test_latex.py

from sympy.tensor.toperators import PartialDerivative

from sympy import (
    Abs, Chi, Ci, CosineTransform, Dict, Ei, Eq, FallingFactorial,
    FiniteSet, Float, FourierTransform, Function, Indexed, IndexedBase, Integral,
    Interval, InverseCosineTransform, InverseFourierTransform, Derivative,
    InverseLaplaceTransform, InverseMellinTransform, InverseSineTransform,
    Lambda, LaplaceTransform, Limit, Matrix, Max, MellinTransform, Min, Mul,
    Order, Piecewise, Poly, ring, field, ZZ, Pow, Product, Range, Rational,
    RisingFactorial, rootof, RootSum, S, Shi, Si, SineTransform, Subs,
    Sum, Symbol, ImageSet, Tuple, Ynm, Znm, arg, asin, acsc, asinh, Mod,
    assoc_laguerre, assoc_legendre, beta, binomial, catalan, ceiling,
    chebyshevt, chebyshevu, conjugate, cot, coth, diff, dirichlet_eta, euler,
    exp, expint, factorial, factorial2, floor, gamma, gegenbauer, hermite,
    hyper, im, jacobi, laguerre, legendre, lerchphi, log, frac,
    meijerg, oo, polar_lift, polylog, re, root, sin, sqrt, symbols,
    uppergamma, zeta, subfactorial, totient, elliptic_k, elliptic_f,
    elliptic_e, elliptic_pi, cos, tan, Wild, true, false, Equivalent, Not,
    Contains, divisor_sigma, SeqPer, SeqFormula, MatrixSlice,
    SeqAdd, SeqMul, fourier_series, pi, ConditionSet, ComplexRegion, fps,
    AccumBounds, reduced_totient, primenu, primeomega, SingularityFunction,
    stieltjes, mathieuc, mathieus, mathieucprime, mathieusprime,
    UnevaluatedExpr, Quaternion, I, KroneckerProduct, LambertW)

from sympy.ntheory.factor_ import udivisor_sigma

from sympy.abc import mu, tau
from sympy.printing.latex import (latex, translate, greek_letters_set,
                                  tex_greek_dictionary, multiline_latex)
from sympy.tensor.array import (ImmutableDenseNDimArray,
                                ImmutableSparseNDimArray,
                                MutableSparseNDimArray,
                                MutableDenseNDimArray,
                                tensorproduct)
from sympy.testing.pytest import XFAIL, raises
from sympy.functions import DiracDelta, Heaviside, KroneckerDelta, LeviCivita
from sympy.functions.combinatorial.numbers import bernoulli, bell, lucas, \
    fibonacci, tribonacci
from sympy.logic import Implies
from sympy.logic.boolalg import And, Or, Xor
from sympy.physics.quantum import Commutator, Operator
from sympy.physics.units import meter, gibibyte, microgram, second
from sympy.core.trace import Tr
from sympy.combinatorics.permutations import \
    Cycle, Permutation, AppliedPermutation
from sympy.matrices.expressions.permutation import PermutationMatrix
from sympy import MatrixSymbol, ln
from sympy.vector import CoordSys3D, Cross, Curl, Dot, Divergence, Gradient, Laplacian
from sympy.sets.setexpr import SetExpr
from sympy.sets.sets import \
    Union, Intersection, Complement, SymmetricDifference, ProductSet

import sympy as sym


class lowergamma(sym.lowergamma):
    pass   # testing notation inheritance by a subclass with same name


x, y, z, t, a, b, c = symbols('x y z t a b c')
k, m, n = symbols('k m n', integer=True)


def test_printmethod():
    class R(Abs):
        def _latex(self, printer):
            return "foo(%s)" % printer._print(self.args[0])
    assert latex(R(x)) == "foo(x)"

    class R(Abs):
        def _latex(self, printer):
            return "foo"
    assert latex(R(x)) == "foo"


def test_latex_basic():
    assert latex(1 + x) == "x + 1"
    assert latex(x**2) == "x^{2}"
    assert latex(x**(1 + x)) == "x^{x + 1}"
    assert latex(x**3 + x + 1 + x**2) == "x^{3} + x^{2} + x + 1"

    assert latex(2*x*y) == "2 x y"
    assert latex(2*x*y, mul_symbol='dot') == r"2 \cdot x \cdot y"
    assert latex(3*x**2*y, mul_symbol='\\,') == r"3\,x^{2}\,y"
    assert latex(1.5*3**x, mul_symbol='\\,') == r"1.5 \cdot 3^{x}"

    assert latex(1/x) == r"\frac{1}{x}"
    assert latex(1/x, fold_short_frac=True) == "1 / x"
    assert latex(-S(3)/2) == r"- \frac{3}{2}"
    assert latex(-S(3)/2, fold_short_frac=True) == r"- 3 / 2"
    assert latex(1/x**2) == r"\frac{1}{x^{2}}"
    assert latex(1/(x + y)/2) == r"\frac{1}{2 \left(x + y\right)}"
    assert latex(x/2) == r"\frac{x}{2}"
    assert latex(x/2, fold_short_frac=True) == "x / 2"
    assert latex((x + y)/(2*x)) == r"\frac{x + y}{2 x}"
    assert latex((x + y)/(2*x), fold_short_frac=True) == \
        r"\left(x + y\right) / 2 x"
    assert latex((x + y)/(2*x), long_frac_ratio=0) == \
        r"\frac{1}{2 x} \left(x + y\right)"
    assert latex((x + y)/x) == r"\frac{x + y}{x}"
    assert latex((x + y)/x, long_frac_ratio=3) == r"\frac{x + y}{x}"
    assert latex((2*sqrt(2)*x)/3) == r"\frac{2 \sqrt{2} x}{3}"
    assert latex((2*sqrt(2)*x)/3, long_frac_ratio=2) == \
        r"\frac{2 x}{3} \sqrt{2}"
    assert latex(binomial(x, y)) == r"{\binom{x}{y}}"

    x_star = Symbol('x^*')
    f = Function('f')
    assert latex(x_star**2) == r"\left(x^{*}\right)^{2}"
    assert latex(x_star**2, parenthesize_super=False) == r"{x^{*}}^{2}"
    assert latex(Derivative(f(x_star), x_star,2)) == r"\frac{d^{2}}{d \left(x^{*}\right)^{2}} f{\left(x^{*} \right)}"
    assert latex(Derivative(f(x_star), x_star,2), parenthesize_super=False) == r"\frac{d^{2}}{d {x^{*}}^{2}} f{\left(x^{*} \right)}"

    assert latex(2*Integral(x, x)/3) == r"\frac{2 \int x\, dx}{3}"
    assert latex(2*Integral(x, x)/3, fold_short_frac=True) == \
        r"\left(2 \int x\, dx\right) / 3"

    assert latex(sqrt(x)) == r"\sqrt{x}"
    assert latex(x**Rational(1, 3)) == r"\sqrt[3]{x}"
    assert latex(x**Rational(1, 3), root_notation=False) == r"x^{\frac{1}{3}}"
    assert latex(sqrt(x)**3) == r"x^{\frac{3}{2}}"
    assert latex(sqrt(x), itex=True) == r"\sqrt{x}"
    assert latex(x**Rational(1, 3), itex=True) == r"\root{3}{x}"
    assert latex(sqrt(x)**3, itex=True) == r"x^{\frac{3}{2}}"
    assert latex(x**Rational(3, 4)) == r"x^{\frac{3}{4}}"
    assert latex(x**Rational(3, 4), fold_frac_powers=True) == "x^{3/4}"
    assert latex((x + 1)**Rational(3, 4)) == \
        r"\left(x + 1\right)^{\frac{3}{4}}"
    assert latex((x + 1)**Rational(3, 4), fold_frac_powers=True) == \
        r"\left(x + 1\right)^{3/4}"

    assert latex(1.5e20*x) == r"1.5 \cdot 10^{20} x"
    assert latex(1.5e20*x, mul_symbol='dot') == r"1.5 \cdot 10^{20} \cdot x"
    assert latex(1.5e20*x, mul_symbol='times') == \
        r"1.5 \times 10^{20} \times x"

    assert latex(1/sin(x)) == r"\frac{1}{\sin{\left(x \right)}}"
    assert latex(sin(x)**-1) == r"\frac{1}{\sin{\left(x \right)}}"
    assert latex(sin(x)**Rational(3, 2)) == \
        r"\sin^{\frac{3}{2}}{\left(x \right)}"
    assert latex(sin(x)**Rational(3, 2), fold_frac_powers=True) == \
        r"\sin^{3/2}{\left(x \right)}"

    assert latex(~x) == r"\neg x"
    assert latex(x & y) == r"x \wedge y"
    assert latex(x & y & z) == r"x \wedge y \wedge z"
    assert latex(x | y) == r"x \vee y"
    assert latex(x | y | z) == r"x \vee y \vee z"
    assert latex((x & y) | z) == r"z \vee \left(x \wedge y\right)"
    assert latex(Implies(x, y)) == r"x \Rightarrow y"
    assert latex(~(x >> ~y)) == r"x \not\Rightarrow \neg y"
    assert latex(Implies(Or(x,y), z)) == r"\left(x \vee y\right) \Rightarrow z"
    assert latex(Implies(z, Or(x,y))) == r"z \Rightarrow \left(x \vee y\right)"
    assert latex(~(x & y)) == r"\neg \left(x \wedge y\right)"

    assert latex(~x, symbol_names={x: "x_i"}) == r"\neg x_i"
    assert latex(x & y, symbol_names={x: "x_i", y: "y_i"}) == \
        r"x_i \wedge y_i"
    assert latex(x & y & z, symbol_names={x: "x_i", y: "y_i", z: "z_i"}) == \
        r"x_i \wedge y_i \wedge z_i"
    assert latex(x | y, symbol_names={x: "x_i", y: "y_i"}) == r"x_i \vee y_i"
    assert latex(x | y | z, symbol_names={x: "x_i", y: "y_i", z: "z_i"}) == \
        r"x_i \vee y_i \vee z_i"
    assert latex((x & y) | z, symbol_names={x: "x_i", y: "y_i", z: "z_i"}) == \
        r"z_i \vee \left(x_i \wedge y_i\right)"
    assert latex(Implies(x, y), symbol_names={x: "x_i", y: "y_i"}) == \
        r"x_i \Rightarrow y_i"

    p = Symbol('p', positive=True)
    assert latex(exp(-p)*log(p)) == r"e^{- p} \log{\left(p \right)}"


def test_latex_builtins():
    assert latex(True) == r"\text{True}"
    assert latex(False) == r"\text{False}"
    assert latex(None) == r"\text{None}"
    assert latex(true) == r"\text{True}"
    assert latex(false) == r'\text{False}'


def test_latex_SingularityFunction():
    assert latex(SingularityFunction(x, 4, 5)) == \
        r"{\left\langle x - 4 \right\rangle}^{5}"
    assert latex(SingularityFunction(x, -3, 4)) == \
        r"{\left\langle x + 3 \right\rangle}^{4}"
    assert latex(SingularityFunction(x, 0, 4)) == \
        r"{\left\langle x \right\rangle}^{4}"
    assert latex(SingularityFunction(x, a, n)) == \
        r"{\left\langle - a + x \right\rangle}^{n}"
    assert latex(SingularityFunction(x, 4, -2)) == \
        r"{\left\langle x - 4 \right\rangle}^{-2}"
    assert latex(SingularityFunction(x, 4, -1)) == \
        r"{\left\langle x - 4 \right\rangle}^{-1}"


