert str(w + 1) == 'x_ + 1'
    assert str(exp(2**w) + 5) == 'E**(2**x_) + 5'
    assert str(3*w + 1) == '3*x_ + 1'
    assert str(1/w + 1) == '1 + 1/x_'
    assert str(w**2 + 1) == 'x_**2 + 1'
    assert str(1/(1 - w)) == '1/(-x_ + 1)'


def test_zeta():
    assert str(zeta(3)) == 'zeta(3)'


def test_sympyissue_3101():
    e = x - y
    a = str(e)
    b = str(e)
    assert a == b


def test_sympyissue_3103():
    e = -2*sqrt(x) - y/sqrt(x)/2
    assert str(e) not in ['(-2)*x**1/2(-1/2)*x**(-1/2)*y',
                          '-2*x**1/2(-1/2)*x**(-1/2)*y', '-2*x**1/2-1/2*x**-1/2*w']
    assert str(e) == '-2*sqrt(x) - y/(2*sqrt(x))'


def test_sympyissue_4021():
    e = Integral(x, x) + 1
    assert str(e) == 'Integral(x, x) + 1'


def test_sstrrepr():
    assert sstr('abc') == 'abc'
    assert sstrrepr('abc') == "'abc'"

    e = ['a', 'b', 'c', x]
    assert sstr(e) == '[a, b, c, x]'
    assert sstrrepr(e) == "['a', 'b', 'c', x]"


def test_infinity():
    assert sstr(oo*I) == 'oo*I'


def test_full_prec():
    assert sstr(Float(0.3), full_prec=True) == '0.300000000000000'
    assert sstr(Float(0.3), full_prec='auto') == '0.300000000000000'
    assert sstr(Float(0.3), full_prec=False) == '0.3'
    assert sstr(Float(0.3)*x, full_prec=True) in [
        '0.300000000000000*x',
        'x*0.300000000000000'
    ]
    assert sstr(Float(0.3)*x, full_prec='auto') in [
        '0.3*x',
        'x*0.3'
    ]
    assert sstr(Float(0.3)*x, full_prec=False) in [
        '0.3*x',
        'x*0.3'
    ]


def test_noncommutative():
    A, B, C = symbols('A,B,C', commutative=False)

    assert sstr(A*B*C**-1) == 'A*B*C**(-1)'
    assert sstr(C**-1*A*B) == 'C**(-1)*A*B'
    assert sstr(A*C**-1*B) == 'A*C**(-1)*B'
    assert sstr(sqrt(A)) == 'sqrt(A)'
    assert sstr(1/sqrt(A)) == 'A**(-1/2)'


def test_empty_printer():
    str_printer = StrPrinter()
    assert str_printer.emptyPrinter('foo') == 'foo'
    assert str_printer.emptyPrinter(x*y) == 'x*y'
    assert str_printer.emptyPrinter(32) == '32'


def test_settings():
    pytest.raises(TypeError, lambda: sstr(Integer(4), method='garbage'))


def test_RandomDomain():
    X = Normal('x1', 0, 1)
    assert str(where(X > 0)) == 'Domain: (0 < x1) & (x1 < oo)'

    D = Die('d1', 6)
    assert str(where(D > 4)) == 'Domain: Eq(d1, 5) | Eq(d1, 6)'

    A = Exponential('a', 1)
    B = Exponential('b', 1)
    assert str(pspace(Tuple(A, B)).domain) == 'Domain: (0 <= a) & (0 <= b) & (a < oo) & (b < oo)'


def test_FiniteSet():
    assert str(FiniteSet(*range(1, 51))) == '{1, 2, 3, ..., 48, 49, 50}'
    assert str(FiniteSet(*range(1, 6))) == '{1, 2, 3, 4, 5}'


def test_PrettyPoly():
    F = QQ.inject(x, y).field
    R = QQ.inject(x, y)
    assert sstr(F.convert(x/(x + y))) == sstr(x/(x + y))
    assert sstr(R.convert(x + y)) == sstr(x + y)


def test_Tr():
    A, B = symbols('A B', commutative=False)
    t = Tr(A*B)
    assert str(t) == 'Tr(A*B)'


def test_sympyissue_6387():
    assert str(factor(-3.0*z + 3)) == '-3.0*(1.0*z - 1.0)'


def test_MatMul_MatAdd():
    assert str(2*(MatrixSymbol('X', 2, 2) + MatrixSymbol('Y', 2, 2))) == \
        '2*(X + Y)'


def test_MatPow():
    assert str(MatrixSymbol('M', 2, 2)**2) == 'M**2'


def test_MatrixSlice():
    assert str(MatrixSymbol('X', 10, 10)[:5, 1:9:2]) == 'X[:5, 1:9:2]'
    assert str(MatrixSymbol('X', 10, 10)[5, :5:2]) == 'X[5, :5:2]'


def test_MatrixInverse():
    assert str(MatrixSymbol('X', 3, 3).inverse()) == 'X^-1'


def test_true_false():
    assert str(true) == repr(true) == sstr(true) == 'true'
    assert str(false) == repr(false) == sstr(false) == 'false'


def test_Equivalent():
    assert str(Equivalent(y, x)) == 'Equivalent(x, y)'


def test_Xor():
    assert str(Xor(y, x, evaluate=False)) == 'Xor(x, y)'


def test_Complement():
    assert str(Complement(S.Reals, S.Naturals)) == '(-oo, oo) \\ Naturals()'


def test_SymmetricDifference():
    assert str(SymmetricDifference(Interval(2, 3), Interval(3, 4), evaluate=False)) == \
        'SymmetricDifference([2, 3], [3, 4])'


def test_AlgebraicElement():
    K = QQ.algebraic_field(sqrt(2))
    assert str(K([0, 1])) == 'sqrt(2)'


def test_Differential():
    tp = TensorProduct(R2.dx, R2.dy)
    assert sstr(LieDerivative(R2.e_x, tp)) == 'LieDerivative(e_x, TensorProduct(dx, dy))'

    g = Function('g')
    s_field = g(R2.x, R2.y)
    assert sstr(Differential(s_field)) == 'd(g(x, y))'


def test_ImmutableDenseNDimArray():
    m = [2*i + j for i in range(2) for j in range(2)]
    assert sstr(ImmutableDenseNDimArray(m, (2, 2))) == '[[0, 1], [2, 3]]'