def test_latex_cycle():
    assert latex(Cycle(1, 2, 4)) == r"\left( 1\; 2\; 4\right)"
    assert latex(Cycle(1, 2)(4, 5, 6)) == \
        r"\left( 1\; 2\right)\left( 4\; 5\; 6\right)"
    assert latex(Cycle()) == r"\left( \right)"


def test_latex_permutation():
    assert latex(Permutation(1, 2, 4)) == r"\left( 1\; 2\; 4\right)"
    assert latex(Permutation(1, 2)(4, 5, 6)) == \
        r"\left( 1\; 2\right)\left( 4\; 5\; 6\right)"
    assert latex(Permutation()) == r"\left( \right)"
    assert latex(Permutation(2, 4)*Permutation(5)) == \
        r"\left( 2\; 4\right)\left( 5\right)"
    assert latex(Permutation(5)) == r"\left( 5\right)"

    assert latex(Permutation(0, 1), perm_cyclic=False) == \
        r"\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}"
    assert latex(Permutation(0, 1)(2, 3), perm_cyclic=False) == \
        r"\begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 2 \end{pmatrix}"
    assert latex(Permutation(), perm_cyclic=False) == \
        r"\left( \right)"


def test_latex_Float():
    assert latex(Float(1.0e100)) == r"1.0 \cdot 10^{100}"
    assert latex(Float(1.0e-100)) == r"1.0 \cdot 10^{-100}"
    assert latex(Float(1.0e-100), mul_symbol="times") == \
        r"1.0 \times 10^{-100}"
    assert latex(Float('10000.0'), full_prec=False, min=-2, max=2) == \
        r"1.0 \cdot 10^{4}"
    assert latex(Float('10000.0'), full_prec=False, min=-2, max=4) == \
        r"1.0 \cdot 10^{4}"
    assert latex(Float('10000.0'), full_prec=False, min=-2, max=5) == \
        r"10000.0"
    assert latex(Float('0.099999'), full_prec=True,  min=-2, max=5) == \
        r"9.99990000000000 \cdot 10^{-2}"


def test_latex_vector_expressions():
    A = CoordSys3D('A')

    assert latex(Cross(A.i, A.j*A.x*3+A.k)) == \
        r"\mathbf{\hat{i}_{A}} \times \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}} + \mathbf{\hat{k}_{A}}\right)"
    assert latex(Cross(A.i, A.j)) == \
        r"\mathbf{\hat{i}_{A}} \times \mathbf{\hat{j}_{A}}"
    assert latex(x*Cross(A.i, A.j)) == \
        r"x \left(\mathbf{\hat{i}_{A}} \times \mathbf{\hat{j}_{A}}\right)"
    assert latex(Cross(x*A.i, A.j)) == \
        r'- \mathbf{\hat{j}_{A}} \times \left((x)\mathbf{\hat{i}_{A}}\right)'

    assert latex(Curl(3*A.x*A.j)) == \
        r"\nabla\times \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)"
    assert latex(Curl(3*A.x*A.j+A.i)) == \
        r"\nabla\times \left(\mathbf{\hat{i}_{A}} + (3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)"
    assert latex(Curl(3*x*A.x*A.j)) == \
        r"\nabla\times \left((3 \mathbf{{x}_{A}} x)\mathbf{\hat{j}_{A}}\right)"
    assert latex(x*Curl(3*A.x*A.j)) == \
        r"x \left(\nabla\times \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)\right)"

    assert latex(Divergence(3*A.x*A.j+A.i)) == \
        r"\nabla\cdot \left(\mathbf{\hat{i}_{A}} + (3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)"
    assert latex(Divergence(3*A.x*A.j)) == \
        r"\nabla\cdot \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)"
    assert latex(x*Divergence(3*A.x*A.j)) == \
        r"x \left(\nabla\cdot \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)\right)"

    assert latex(Dot(A.i, A.j*A.x*3+A.k)) == \
        r"\mathbf{\hat{i}_{A}} \cdot \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}} + \mathbf{\hat{k}_{A}}\right)"
    assert latex(Dot(A.i, A.j)) == \
        r"\mathbf{\hat{i}_{A}} \cdot \mathbf{\hat{j}_{A}}"
    assert latex(Dot(x*A.i, A.j)) == \
        r"\mathbf{\hat{j}_{A}} \cdot \left((x)\mathbf{\hat{i}_{A}}\right)"
    assert latex(x*Dot(A.i, A.j)) == \
        r"x \left(\mathbf{\hat{i}_{A}} \cdot \mathbf{\hat{j}_{A}}\right)"

    assert latex(Gradient(A.x)) == r"\nabla \mathbf{{x}_{A}}"
    assert latex(Gradient(A.x + 3*A.y)) == \
        r"\nabla \left(\mathbf{{x}_{A}} + 3 \mathbf{{y}_{A}}\right)"
    assert latex(x*Gradient(A.x)) == r"x \left(\nabla \mathbf{{x}_{A}}\right)"
    assert latex(Gradient(x*A.x)) == r"\nabla \left(\mathbf{{x}_{A}} x\right)"

    assert latex(Laplacian(A.x)) == r"\triangle \mathbf{{x}_{A}}"
    assert latex(Laplacian(A.x + 3*A.y)) == \
        r"\triangle \left(\mathbf{{x}_{A}} + 3 \mathbf{{y}_{A}}\right)"
    assert latex(x*Laplacian(A.x)) == r"x \left(\triangle \mathbf{{x}_{A}}\right)"
    assert latex(Laplacian(x*A.x)) == r"\triangle \left(\mathbf{{x}_{A}} x\right)"

def test_latex_symbols():
    Gamma, lmbda, rho = symbols('Gamma, lambda, rho')
    tau, Tau, TAU, taU = symbols('tau, Tau, TAU, taU')
    assert latex(tau) == r"\tau"
    assert latex(Tau) == "T"
    assert latex(TAU) == r"\tau"
    assert latex(taU) == r"\tau"
    # Check that all capitalized greek letters are handled explicitly
    capitalized_letters = set(l.capitalize() for l in greek_letters_set)
    assert len(capitalized_letters - set(tex_greek_dictionary.keys())) == 0
    assert latex(Gamma + lmbda) == r"\Gamma + \lambda"
    assert latex(Gamma * lmbda) == r"\Gamma \lambda"
    assert latex(Symbol('q1')) == r"q_{1}"
    assert latex(Symbol('q21')) == r"q_{21}"
    assert latex(Symbol('epsilon0')) == r"\epsilon_{0}"
    assert latex(Symbol('omega1')) == r"\omega_{1}"
    assert latex(Symbol('91')) == r"91"
    assert latex(Symbol('alpha_new')) == r"\alpha_{new}"
    assert latex(Symbol('C^orig')) == r"C^{orig}"
    assert latex(Symbol('x^alpha')) == r"x^{\alpha}"
    assert latex(Symbol('beta^alpha')) == r"\beta^{\alpha}"
    assert latex(Symbol('e^Alpha')) == r"e^{A}"
    assert latex(Symbol('omega_alpha^beta')) == r"\omega^{\beta}_{\alpha}"
    assert latex(Symbol('omega') ** Symbol('beta')) == r"\omega^{\beta}"


@XFAIL
def test_latex_symbols_failing():
    rho, mass, volume = symbols('rho, mass, volume')
    assert latex(
        volume * rho == mass) == r"\rho \mathrm{volume} = \mathrm{mass}"
    assert latex(volume / mass * rho == 1) == \
        r"\rho \mathrm{volume} {\mathrm{mass}}^{(-1)} = 1"
    assert latex(mass**3 * volume**3) == \
        r"{\mathrm{mass}}^{3} \cdot {\mathrm{volume}}^{3}"


def test_latex_functions():
    assert latex(exp(x)) == "e^{x}"
    assert latex(exp(1) + exp(2)) == "e + e^{2}"

    f = Function('f')
    assert latex(f(x)) == r'f{\left(x \right)}'
    assert latex(f) == r'f'

    g = Function('g')
    assert latex(g(x, y)) == r'g{\left(x,y \right)}'
    assert latex(g) == r'g'

    h = Function('h')
    assert latex(h(x, y, z)) == r'h{\left(x,y,z \right)}'
    assert latex(h) == r'h'

    Li = Function('Li')
    assert latex(Li) == r'\operatorname{Li}'
    assert latex(Li(x)) == r'\operatorname{Li}{\left(x \right)}'

    mybeta = Function('beta')
    # not to be confused with the beta function
    assert latex(mybeta(x, y, z)) == r"\beta{\left(x,y,z \right)}"
    assert latex(beta(x, y)) == r'\operatorname{B}\left(x, y\right)'
    assert latex(beta(x, y)**2) == r'\operatorname{B}^{2}\left(x, y\right)'
    assert latex(mybeta(x)) == r"\beta{\left(x \right)}"
    assert latex(mybeta) == r"\beta"

    g = Function('gamma')
    # not to be confused with the gamma function
    assert latex(g(x, y, z)) == r"\gamma{\left(x,y,z \right)}"
    assert latex(g(x)) == r"\gamma{\left(x \right)}"
    assert latex(g) == r"\gamma"

    a1 = Function('a_1')

    assert latex(a1) == r"\operatorname{a_{1}}"
    assert latex(a1(x)) == r"\operatorname{a_{1}}{\left(x \right)}"

    # issue 5868
    omega1 = Function('omega1')
    assert latex(omega1) == r"\omega_{1}"
    assert latex(omega1(x)) == r"\omega_{1}{\left(x \right)}"

    assert latex(sin(x)) == r"\sin{\left(x \right)}"
    assert latex(sin(x), fold_func_brackets=True) == r"\sin {x}"
    assert latex(sin(2*x**2), fold_func_brackets=True) == \
        r"\sin {2 x^{2}}"
    assert latex(sin(x**2), fold_func_brackets=True) == \
        r"\sin {x^{2}}"

    assert latex(asin(x)**2) == r"\operatorname{asin}^{2}{\left(x \right)}"
    assert latex(asin(x)**2, inv_trig_style="full") == \
        r"\arcsin^{2}{\left(x \right)}"
    assert latex(asin(x)**2, inv_trig_style="power") == \
        r"\sin^{-1}{\left(x \right)}^{2}"
    assert latex(asin(x**2), inv_trig_style="power",
                 fold_func_brackets=True) == \
        r"\sin^{-1} {x^{2}}"
    assert latex(acsc(x), inv_trig_style="full") == \
        r"\operatorname{arccsc}{\left(x \right)}"
    assert latex(asinh(x), inv_trig_style="full") == \
        r"\operatorname{arcsinh}{\left(x \right)}"

    assert latex(factorial(k)) == r"k!"
    assert latex(factorial(-k)) == r"\left(- k\right)!"
    assert latex(factorial(k)**2) == r"k!^{2}"

    assert latex(subfactorial(k)) == r"!k"
    assert latex(subfactorial(-k)) == r"!\left(- k\right)"
    assert latex(subfactorial(k)**2) == r"\left(!k\right)^{2}"

    assert latex(factorial2(k)) == r"k!!"
    assert latex(factorial2(-k)) == r"\left(- k\right)!!"
    assert latex(factorial2(k)**2) == r"k!!^{2}"

    assert latex(binomial(2, k)) == r"{\binom{2}{k}}"
    assert latex(binomial(2, k)**2) == r"{\binom{2}{k}}^{2}"

    assert latex(FallingFactorial(3, k)) == r"{\left(3\right)}_{k}"
    assert latex(RisingFactorial(3, k)) == r"{3}^{\left(k\right)}"

    assert latex(floor(x)) == r"\left\lfloor{x}\right\rfloor"
    assert latex(ceiling(x)) == r"\left\lceil{x}\right\rceil"
    assert latex(frac(x)) == r"\operatorname{frac}{\left(x\right)}"
    assert latex(floor(x)**2) == r"\left\lfloor{x}\right\rfloor^{2}"
    assert latex(ceiling(x)**2) == r"\left\lceil{x}\right\rceil^{2}"
    assert latex(frac(x)**2) == r"\operatorname{frac}{\left(x\right)}^{2}"

    assert latex(Min(x, 2, x**3)) == r"\min\left(2, x, x^{3}\right)"
    assert latex(Min(x, y)**2) == r"\min\left(x, y\right)^{2}"
    assert latex(Max(x, 2, x**3)) == r"\max\left(2, x, x^{3}\right)"
    assert latex(Max(x, y)**2) == r"\max\left(x, y\right)^{2}"
    assert latex(Abs(x)) == r"\left|{x}\right|"
    assert latex(Abs(x)**2) == r"\left|{x}\right|^{2}"
    assert latex(re(x)) == r"\operatorname{re}{\left(x\right)}"
    assert latex(re(x + y)) == \
        r"\operatorname{re}{\left(x\right)} + \operatorname{re}{\left(y\right)}"
    assert latex(im(x)) == r"\operatorname{im}{\left(x\right)}"
    assert latex(conjugate(x)) == r"\overline{x}"
    assert latex(conjugate(x)**2) == r"\overline{x}^{2}"
    assert latex(conjugate(x**2)) == r"\overline{x}^{2}"
    assert latex(gamma(x)) == r"\Gamma\left(x\right)"
    w = Wild('w')
    assert latex(gamma(w)) == r"\Gamma\left(w\right)"
    assert latex(Order(x)) == r"O\left(x\right)"
    assert latex(Order(x, x)) == r"O\left(x\right)"
    assert latex(Order(x, (x, 0))) == r"O\left(x\right)"
    assert latex(Order(x, (x, oo))) == r"O\left(x; x\rightarrow \infty\right)"
    assert latex(Order(x - y, (x, y))) == \
        r"O\left(x - y; x\rightarrow y\right)"
    assert latex(Order(x, x, y)) == \
        r"O\left(x; \left( x, \  y\right)\rightarrow \left( 0, \  0\right)\right)"
    assert latex(Order(x, x, y)) == \
        r"O\left(x; \left( x, \  y\right)\rightarrow \left( 0, \  0\right)\right)"
    assert latex(Order(x, (x, oo), (y, oo))) == \
        r"O\left(x; \left( x, \  y\right)\rightarrow \left( \infty, \  \infty\right)\right)"
    assert latex(lowergamma(x, y)) == r'\gamma\left(x, y\right)'
    assert latex(lowergamma(x, y)**2) == r'\gamma^{2}\left(x, y\right)'
    assert latex(uppergamma(x, y)) == r'\Gamma\left(x, y\right)'
    assert latex(uppergamma(x, y)**2) == r'\Gamma^{2}\left(x, y\right)'

    assert latex(cot(x)) == r'\cot{\left(x \right)}'
    assert latex(coth(x)) == r'\coth{\left(x \right)}'
    assert latex(re(x)) == r'\operatorname{re}{\left(x\right)}'
    assert latex(im(x)) == r'\operatorname{im}{\left(x\right)}'
    assert latex(root(x, y)) == r'x^{\frac{1}{y}}'
    assert latex(arg(x)) == r'\arg{\left(x \right)}'

    assert latex(zeta(x)) == r"\zeta\left(x\right)"
    assert latex(zeta(x)**2) == r"\zeta^{2}\left(x\right)"
    assert latex(zeta(x, y)) == r"\zeta\left(x, y\right)"
    assert latex(zeta(x, y)**2) == r"\zeta^{2}\left(x, y\right)"
    assert latex(dirichlet_eta(x)) == r"\eta\left(x\right)"
    assert latex(dirichlet_eta(x)**2) == r"\eta^{2}\left(x\right)"
    assert latex(polylog(x, y)) == r"\operatorname{Li}_{x}\left(y\right)"
    assert latex(
        polylog(x, y)**2) == r"\operatorname{Li}_{x}^{2}\left(y\right)"
    assert latex(lerchphi(x, y, n)) == r"\Phi\left(x, y, n\right)"
    assert latex(lerchphi(x, y, n)**2) == r"\Phi^{2}\left(x, y, n\right)"
    assert latex(stieltjes(x)) == r"\gamma_{x}"
    assert latex(stieltjes(x)**2) == r"\gamma_{x}^{2}"
    assert latex(stieltjes(x, y)) == r"\gamma_{x}\left(y\right)"
    assert latex(stieltjes(x, y)**2) == r"\gamma_{x}\left(y\right)^{2}"

    assert latex(elliptic_k(z)) == r"K\left(z\right)"
    assert latex(elliptic_k(z)**2) == r"K^{2}\left(z\right)"
    assert latex(elliptic_f(x, y)) == r"F\left(x\middle| y\right)"
    assert latex(elliptic_f(x, y)**2) == r"F^{2}\left(x\middle| y\right)"
    assert latex(elliptic_e(x, y)) == r"E\left(x\middle| y\right)"
    assert latex(elliptic_e(x, y)**2) == r"E^{2}\left(x\middle| y\right)"
    assert latex(elliptic_e(z)) == r"E\left(z\right)"
    assert latex(elliptic_e(z)**2) == r"E^{2}\left(z\right)"
    assert latex(elliptic_pi(x, y, z)) == r"\Pi\left(x; y\middle| z\right)"
    assert latex(elliptic_pi(x, y, z)**2) == \
        r"\Pi^{2}\left(x; y\middle| z\right)"
    assert latex(elliptic_pi(x, y)) == r"\Pi\left(x\middle| y\right)"
    assert latex(elliptic_pi(x, y)**2) == r"\Pi^{2}\left(x\middle| y\right)"

    assert latex(Ei(x)) == r'\operatorname{Ei}{\left(x \right)}'
    assert latex(Ei(x)**2) == r'\operatorname{Ei}^{2}{\left(x \right)}'
    assert latex(expint(x, y)) == r'\operatorname{E}_{x}\left(y\right)'
    assert latex(expint(x, y)**2) == r'\operatorname{E}_{x}^{2}\left(y\right)'
    assert latex(Shi(x)**2) == r'\operatorname{Shi}^{2}{\left(x \right)}'
    assert latex(Si(x)**2) == r'\operatorname{Si}^{2}{\left(x \right)}'
    assert latex(Ci(x)**2) == r'\operatorname{Ci}^{2}{\left(x \right)}'
    assert latex(Chi(x)**2) == r'\operatorname{Chi}^{2}\left(x\right)'
    assert latex(Chi(x)) == r'\operatorname{Chi}\left(x\right)'
    assert latex(jacobi(n, a, b, x)) == \
        r'P_{n}^{\left(a,b\right)}\left(x\right)'
    assert latex(jacobi(n, a, b, x)**2) == \
        r'\left(P_{n}^{\left(a,b\right)}\left(x\right)\right)^{2}'
    assert latex(gegenbauer(n, a, x)) == \
        r'C_{n}^{\left(a\right)}\left(x\right)'
    assert latex(gegenbauer(n, a, x)**2) == \
        r'\left(C_{n}^{\left(a\right)}\left(x\right)\right)^{2}'
    assert latex(chebyshevt(n, x)) == r'T_{n}\left(x\right)'
    assert latex(chebyshevt(n, x)**2) == \
        r'\left(T_{n}\left(x\right)\right)^{2}'
    assert latex(chebyshevu(n, x)) == r'U_{n}\left(x\right)'
    assert latex(chebyshevu(n, x)**2) == \
        r'\left(U_{n}\left(x\right)\right)^{2}'
    assert latex(legendre(n, x)) == r'P_{n}\left(x\right)'
    assert latex(legendre(n, x)**2) == r'\left(P_{n}\left(x\right)\right)^{2}'
    assert latex(assoc_legendre(n, a, x)) == \
        r'P_{n}^{\left(a\right)}\left(x\right)'
    assert latex(assoc_legendre(n, a, x)**2) == \
        r'\left(P_{n}^{\left(a\right)}\left(x\right)\right)^{2}'
    assert latex(laguerre(n, x)) == r'L_{n}\left(x\right)'
    assert latex(laguerre(n, x)**2) == r'\left(L_{n}\left(x\right)\right)^{2}'
    assert latex(assoc_laguerre(n, a, x)) == \
        r'L_{n}^{\left(a\right)}\left(x\right)'
    assert latex(assoc_laguerre(n, a, x)**2) == \
        r'\left(L_{n}^{\left(a\right)}\left(x\right)\right)^{2}'
    assert latex(hermite(n, x)) == r'H_{n}\left(x\right)'
    assert latex(hermite(n, x)**2) == r'\left(H_{n}\left(x\right)\right)^{2}'

    theta = Symbol("theta", real=True)
    phi = Symbol("phi", real=True)
    assert latex(Ynm(n, m, theta, phi)) == r'Y_{n}^{m}\left(\theta,\phi\right)'
    assert latex(Ynm(n, m, theta, phi)**3) == \
        r'\left(Y_{n}^{m}\left(\theta,\phi\right)\right)^{3}'
    assert latex(Znm(n, m, theta, phi)) == r'Z_{n}^{m}\left(\theta,\phi\right)'
    assert latex(Znm(n, m, theta, phi)**3) == \
        r'\left(Z_{n}^{m}\left(\theta,\phi\right)\right)^{3}'

    # Test latex printing of function names with "_"
    assert latex(polar_lift(0)) == \
        r"\operatorname{polar\_lift}{\left(0 \right)}"
    assert latex(polar_lift(0)**3) == \
        r"\operatorname{polar\_lift}^{3}{\left(0 \right)}"

    assert latex(totient(n)) == r'\phi\left(n\right)'
    assert latex(totient(n) ** 2) == r'\left(\phi\left(n\right)\right)^{2}'

    assert latex(reduced_totient(n)) == r'\lambda\left(n\right)'
    assert latex(reduced_totient(n) ** 2) == \
        r'\left(\lambda\left(n\right)\right)^{2}'

    assert latex(divisor_sigma(x)) == r"\sigma\left(x\right)"
    assert latex(divisor_sigma(x)**2) == r"\sigma^{2}\left(x\right)"
    assert latex(divisor_sigma(x, y)) == r"\sigma_y\left(x\right)"
    assert latex(divisor_sigma(x, y)**2) == r"\sigma^{2}_y\left(x\right)"

    assert latex(udivisor_sigma(x)) == r"\sigma^*\left(x\right)"
    assert latex(udivisor_sigma(x)**2) == r"\sigma^*^{2}\left(x\right)"
    assert latex(udivisor_sigma(x, y)) == r"\sigma^*_y\left(x\right)"
    assert latex(udivisor_sigma(x, y)**2) == r"\sigma^*^{2}_y\left(x\right)"

    assert latex(primenu(n)) == r'\nu\left(n\right)'
    assert latex(primenu(n) ** 2) == r'\left(\nu\left(n\right)\right)^{2}'

    assert latex(primeomega(n)) == r'\Omega\left(n\right)'
    assert latex(primeomega(n) ** 2) == \
        r'\left(\Omega\left(n\right)\right)^{2}'

    assert latex(LambertW(n)) == r'W\left(n\right)'
    assert latex(LambertW(n, -1)) == r'W_{-1}\left(n\right)'
    assert latex(LambertW(n, k)) == r'W_{k}\left(n\right)'

    assert latex(Mod(x, 7)) == r'x\bmod{7}'
    assert latex(Mod(x + 1, 7)) == r'\left(x + 1\right)\bmod{7}'
    assert latex(Mod(2 * x, 7)) == r'2 x\bmod{7}'
    assert latex(Mod(x, 7) + 1) == r'\left(x\bmod{7}\right) + 1'
    assert latex(2 * Mod(x, 7)) == r'2 \left(x\bmod{7}\right)'

    # some unknown function name should get rendered with \operatorname
    fjlkd = Function('fjlkd')
    assert latex(fjlkd(x)) == r'\operatorname{fjlkd}{\left(x \right)}'
    # even when it is referred to without an argument
    assert latex(fjlkd) == r'\operatorname{fjlkd}'


# test that notation passes to subclasses of the same name only
def test_function_subclass_different_name():
    class mygamma(gamma):
        pass
    assert latex(mygamma) == r"\operatorname{mygamma}"
    assert latex(mygamma(x)) == r"\operatorname{mygamma}{\left(x \right)}"


def test_hyper_printing():
    from sympy import pi
    from sympy.abc import x, z

    assert latex(meijerg(Tuple(pi, pi, x), Tuple(1),
                         (0, 1), Tuple(1, 2, 3/pi), z)) == \
        r'{G_{4, 5}^{2, 3}\left(\begin{matrix} \pi, \pi, x & 1 \\0, 1 & 1, 2, '\
        r'\frac{3}{\pi} \end{matrix} \middle| {z} \right)}'
    assert latex(meijerg(Tuple(), Tuple(1), (0,), Tuple(), z)) == \
        r'{G_{1, 1}^{1, 0}\left(\begin{matrix}  & 1 \\0 &  \end{matrix} \middle| {z} \right)}'
    assert latex(hyper((x, 2), (3,), z)) == \
        r'{{}_{2}F_{1}\left(\begin{matrix} x, 2 ' \
        r'\\ 3 \end{matrix}\middle| {z} \right)}'
    assert latex(hyper(Tuple(), Tuple(1), z)) == \
        r'{{}_{0}F_{1}\left(\begin{matrix}  ' \
        r'\\ 1 \end{matrix}\middle| {z} \right)}'


def test_latex_bessel():
    from sympy.functions.special.bessel import (besselj, bessely, besseli,
                                                besselk, hankel1, hankel2,
                                                jn, yn, hn1, hn2)
    from sympy.abc import z
    assert latex(besselj(n, z**2)**k) == r'J^{k}_{n}\left(z^{2}\right)'
    assert latex(bessely(n, z)) == r'Y_{n}\left(z\right)'
    assert latex(besseli(n, z)) == r'I_{n}\left(z\right)'
    assert latex(besselk(n, z)) == r'K_{n}\left(z\right)'
    assert latex(hankel1(n, z**2)**2) == \
        r'\left(H^{(1)}_{n}\left(z^{2}\right)\right)^{2}'
    assert latex(hankel2(n, z)) == r'H^{(2)}_{n}\left(z\right)'
    assert latex(jn(n, z)) == r'j_{n}\left(z\right)'
    assert latex(yn(n, z)) == r'y_{n}\left(z\right)'
    assert latex(hn1(n, z)) == r'h^{(1)}_{n}\left(z\right)'
    assert latex(hn2(n, z)) == r'h^{(2)}_{n}\left(z\right)'


def test_latex_fresnel():
    from sympy.functions.special.error_functions import (fresnels, fresnelc)
    from sympy.abc import z
    assert latex(fresnels(z)) == r'S\left(z\right)'
    assert latex(fresnelc(z)) == r'C\left(z\right)'
    assert latex(fresnels(z)**2) == r'S^{2}\left(z\right)'
    assert latex(fresnelc(z)**2) == r'C^{2}\left(z\right)'


def test_latex_brackets():
    assert latex((-1)**x) == r"\left(-1\right)^{x}"


def test_latex_indexed():
    Psi_symbol = Symbol('Psi_0', complex=True, real=False)
    Psi_indexed = IndexedBase(Symbol('Psi', complex=True, real=False))
    symbol_latex = latex(Psi_symbol * conjugate(Psi_symbol))
    indexed_latex = latex(Psi_indexed[0] * conjugate(Psi_indexed[0]))
    # \\overline{{\\Psi}_{0}} {\\Psi}_{0}  vs.  \\Psi_{0} \\overline{\\Psi_{0}}
    assert symbol_latex == '\\Psi_{0} \\overline{\\Psi_{0}}'
    assert indexed_latex == '\\overline{{\\Psi}_{0}} {\\Psi}_{0}'

    # Symbol('gamma') gives r'\gamma'
    assert latex(Indexed('x1', Symbol('i'))) == '{x_{1}}_{i}'
    assert latex(IndexedBase('gamma')) == r'\gamma'
    assert latex(IndexedBase('a b')) == 'a b'
    assert latex(IndexedBase('a_b')) == 'a_{b}'


def test_latex_derivatives():
    # regular "d" for ordinary derivatives
    assert latex(diff(x**3, x, evaluate=False)) == \
        r"\frac{d}{d x} x^{3}"
    assert latex(diff(sin(x) + x**2, x, evaluate=False)) == \
        r"\frac{d}{d x} \left(x^{2} + \sin{\left(x \right)}\right)"
    assert latex(diff(diff(sin(x) + x**2, x, evaluate=False), evaluate=False))\
        == \
        r"\frac{d^{2}}{d x^{2}} \left(x^{2} + \sin{\left(x \right)}\right)"
    assert latex(diff(diff(diff(sin(x) + x**2, x, evaluate=False), evaluate=False), evaluate=False)) == \
        r"\frac{d^{3}}{d x^{3}} \left(x^{2} + \sin{\left(x \right)}\right)"

    # \partial for partial derivatives
    assert latex(diff(sin(x * y), x, evaluate=False)) == \
        r"\frac{\partial}{\partial x} \sin{\left(x y \right)}"
    assert latex(diff(sin(x * y) + x**2, x, evaluate=False)) == \
        r"\frac{\partial}{\partial x} \left(x^{2} + \sin{\left(x y \right)}\right)"
    assert latex(diff(diff(sin(x*y) + x**2, x, evaluate=False), x, evaluate=False)) == \
        r"\frac{\partial^{2}}{\partial x^{2}} \left(x^{2} + \sin{\left(x y \right)}\right)"
    assert latex(diff(diff(diff(sin(x*y) + x**2, x, evaluate=False), x, evaluate=False), x, evaluate=False)) == \
        r"\frac{\partial^{3}}{\partial x^{3}} \left(x^{2} + \sin{\left(x y \right)}\right)"

    # mixed partial derivatives
    f = Function("f")
    assert latex(diff(diff(f(x, y), x, evaluate=False), y, evaluate=False)) == \
        r"\frac{\partial^{2}}{\partial y\partial x} " + latex(f(x, y))

    assert latex(diff(diff(diff(f(x, y), x, evaluate=False), x, evaluate=False), y, evaluate=False)) == \
        r"\frac{\partial^{3}}{\partial y\partial x^{2}} " + latex(f(x, y))

    # for negative nested Derivative
    assert latex(diff(-diff(y**2,x,evaluate=False),x,evaluate=False)) == r'\frac{d}{d x} \left(- \frac{d}{d x} y^{2}\right)'
    assert latex(diff(diff(-diff(diff(y,x,evaluate=False),x,evaluate=False),x,evaluate=False),x,evaluate=False)) == \
        r'\frac{d^{2}}{d x^{2}} \left(- \frac{d^{2}}{d x^{2}} y\right)'

    # use ordinary d when one of the variables has been integrated out
    assert latex(diff(Integral(exp(-x*y), (x, 0, oo)), y, evaluate=False)) == \
        r"\frac{d}{d y} \int\limits_{0}^{\infty} e^{- x y}\, dx"

    # Derivative wrapped in power:
    assert latex(diff(x, x, evaluate=False)**2) == \
        r"\left(\frac{d}{d x} x\right)^{2}"

    assert latex(diff(f(x), x)**2) == \
        r"\left(\frac{d}{d x} f{\left(x \right)}\right)^{2}"

    assert latex(diff(f(x), (x, n))) == \
        r"\frac{d^{n}}{d x^{n}} f{\left(x \right)}"

    x1 = Symbol('x1')
    x2 = Symbol('x2')
    assert latex(diff(f(x1, x2), x1)) == r'\frac{\partial}{\partial x_{1}} f{\left(x_{1},x_{2} \right)}'

    n1 = Symbol('n1')
    assert latex(diff(f(x), (x, n1))) ==  r'\frac{d^{n_{1}}}{d x^{n_{1}}} f{\left(x \right)}'

    n2 = Symbol('n2')
    assert latex(diff(f(x), (x, Max(n1, n2)))) == \
        r'\frac{d^{\max\left(n_{1}, n_{2}\right)}}{d x^{\max\left(n_{1}, n_{2}\right)}} f{\left(x \right)}'


def test_latex_subs():
    assert latex(Subs(x*y, (
        x, y), (1, 2))) == r'\left. x y \right|_{\substack{ x=1\\ y=2 }}'


def test_latex_integrals():
    assert latex(Integral(log(x), x)) == r"\int \log{\left(x \right)}\, dx"
    assert latex(Integral(x**2, (x, 0, 1))) == \
        r"\int\limits_{0}^{1} x^{2}\, dx"
    assert latex(Integral(x**2, (x, 10, 20))) == \
        r"\int\limits_{10}^{20} x^{2}\, dx"
    assert latex(Integral(y*x**2, (x, 0, 1), y)) == \
        r"\int\int\limits_{0}^{1} x^{2} y\, dx\, dy"
    assert latex(Integral(y*x**2, (x, 0, 1), y), mode='equation*') == \
        r"\begin{equation*}\int\int\limits_{0}^{1} x^{2} y\, dx\, dy\end{equation*}"
    assert latex(Integral(y*x**2, (x, 0, 1), y), mode='equation*', itex=True) \
        == r"$$\int\int_{0}^{1} x^{2} y\, dx\, dy$$"
    assert latex(Integral(x, (x, 0))) == r"\int\limits^{0} x\, dx"
    assert latex(Integral(x*y, x, y)) == r"\iint x y\, dx\, dy"
    assert latex(Integral(x*y*z, x, y, z)) == r"\iiint x y z\, dx\, dy\, dz"
    assert latex(Integral(x*y*z*t, x, y, z, t)) == \
        r"\iiiint t x y z\, dx\, dy\, dz\, dt"
    assert latex(Integral(x, x, x, x, x, x, x)) == \
        r"\int\int\int\int\int\int x\, dx\, dx\, dx\, dx\, dx\, dx"
    assert latex(Integral(x, x, y, (z, 0, 1))) == \
        r"\int\limits_{0}^{1}\int\int x\, dx\, dy\, dz"

    # for negative nested Integral
    assert latex(Integral(-Integral(y**2,x),x)) == \
        r'\int \left(- \int y^{2}\, dx\right)\, dx'
    assert latex(Integral(-Integral(-Integral(y,x),x),x)) == \
        r'\int \left(- \int \left(- \int y\, dx\right)\, dx\right)\, dx'

    # fix issue #10806
    assert latex(Integral(z, z)**2) == r"\left(\int z\, dz\right)^{2}"
    assert latex(Integral(x + z, z)) == r"\int \left(x + z\right)\, dz"
    assert latex(Integral(x+z/2, z)) == \
        r"\int \left(x + \frac{z}{2}\right)\, dz"
    assert latex(Integral(x**y, z)) == r"\int x^{y}\, dz"


def test_latex_sets():
    for s in (frozenset, set):
        assert latex(s([x*y, x**2])) == r"\left\{x^{2}, x y\right\}"
        assert latex(s(range(1, 6))) == r"\left\{1, 2, 3, 4, 5\right\}"
        assert latex(s(range(1, 13))) == \
            r"\left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right\}"

    s = FiniteSet
    assert latex(s(*[x*y, x**2])) == r"\left\{x^{2}, x y\right\}"
    assert latex(s(*range(1, 6))) == r"\left\{1, 2, 3, 4, 5\right\}"
    assert latex(s(*range(1, 13))) == \
        r"\left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right\}"


def test_latex_SetExpr():
    iv = Interval(1, 3)
    se = SetExpr(iv)
    assert latex(se) == r"SetExpr\left(\left[1, 3\right]\right)"


def test_latex_Range():
    assert latex(Range(1, 51)) == r'\left\{1, 2, \ldots, 50\right\}'
    assert latex(Range(1, 4)) == r'\left\{1, 2, 3\right\}'
    assert latex(Range(0, 3, 1)) == r'\left\{0, 1, 2\right\}'
    assert latex(Range(0, 30, 1)) == r'\left\{0, 1, \ldots, 29\right\}'
    assert latex(Range(30, 1, -1)) == r'\left\{30, 29, \ldots, 2\right\}'
    assert latex(Range(0, oo, 2)) == r'\left\{0, 2, \ldots\right\}'
    assert latex(Range(oo, -2, -2)) == r'\left\{\ldots, 2, 0\right\}'
    assert latex(Range(-2, -oo, -1)) == r'\left\{-2, -3, \ldots\right\}'
    assert latex(Range(-oo, oo)) == r'\left\{\ldots, -1, 0, 1, \ldots\right\}'
    assert latex(Range(oo, -oo, -1)) == \
        r'\left\{\ldots, 1, 0, -1, \ldots\right\}'

    a, b, c = symbols('a:c')
    assert latex(Range(a, b, c)) == r'Range\left(a, b, c\right)'
    assert latex(Range(a, 10, 1)) == r'Range\left(a, 10, 1\right)'
    assert latex(Range(0, b, 1)) == r'Range\left(0, b, 1\right)'
    assert latex(Range(0, 10, c)) == r'Range\left(0, 10, c\right)'


def test_latex_sequences():
    s1 = SeqFormula(a**2, (0, oo))
    s2 = SeqPer((1, 2))

    latex_str = r'\left[0, 1, 4, 9, \ldots\right]'
    assert latex(s1) == latex_str

    latex_str = r'\left[1, 2, 1, 2, \ldots\right]'
    assert latex(s2) == latex_str

    s3 = SeqFormula(a**2, (0, 2))
    s4 = SeqPer((1, 2), (0, 2))

    latex_str = r'\left[0, 1, 4\right]'
    assert latex(s3) == latex_str

    latex_str = r'\left[1, 2, 1\right]'
    assert latex(s4) == latex_str

    s5 = SeqFormula(a**2, (-oo, 0))
    s6 = SeqPer((1, 2), (-oo, 0))

    latex_str = r'\left[\ldots, 9, 4, 1, 0\right]'
    assert latex(s5) == latex_str

    latex_str = r'\left[\ldots, 2, 1, 2, 1\right]'
    assert latex(s6) == latex_str

    latex_str = r'\left[1, 3, 5, 11, \ldots\right]'
    assert latex(SeqAdd(s1, s2)) == latex_str

    latex_str = r'\left[1, 3, 5\right]'
    assert latex(SeqAdd(s3, s4)) == latex_str

    latex_str = r'\left[\ldots, 11, 5, 3, 1\right]'
    assert latex(SeqAdd(s5, s6)) == latex_str

    latex_str = r'\left[0, 2, 4, 18, \ldots\right]'
    assert latex(SeqMul(s1, s2)) == latex_str

    latex_str = r'\left[0, 2, 4\right]'
    assert latex(SeqMul(s3, s4)) == latex_str

    latex_str = r'\left[\ldots, 18, 4, 2, 0\right]'
    assert latex(SeqMul(s5, s6)) == latex_str

    # Sequences with symbolic limits, issue 12629
    s7 = SeqFormula(a**2, (a, 0, x))
    latex_str = r'\left\{a^{2}\right\}_{a=0}^{x}'
    assert latex(s7) == latex_str

    b = Symbol('b')
    s8 = SeqFormula(b*a**2, (a, 0, 2))
    latex_str = r'\left[0, b, 4 b\right]'
    assert latex(s8) == latex_str


def test_latex_FourierSeries():
    latex_str = \
        r'2 \sin{\left(x \right)} - \sin{\left(2 x \right)} + \frac{2 \sin{\left(3 x \right)}}{3} + \ldots'
    assert latex(fourier_series(x, (x, -pi, pi))) == latex_str


def test_latex_FormalPowerSeries():
    latex_str = r'\sum_{k=1}^{\infty} - \frac{\left(-1\right)^{- k} x^{k}}{k}'
    assert latex(fps(log(1 + x))) == latex_str


def test_latex_intervals():
    a = Symbol('a', real=True)
    assert latex(Interval(0, 0)) == r"\left\{0\right\}"
    assert latex(Interval(0, a)) == r"\left[0, a\right]"
    assert latex(Interval(0, a, False, False)) == r"\left[0, a\right]"
    assert latex(Interval(0, a, True, False)) == r"\left(0, a\right]"
    assert latex(Interval(0, a, False, True)) == r"\left[0, a\right)"
    assert latex(Interval(0, a, True, True)) == r"\left(0, a\right)"


def test_latex_AccumuBounds():
    a = Symbol('a', real=True)
    assert latex(AccumBounds(0, 1)) == r"\left\langle 0, 1\right\rangle"
    assert latex(AccumBounds(0, a)) == r"\left\langle 0, a\right\rangle"
    assert latex(AccumBounds(a + 1, a + 2)) == \
        r"\left\langle a + 1, a + 2\right\rangle"


def test_latex_emptyset():
    assert latex(S.EmptySet) == r"\emptyset"


def test_latex_universalset():
    assert latex(S.UniversalSet) == r"\mathbb{U}"


def test_latex_commutator():
    A = Operator('A')
    B = Operator('B')
    comm = Commutator(B, A)
    assert latex(comm.doit()) == r"- (A B - B A)"


def test_latex_union():
    assert latex(Union(Interval(0, 1), Interval(2, 3))) == \
        r"\left[0, 1\right] \cup \left[2, 3\right]"
    assert latex(Union(Interval(1, 1), Interval(2, 2), Interval(3, 4))) == \
        r"\left\{1, 2\right\} \cup \left[3, 4\right]"


def test_latex_intersection():
    assert latex(Intersection(Interval(0, 1), Interval(x, y))) == \
        r"\left[0, 1\right] \cap \left[x, y\right]"


def test_latex_symmetric_difference():
    assert latex(SymmetricDifference(Interval(2, 5), Interval(4, 7),
                                     evaluate=False)) == \
        r'\left[2, 5\right] \triangle \left[4, 7\right]'


def test_latex_Complement():
    assert latex(Complement(S.Reals, S.Naturals)) == \
        r"\mathbb{R} \setminus \mathbb{N}"


def test_latex_productset():
    line = Interval(0, 1)
    bigline = Interval(0, 10)
    fset = FiniteSet(1, 2, 3)
    assert latex(line**2) == r"%s^{2}" % latex(line)
    assert latex(line**10) == r"%s^{10}" % latex(line)
    assert latex((line * bigline * fset).flatten()) == r"%s \times %s \times %s" % (
        latex(line), latex(bigline), latex(fset))


def test_set_operators_parenthesis():
    a, b, c, d = symbols('a:d')
    A = FiniteSet(a)
    B = FiniteSet(b)
    C = FiniteSet(c)
    D = FiniteSet(d)

    U1 = Union(A, B, evaluate=False)
    U2 = Union(C, D, evaluate=False)
    I1 = Intersection(A, B, evaluate=False)
    I2 = Intersection(C, D, evaluate=False)
    C1 = Complement(A, B, evaluate=False)
    C2 = Complement(C, D, evaluate=False)
    D1 = SymmetricDifference(A, B, evaluate=False)
    D2 = SymmetricDifference(C, D, evaluate=False)
    # XXX ProductSet does not support evaluate keyword
    P1 = ProductSet(A, B)
    P2 = ProductSet(C, D)

    assert latex(Intersection(A, U2, evaluate=False)) == \
        '\\left\\{a\\right\\} \\cap ' \
        '\\left(\\left\\{c\\right\\} \\cup \\left\\{d\\right\\}\\right)'
    assert latex(Intersection(U1, U2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\cup \\left\\{b\\right\\}\\right) ' \
        '\\cap \\left(\\left\\{c\\right\\} \\cup \\left\\{d\\right\\}\\right)'
    assert latex(Intersection(C1, C2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\setminus ' \
        '\\left\\{b\\right\\}\\right) \\cap \\left(\\left\\{c\\right\\} ' \
        '\\setminus \\left\\{d\\right\\}\\right)'
    assert latex(Intersection(D1, D2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\triangle ' \
        '\\left\\{b\\right\\}\\right) \\cap \\left(\\left\\{c\\right\\} ' \
        '\\triangle \\left\\{d\\right\\}\\right)'
    assert latex(Intersection(P1, P2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\times \\left\\{b\\right\\}\\right) ' \
        '\\cap \\left(\\left\\{c\\right\\} \\times ' \
        '\\left\\{d\\right\\}\\right)'

    assert latex(Union(A, I2, evaluate=False)) == \
        '\\left\\{a\\right\\} \\cup ' \
        '\\left(\\left\\{c\\right\\} \\cap \\left\\{d\\right\\}\\right)'
    assert latex(Union(I1, I2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\cap ''\\left\\{b\\right\\}\\right) ' \
        '\\cup \\left(\\left\\{c\\right\\} \\cap \\left\\{d\\right\\}\\right)'
    assert latex(Union(C1, C2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\setminus ' \
        '\\left\\{b\\right\\}\\right) \\cup \\left(\\left\\{c\\right\\} ' \
        '\\setminus \\left\\{d\\right\\}\\right)'
    assert latex(Union(D1, D2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\triangle ' \
        '\\left\\{b\\right\\}\\right) \\cup \\left(\\left\\{c\\right\\} ' \
        '\\triangle \\left\\{d\\right\\}\\right)'
    assert latex(Union(P1, P2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\times \\left\\{b\\right\\}\\right) ' \
        '\\cup \\left(\\left\\{c\\right\\} \\times ' \
        '\\left\\{d\\right\\}\\right)'

    assert latex(Complement(A, C2, evaluate=False)) == \
        '\\left\\{a\\right\\} \\setminus \\left(\\left\\{c\\right\\} ' \
        '\\setminus \\left\\{d\\right\\}\\right)'
    assert latex(Complement(U1, U2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\cup \\left\\{b\\right\\}\\right) ' \
        '\\setminus \\left(\\left\\{c\\right\\} \\cup ' \
        '\\left\\{d\\right\\}\\right)'
    assert latex(Complement(I1, I2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\cap \\left\\{b\\right\\}\\right) ' \
        '\\setminus \\left(\\left\\{c\\right\\} \\cap ' \
        '\\left\\{d\\right\\}\\right)'
    assert latex(Complement(D1, D2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\triangle ' \
        '\\left\\{b\\right\\}\\right) \\setminus ' \
        '\\left(\\left\\{c\\right\\} \\triangle \\left\\{d\\right\\}\\right)'
    assert latex(Complement(P1, P2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\times \\left\\{b\\right\\}\\right) '\
        '\\setminus \\left(\\left\\{c\\right\\} \\times '\
        '\\left\\{d\\right\\}\\right)'

    assert latex(SymmetricDifference(A, D2, evaluate=False)) == \
        '\\left\\{a\\right\\} \\triangle \\left(\\left\\{c\\right\\} ' \
        '\\triangle \\left\\{d\\right\\}\\right)'
    assert latex(SymmetricDifference(U1, U2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\cup \\left\\{b\\right\\}\\right) ' \
        '\\triangle \\left(\\left\\{c\\right\\} \\cup ' \
        '\\left\\{d\\right\\}\\right)'
    assert latex(SymmetricDifference(I1, I2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\cap \\left\\{b\\right\\}\\right) ' \
        '\\triangle \\left(\\left\\{c\\right\\} \\cap ' \
        '\\left\\{d\\right\\}\\right)'
    assert latex(SymmetricDifference(C1, C2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\setminus ' \
        '\\left\\{b\\right\\}\\right) \\triangle ' \
        '\\left(\\left\\{c\\right\\} \\setminus \\left\\{d\\right\\}\\right)'
    assert latex(SymmetricDifference(P1, P2, evaluate=False)) == \
        '\\left(\\left\\{a\\right\\} \\times \\left\\{b\\right\\}\\right) ' \
        '\\triangle \\left(\\left\\{c\\right\\} \\times ' \
        '\\left\\{d\\right\\}\\right)'

    # XXX This can be incorrect since cartesian product is not associative
    assert latex(ProductSet(A, P2).flatten()) == \
        '\\left\\{a\\right\\} \\times \\left\\{c\\right\\} \\times ' \
        '\\left\\{d\\right\\}'
    assert latex(ProductSet(U1, U2)) == \
        '\\left(\\left\\{a\\right\\} \\cup \\left\\{b\\right\\}\\right) ' \
        '\\times \\left(\\left\\{c\\right\\} \\cup ' \
        '\\left\\{d\\right\\}\\right)'
    assert latex(ProductSet(I1, I2)) == \
        '\\left(\\left\\{a\\right\\} \\cap \\left\\{b\\right\\}\\right) ' \
        '\\times \\left(\\left\\{c\\right\\} \\cap ' \
        '\\left\\{d\\right\\}\\right)'
    assert latex(ProductSet(C1, C2)) == \
        '\\left(\\left\\{a\\right\\} \\setminus ' \
        '\\left\\{b\\right\\}\\right) \\times \\left(\\left\\{c\\right\\} ' \
        '\\setminus \\left\\{d\\right\\}\\right)'
    assert latex(ProductSet(D1, D2)) == \
        '\\left(\\left\\{a\\right\\} \\triangle ' \
        '\\left\\{b\\right\\}\\right) \\times \\left(\\left\\{c\\right\\} ' \
        '\\triangle \\left\\{d\\right\\}\\right)'


def test_latex_Complexes():
    assert latex(S.Complexes) == r"\mathbb{C}"


def test_latex_Naturals():
    assert latex(S.Naturals) == r"\mathbb{N}"


def test_latex_Naturals0():
    assert latex(S.Naturals0) == r"\mathbb{N}_0"


def test_latex_Integers():
    assert latex(S.Integers) == r"\mathbb{Z}"


def test_latex_ImageSet():
    x = Symbol('x')
    assert latex(ImageSet(Lambda(x, x**2), S.Naturals)) == \
        r"\left\{x^{2}\; |\; x \in \mathbb{N}\right\}"
    y = Symbol('y')

    imgset = ImageSet(Lambda((x, y), x + y), {1, 2, 3}, {3, 4})
    assert latex(imgset) == \
        r"\left\{x + y\; |\; x \in \left\{1, 2, 3\right\} , y \in \left\{3, 4\right\}\right\}"

    imgset = ImageSet(Lambda(((x, y),), x + y), ProductSet({1, 2, 3}, {3, 4}))
    assert latex(imgset) == \
        r"\left\{x + y\; |\; \left( x, \  y\right) \in \left\{1, 2, 3\right\} \times \left\{3, 4\right\}\right\}"


def test_latex_ConditionSet():
    x = Symbol('x')
    assert latex(ConditionSet(x, Eq(x**2, 1), S.Reals)) == \
        r"\left\{x \mid x \in \mathbb{R} \wedge x^{2} = 1 \right\}"
    assert latex(ConditionSet(x, Eq(x**2, 1), S.UniversalSet)) == \
        r"\left\{x \mid x^{2} = 1 \right\}"


def test_latex_ComplexRegion():
    assert latex(ComplexRegion(Interval(3, 5)*Interval(4, 6))) == \
        r"\left\{x + y i\; |\; x, y \in \left[3, 5\right] \times \left[4, 6\right] \right\}"
    assert latex(ComplexRegion(Interval(0, 1)*Interval(0, 2*pi), polar=True)) == \
        r"\left\{r \left(i \sin{\left(\theta \right)} + \cos{\left(\theta "\
        r"\right)}\right)\; |\; r, \theta \in \left[0, 1\right] \times \left[0, 2 \pi\right) \right\}"


def test_latex_Contains():
    x = Symbol('x')
    assert latex(Contains(x, S.Naturals)) == r"x \in \mathbb{N}"


def test_latex_sum():
    assert latex(Sum(x*y**2, (x, -2, 2), (y, -5, 5))) == \
        r"\sum_{\substack{-2 \leq x \leq 2\\-5 \leq y \leq 5}} x y^{2}"
    assert latex(Sum(x**2, (x, -2, 2))) == \
        r"\sum_{x=-2}^{2} x^{2}"
    assert latex(Sum(x**2 + y, (x, -2, 2))) == \
        r"\sum_{x=-2}^{2} \left(x^{2} + y\right)"

    assert latex(Sum(x**2 + y, (x, -2, 2))**2) == \
        r"\left(\sum_{x=-2}^{2} \left(x^{2} + y\right)\right)^{2}"


def test_latex_product():
    assert latex(Product(x*y**2, (x, -2, 2), (y, -5, 5))) == \
        r"\prod_{\substack{-2 \leq x \leq 2\\-5 \leq y \leq 5}} x y^{2}"
    assert latex(Product(x**2, (x, -2, 2))) == \
        r"\prod_{x=-2}^{2} x^{2}"
    assert latex(Product(x**2 + y, (x, -2, 2))) == \
        r"\prod_{x=-2}^{2} \left(x^{2} + y\right)"

    assert latex(Product(x, (x, -2, 2))**2) == \
        r"\left(\prod_{x=-2}^{2} x\right)^{2}"


def test_latex_limits():
    assert latex(Limit(x, x, oo)) == r"\lim_{x \to \infty} x"

    # issue 8175
    f = Function('f')
    assert latex(Limit(f(x), x, 0)) == r"\lim_{x \to 0^+} f{\left(x \right)}"
    assert latex(Limit(f(x), x, 0, "-")) == \
        r"\lim_{x \to 0^-} f{\left(x \right)}"

    # issue #10806
    assert latex(Limit(f(x), x, 0)**2) == \
        r"\left(\lim_{x \to 0^+} f{\left(x \right)}\right)^{2}"
    # bi-directional limit
    assert latex(Limit(f(x), x, 0, dir='+-')) == \
        r"\lim_{x \to 0} f{\left(x \right)}"


def test_latex_log():
    assert latex(log(x)) == r"\log{\left(x \right)}"
    assert latex(ln(x)) == r"\log{\left(x \right)}"
    assert latex(log(x), ln_notation=True) == r"\ln{\left(x \right)}"
    assert latex(log(x)+log(y)) == \
        r"\log{\left(x \right)} + \log{\left(y \right)}"
    assert latex(log(x)+log(y), ln_notation=True) == \
        r"\ln{\left(x \right)} + \ln{\left(y \right)}"
    assert latex(pow(log(x), x)) == r"\log{\left(x \right)}^{x}"
    assert latex(pow(log(x), x), ln_notation=True) == \
        r"\ln{\left(x \right)}^{x}"


def test_issue_3568():
    beta = Symbol(r'\beta')
    y = beta + x
    assert latex(y) in [r'\beta + x', r'x + \beta']

    beta = Symbol(r'beta')
    y = beta + x
    assert latex(y) in [r'\beta + x', r'x + \beta']


def test_latex():
    assert latex((2*tau)**Rational(7, 2)) == "8 \\sqrt{2} \\tau^{\\frac{7}{2}}"
    assert latex((2*mu)**Rational(7, 2), mode='equation*') == \
        "\\begin{equation*}8 \\sqrt{2} \\mu^{\\frac{7}{2}}\\end{equation*}"
    assert latex((2*mu)**Rational(7, 2), mode='equation', itex=True) == \
        "$$8 \\sqrt{2} \\mu^{\\frac{7}{2}}$$"
    assert latex([2/x, y]) == r"\left[ \frac{2}{x}, \  y\right]"


def test_latex_dict():
    d = {Rational(1): 1, x**2: 2, x: 3, x**3: 4}
    assert latex(d) == \
        r'\left\{ 1 : 1, \  x : 3, \  x^{2} : 2, \  x^{3} : 4\right\}'
    D = Dict(d)
    assert latex(D) == \
        r'\left\{ 1 : 1, \  x : 3, \  x^{2} : 2, \  x^{3} : 4\right\}'


def test_latex_list():
    ll = [Symbol('omega1'), Symbol('a'), Symbol('alpha')]
    assert latex(ll) == r'\left[ \omega_{1}, \  a, \  \alpha\right]'


def test_latex_rational():
    # tests issue 3973
    assert latex(-Rational(1, 2)) == "- \\frac{1}{2}"
    assert latex(Rational(-1, 2)) == "- \\frac{1}{2}"
    assert latex(Rational(1, -2)) == "- \\frac{1}{2}"
    assert latex(-Rational(-1, 2)) == "\\frac{1}{2}"
    assert latex(-Rational(1, 2)*x) == "- \\frac{x}{2}"
    assert latex(-Rational(1, 2)*x + Rational(-2, 3)*y) == \
        "- \\frac{x}{2} - \\frac{2 y}{3}"


def test_latex_inverse():
    # tests issue 4129
    assert latex(1/x) == "\\frac{1}{x}"
    assert latex(1/(x + y)) == "\\frac{1}{x + y}"


def test_latex_DiracDelta():
    assert latex(DiracDelta(x)) == r"\delta\left(x\right)"
    assert latex(DiracDelta(x)**2) == r"\left(\delta\left(x\right)\right)^{2}"
    assert latex(DiracDelta(x, 0)) == r"\delta\left(x\right)"
    assert latex(DiracDelta(x, 5)) == \
        r"\delta^{\left( 5 \right)}\left( x \right)"
    assert latex(DiracDelta(x, 5)**2) == \
        r"\left(\delta^{\left( 5 \right)}\left( x \right)\right)^{2}"


def test_latex_Heaviside():
    assert latex(Heaviside(x)) == r"\theta\left(x\right)"
    assert latex(Heaviside(x)**2) == r"\left(\theta\left(x\right)\right)^{2}"


def test_latex_KroneckerDelta():
    assert latex(KroneckerDelta(x, y)) == r"\delta_{x y}"
    assert latex(KroneckerDelta(x, y + 1)) == r"\delta_{x, y + 1}"
    # issue 6578
    assert latex(KroneckerDelta(x + 1, y)) == r"\delta_{y, x + 1}"
    assert latex(Pow(KroneckerDelta(x, y), 2, evaluate=False)) == \
        r"\left(\delta_{x y}\right)^{2}"


def test_latex_LeviCivita():
    assert latex(LeviCivita(x, y, z)) == r"\varepsilon_{x y z}"
    assert latex(LeviCivita(x, y, z)**2) == \
        r"\left(\varepsilon_{x y z}\right)^{2}"
    assert latex(LeviCivita(x, y, z + 1)) == r"\varepsilon_{x, y, z + 1}"
    assert latex(LeviCivita(x, y + 1, z)) == r"\varepsilon_{x, y + 1, z}"
    assert latex(LeviCivita(x + 1, y, z)) == r"\varepsilon_{x + 1, y, z}"


def test_mode():
    expr = x + y
    assert latex(expr) == 'x + y'
    assert latex(expr, mode='plain') == 'x + y'
    assert latex(expr, mode='inline') == '$x + y$'
    assert latex(
        expr, mode='equation*') == '\\begin{equation*}x + y\\end{equation*}'
    assert latex(
        expr, mode='equation') == '\\begin{equation}x + y\\end{equation}'
    raises(ValueError, lambda: latex(expr, mode='foo'))


def test_latex_mathieu():
    assert latex(mathieuc(x, y, z)) == r"C\left(x, y, z\right)"
    assert latex(mathieus(x, y, z)) == r"S\left(x, y, z\right)"
    assert latex(mathieuc(x, y, z)**2) == r"C\left(x, y, z\right)^{2}"
    assert latex(mathieus(x, y, z)**2) == r"S\left(x, y, z\right)^{2}"
    assert latex(mathieucprime(x, y, z)) == r"C^{\prime}\left(x, y, z\right)"
    assert latex(mathieusprime(x, y, z)) == r"S^{\prime}\left(x, y, z\right)"
    assert latex(mathieucprime(x, y, z)**2) == r"C^{\prime}\left(x, y, z\right)^{2}"
    assert latex(mathieusprime(x, y, z)**2) == r"S^{\prime}\left(x, y, z\right)^{2}"

def test_latex_Piecewise():
    p = Piecewise((x, x < 1), (x**2, True))
    assert latex(p) == "\\begin{cases} x & \\text{for}\\: x < 1 \\\\x^{2} &" \
                       " \\text{otherwise} \\end{cases}"
    assert latex(p, itex=True) == \
        "\\begin{cases} x & \\text{for}\\: x \\lt 1 \\\\x^{2} &" \
        " \\text{otherwise} \\end{cases}"
    p = Piecewise((x, x < 0), (0, x >= 0))
    assert latex(p) == '\\begin{cases} x & \\text{for}\\: x < 0 \\\\0 &' \
                       ' \\text{otherwise} \\end{cases}'
    A, B = symbols("A B", commutative=False)
    p = Piecewise((A**2, Eq(A, B)), (A*B, True))
    s = r"\begin{cases} A^{2} & \text{for}\: A = B \\A B & \text{otherwise} \end{cases}"
    assert latex(p) == s
    assert latex(A*p) == r"A \left(%s\right)" % s
    assert latex(p*A) == r"\left(%s\right) A" % s
    assert latex(Piecewise((x, x < 1), (x**2, x < 2))) == \
        '\\begin{cases} x & ' \
        '\\text{for}\\: x < 1 \\\\x^{2} & \\text{for}\\: x < 2 \\end{cases}'


def test_latex_Matrix():
    M = Matrix([[1 + x, y], [y, x - 1]])
    assert latex(M) == \
        r'\left[\begin{matrix}x + 1 & y\\y & x - 1\end{matrix}\right]'
    assert latex(M, mode='inline') == \
        r'$\left[\begin{smallmatrix}x + 1 & y\\' \
        r'y & x - 1\end{smallmatrix}\right]$'
    assert latex(M, mat_str='array') == \
        r'\left[\begin{array}{cc}x + 1 & y\\y & x - 1\end{array}\right]'
    assert latex(M, mat_str='bmatrix') == \
        r'\left[\begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}\right]'
    assert latex(M, mat_delim=None, mat_str='bmatrix') == \
        r'\begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}'
    M2 = Matrix(1, 11, range(11))
    assert latex(M2) == \
        r'\left[\begin{array}{ccccccccccc}' \
        r'0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array}\right]'


def test_latex_matrix_with_functions():
    t = symbols('t')
    theta1 = symbols('theta1', cls=Function)

    M = Matrix([[sin(theta1(t)), cos(theta1(t))],
                [cos(theta1(t).diff(t)), sin(theta1(t).diff(t))]])

    expected = (r'\left[\begin{matrix}\sin{\left('
                r'\theta_{1}{\left(t \right)} \right)} & '
                r'\cos{\left(\theta_{1}{\left(t \right)} \right)'
                r'}\\\cos{\left(\frac{d}{d t} \theta_{1}{\left(t '
                r'\right)} \right)} & \sin{\left(\frac{d}{d t} '
                r'\theta_{1}{\left(t \right)} \right'
                r')}\end{matrix}\right]')

    assert latex(M) == expected


def test_latex_NDimArray():
    x, y, z, w = symbols("x y z w")

    for ArrayType in (ImmutableDenseNDimArray, ImmutableSparseNDimArray,
                      MutableDenseNDimArray, MutableSparseNDimArray):
        # Basic: scalar array
        M = ArrayType(x)

        assert latex(M) == "x"

        M = ArrayType([[1 / x, y], [z, w]])
        M1 = ArrayType([1 / x, y, z])

        M2 = tensorproduct(M1, M)
        M3 = tensorproduct(M, M)

        assert latex(M) == \
            '\\left[\\begin{matrix}\\frac{1}{x} & y\\\\z & w\\end{matrix}\\right]'
        assert latex(M1) == \
            "\\left[\\begin{matrix}\\frac{1}{x} & y & z\\end{matrix}\\right]"
        assert latex(M2) == \
            r"\left[\begin{matrix}" \
            r"\left[\begin{matrix}\frac{1}{x^{2}} & \frac{y}{x}\\\frac{z}{x} & \frac{w}{x}\end{matrix}\right] & " \
            r"\left[\begin{matrix}\frac{y}{x} & y^{2}\\y z & w y\end{matrix}\right] & " \
            r"\left[\begin{matrix}\frac{z}{x} & y z\\z^{2} & w z\end{matrix}\right]" \
            r"\end{matrix}\right]"
        assert latex(M3) == \
            r"""\left[\begin{matrix}"""\
            r"""\left[\begin{matrix}\frac{1}{x^{2}} & \frac{y}{x}\\\frac{z}{x} & \frac{w}{x}\end{matrix}\right] & """\
            r"""\left[\begin{matrix}\frac{y}{x} & y^{2}\\y z & w y\end{matrix}\right]\\"""\
            r"""\left[\begin{matrix}\frac{z}{x} & y z\\z^{2} & w z\end{matrix}\right] & """\
            r"""\left[\begin{matrix}\frac{w}{x} & w y\\w z & w^{2}\end{matrix}\right]"""\
            r"""\end{matrix}\right]"""

        Mrow = ArrayType([[x, y, 1/z]])
        Mcolumn = ArrayType([[x], [y], [1/z]])
        Mcol2 = ArrayType([Mcolumn.tolist()])

        assert latex(Mrow) == \
            r"\left[\left[\begin{matrix}x & y & \frac{1}{z}\end{matrix}\right]\right]"
        assert latex(Mcolumn) == \
            r"\left[\begin{matrix}x\\y\\\frac{1}{z}\end{matrix}\right]"
        assert latex(Mcol2) == \
            r'\left[\begin{matrix}\left[\begin{matrix}x\\y\\\frac{1}{z}\end{matrix}\right]\end{matrix}\right]'


def test_latex_mul_symbol():
    assert latex(4*4**x, mul_symbol='times') == "4 \\times 4^{x}"
    assert latex(4*4**x, mul_symbol='dot') == "4 \\cdot 4^{x}"
    assert latex(4*4**x, mul_symbol='ldot') == r"4 \,.\, 4^{x}"

    assert latex(4*x, mul_symbol='times') == "4 \\times x"
    assert latex(4*x, mul_symbol='dot') == "4 \\cdot x"
    assert latex(4*x, mul_symbol='ldot') == r"4 \,.\, x"


def test_latex_issue_4381():
    y = 4*4**log(2)
    assert latex(y) == r'4 \cdot 4^{\log{\left(2 \right)}}'
    assert latex(1/y) == r'\frac{1}{4 \cdot 4^{\log{\left(2 \right)}}}'


def test_latex_issue_4576():
    assert latex(Symbol("beta_13_2")) == r"\beta_{13 2}"
    assert latex(Symbol("beta_132_20")) == r"\beta_{132 20}"
    assert latex(Symbol("beta_13")) == r"\beta_{13}"
    assert latex(Symbol("x_a_b")) == r"x_{a b}"
    assert latex(Symbol("x_1_2_3")) == r"x_{1 2 3}"
    assert latex(Symbol("x_a_b1")) == r"x_{a b1}"
    assert latex(Symbol("x_a_1")) == r"x_{a 1}"
    assert latex(Symbol("x_1_a")) == r"x_{1 a}"
    assert latex(Symbol("x_1^aa")) == r"x^{aa}_{1}"
    assert latex(Symbol("x_1__aa")) == r"x^{aa}_{1}"
    assert latex(Symbol("x_11^a")) == r"x^{a}_{11}"
    assert latex(Symbol("x_11__a")) == r"x^{a}_{11}"
    assert latex(Symbol("x_a_a_a_a")) == r"x_{a a a a}"
    assert latex(Symbol("x_a_a^a^a")) == r"x^{a a}_{a a}"
    assert latex(Symbol("x_a_a__a__a")) == r"x^{a a}_{a a}"
    assert latex(Symbol("alpha_11")) == r"\alpha_{11}"
    assert latex(Symbol("alpha_11_11")) == r"\alpha_{11 11}"
    assert latex(Symbol("alpha_alpha")) == r"\alpha_{\alpha}"
    assert latex(Symbol("alpha^aleph")) == r"\alpha^{\aleph}"
    assert latex(Symbol("alpha__aleph")) == r"\alpha^{\aleph}"


def test_latex_pow_fraction():
    x = Symbol('x')
    # Testing exp
    assert 'e^{-x}' in latex(exp(-x)/2).replace(' ', '')  # Remove Whitespace

    # Testing e^{-x} in case future changes alter behavior of muls or fracs
    # In particular current output is \frac{1}{2}e^{- x} but perhaps this will
    # change to \frac{e^{-x}}{2}

    # Testing general, non-exp, power
    assert '3^{-x}' in latex(3**-x/2).replace(' ', '')


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

    assert latex(A*B*C**-1) == "A B C^{-1}"
    assert latex(C**-1*A*B) == "C^{-1} A B"
    assert latex(A*C**-1*B) == "A C^{-1} B"


def test_latex_order():
    expr = x**3 + x**2*y + y**4 + 3*x*y**3

    assert latex(expr, order='lex') == "x^{3} + x^{2} y + 3 x y^{3} + y^{4}"
    assert latex(
        expr, order='rev-lex') == "y^{4} + 3 x y^{3} + x^{2} y + x^{3}"
    assert latex(expr, order='none') == "x^{3} + y^{4} + y x^{2} + 3 x y^{3}"


def test_latex_Lambda():
    assert latex(Lambda(x, x + 1)) == \
        r"\left( x \mapsto x + 1 \right)"
    assert latex(Lambda((x, y), x + 1)) == \
        r"\left( \left( x, \  y\right) \mapsto x + 1 \right)"
    assert latex(Lambda(x, x)) == \
        r"\left( x \mapsto x \right)"

def test_latex_PolyElement():
    Ruv, u, v = ring("u,v", ZZ)
    Rxyz, x, y, z = ring("x,y,z", Ruv)

    assert latex(x - x) == r"0"
    assert latex(x - 1) == r"x - 1"
    assert latex(x + 1) == r"x + 1"

    assert latex((u**2 + 3*u*v + 1)*x**2*y + u + 1) == \
        r"\left({u}^{2} + 3 u v + 1\right) {x}^{2} y + u + 1"
    assert latex((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x) == \
        r"\left({u}^{2} + 3 u v + 1\right) {x}^{2} y + \left(u + 1\right) x"
    assert latex((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1) == \
        r"\left({u}^{2} + 3 u v + 1\right) {x}^{2} y + \left(u + 1\right) x + 1"
    assert latex((-u**2 + 3*u*v - 1)*x**2*y - (u + 1)*x - 1) == \
        r"-\left({u}^{2} - 3 u v + 1\right) {x}^{2} y - \left(u + 1\right) x - 1"

    assert latex(-(v**2 + v + 1)*x + 3*u*v + 1) == \
        r"-\left({v}^{2} + v + 1\right) x + 3 u v + 1"
    assert latex(-(v**2 + v + 1)*x - 3*u*v + 1) == \
        r"-\left({v}^{2} + v + 1\right) x - 3 u v + 1"


def test_latex_FracElement():
    Fuv, u, v = field("u,v", ZZ)
    Fxyzt, x, y, z, t = field("x,y,z,t", Fuv)

    assert latex(x - x) == r"0"
    assert latex(x - 1) == r"x - 1"
    assert latex(x + 1) == r"x + 1"

    assert latex(x/3) == r"\frac{x}{3}"
    assert latex(x/z) == r"\frac{x}{z}"
    assert latex(x*y/z) == r"\frac{x y}{z}"
    assert latex(x/(z*t)) == r"\frac{x}{z t}"
    assert latex(x*y/(z*t)) == r"\frac{x y}{z t}"

    assert latex((x - 1)/y) == r"\frac{x - 1}{y}"
    assert latex((x + 1)/y) == r"\frac{x + 1}{y}"
    assert latex((-x - 1)/y) == r"\frac{-x - 1}{y}"
    assert latex((x + 1)/(y*z)) == r"\frac{x + 1}{y z}"
    assert latex(-y/(x + 1)) == r"\frac{-y}{x + 1}"
    assert latex(y*z/(x + 1)) == r"\frac{y z}{x + 1}"

    assert latex(((u + 1)*x*y + 1)/((v - 1)*z - 1)) == \
        r"\frac{\left(u + 1\right) x y + 1}{\left(v - 1\right) z - 1}"
    assert latex(((u + 1)*x*y + 1)/((v - 1)*z - t*u*v - 1)) == \
        r"\frac{\left(u + 1\right) x y + 1}{\left(v - 1\right) z - u v t - 1}"


def test_latex_Poly():
    assert latex(Poly(x**2 + 2 * x, x)) == \
        r"\operatorname{Poly}{\left( x^{2} + 2 x, x, domain=\mathbb{Z} \right)}"
    assert latex(Poly(x/y, x)) == \
        r"\operatorname{Poly}{\left( \frac{1}{y} x, x, domain=\mathbb{Z}\left(y\right) \right)}"
    assert latex(Poly(2.0*x + y)) == \
        r"\operatorname{Poly}{\left( 2.0 x + 1.0 y, x, y, domain=\mathbb{R} \right)}"


def test_latex_Poly_order():
    assert latex(Poly([a, 1, b, 2, c, 3], x)) == \
        '\\operatorname{Poly}{\\left( a x^{5} + x^{4} + b x^{3} + 2 x^{2} + c'\
        ' x + 3, x, domain=\\mathbb{Z}\\left[a, b, c\\right] \\right)}'
    assert latex(Poly([a, 1, b+c, 2, 3], x)) == \
        '\\operatorname{Poly}{\\left( a x^{4} + x^{3} + \\left(b + c\\right) '\
        'x^{2} + 2 x + 3, x, domain=\\mathbb{Z}\\left[a, b, c\\right] \\right)}'
    assert latex(Poly(a*x**3 + x**2*y - x*y - c*y**3 - b*x*y**2 + y - a*x + b,
                      (x, y))) == \
        '\\operatorname{Poly}{\\left( a x^{3} + x^{2}y -  b xy^{2} - xy -  '\
        'a x -  c y^{3} + y + b, x, y, domain=\\mathbb{Z}\\left[a, b, c\\right] \\right)}'


def test_latex_ComplexRootOf():
    assert latex(rootof(x**5 + x + 3, 0)) == \
        r"\operatorname{CRootOf} {\left(x^{5} + x + 3, 0\right)}"


def test_latex_RootSum():
    assert latex(RootSum(x**5 + x + 3, sin)) == \
        r"\operatorname{RootSum} {\left(x^{5} + x + 3, \left( x \mapsto \sin{\left(x \right)} \right)\right)}"


def test_settings():
    raises(TypeError, lambda: latex(x*y, method="garbage"))


def test_latex_numbers():
    assert latex(catalan(n)) == r"C_{n}"
    assert latex(catalan(n)**2) == r"C_{n}^{2}"
    assert latex(bernoulli(n)) == r"B_{n}"
    assert latex(bernoulli(n, x)) == r"B_{n}\left(x\right)"
    assert latex(bernoulli(n)**2) == r"B_{n}^{2}"
    assert latex(bernoulli(n, x)**2) == r"B_{n}^{2}\left(x\right)"
    assert latex(bell(n)) == r"B_{n}"
    assert latex(bell(n, x)) == r"B_{n}\left(x\right)"
    assert latex(bell(n, m, (x, y))) == r"B_{n, m}\left(x, y\right)"
    assert latex(bell(n)**2) == r"B_{n}^{2}"
    assert latex(bell(n, x)**2) == r"B_{n}^{2}\left(x\right)"
    assert latex(bell(n, m, (x, y))**2) == r"B_{n, m}^{2}\left(x, y\right)"
    assert latex(fibonacci(n)) == r"F_{n}"
    assert latex(fibonacci(n, x)) == r"F_{n}\left(x\right)"
    assert latex(fibonacci(n)**2) == r"F_{n}^{2}"
    assert latex(fibonacci(n, x)**2) == r"F_{n}^{2}\left(x\right)"
    assert latex(lucas(n)) == r"L_{n}"
    assert latex(lucas(n)**2) == r"L_{n}^{2}"
    assert latex(tribonacci(n)) == r"T_{n}"
    assert latex(tribonacci(n, x)) == r"T_{n}\left(x\right)"
    assert latex(tribonacci(n)**2) == r"T_{n}^{2}"
    assert latex(tribonacci(n, x)**2) == r"T_{n}^{2}\left(x\right)"


def test_latex_euler():
    assert latex(euler(n)) == r"E_{n}"
    assert latex(euler(n, x)) == r"E_{n}\left(x\right)"
    assert latex(euler(n, x)**2) == r"E_{n}^{2}\left(x\right)"


def test_lamda():
    assert latex(Symbol('lamda')) == r"\lambda"
    assert latex(Symbol('Lamda')) == r"\Lambda"


def test_custom_symbol_names():
    x = Symbol('x')
    y = Symbol('y')
    assert latex(x) == "x"
    assert latex(x, symbol_names={x: "x_i"}) == "x_i"
    assert latex(x + y, symbol_names={x: "x_i"}) == "x_i + y"
    assert latex(x**2, symbol_names={x: "x_i"}) == "x_i^{2}"
    assert latex(x + y, symbol_names={x: "x_i", y: "y_j"}) == "x_i + y_j"


def test_matAdd():
    from sympy import MatrixSymbol
    from sympy.printing.latex import LatexPrinter
    C = MatrixSymbol('C', 5, 5)
    B = MatrixSymbol('B', 5, 5)
    l = LatexPrinter()
    assert l._print(C - 2*B) in ['- 2 B + C', 'C -2 B']
    assert l._print(C + 2*B) in ['2 B + C', 'C + 2 B']
    assert l._print(B - 2*C) in ['B - 2 C', '- 2 C + B']
    assert l._print(B + 2*C) in ['B + 2 C', '2 C + B']


def test_matMul():
    from sympy import MatrixSymbol
    from sympy.printing.latex import LatexPrinter
    A = MatrixSymbol('A', 5, 5)
    B = MatrixSymbol('B', 5, 5)
    x = Symbol('x')
    lp = LatexPrinter()
    assert lp._print_MatMul(2*A) == '2 A'
    assert lp._print_MatMul(2*x*A) == '2 x A'
    assert lp._print_MatMul(-2*A) == '- 2 A'
    assert lp._print_MatMul(1.5*A) == '1.5 A'
    assert lp._print_MatMul(sqrt(2)*A) == r'\sqrt{2} A'
    assert lp._print_MatMul(-sqrt(2)*A) == r'- \sqrt{2} A'
    assert lp._print_MatMul(2*sqrt(2)*x*A) == r'2 \sqrt{2} x A'
    assert lp._print_MatMul(-2*A*(A + 2*B)) in [r'- 2 A \left(A + 2 B\right)',
                                                r'- 2 A \left(2 B + A\right)']


def test_latex_MatrixSlice():
    n = Symbol('n', integer=True)
    x, y, z, w, t, = symbols('x y z w t')
    X = MatrixSymbol('X', n, n)
    Y = MatrixSymbol('Y', 10, 10)
    Z = MatrixSymbol('Z', 10, 10)

    assert latex(MatrixSlice(X, (None, None, None), (None, None, None))) == r'X\left[:, :\right]'
    assert latex(X[x:x + 1, y:y + 1]) == r'X\left[x:x + 1, y:y + 1\right]'
    assert latex(X[x:x + 1:2, y:y + 1:2]) == r'X\left[x:x + 1:2, y:y + 1:2\right]'
    assert latex(X[:x, y:]) == r'X\left[:x, y:\right]'
    assert latex(X[:x, y:]) == r'X\left[:x, y:\right]'
    assert latex(X[x:, :y]) == r'X\left[x:, :y\right]'
    assert latex(X[x:y, z:w]) == r'X\left[x:y, z:w\right]'
    assert latex(X[x:y:t, w:t:x]) == r'X\left[x:y:t, w:t:x\right]'
    assert latex(X[x::y, t::w]) == r'X\left[x::y, t::w\right]'
    assert latex(X[:x:y, :t:w]) == r'X\left[:x:y, :t:w\right]'
    assert latex(X[::x, ::y]) == r'X\left[::x, ::y\right]'
    assert latex(MatrixSlice(X, (0, None, None), (0, None, None))) == r'X\left[:, :\right]'
    assert latex(MatrixSlice(X, (None, n, None), (None, n, None))) == r'X\left[:, :\right]'
    assert latex(MatrixSlice(X, (0, n, None), (0, n, None))) == r'X\left[:, :\right]'
    assert latex(MatrixSlice(X, (0, n, 2), (0, n, 2))) == r'X\left[::2, ::2\right]'
    assert latex(X[1:2:3, 4:5:6]) == r'X\left[1:2:3, 4:5:6\right]'
    assert latex(X[1:3:5, 4:6:8]) == r'X\left[1:3:5, 4:6:8\right]'
    assert latex(X[1:10:2]) == r'X\left[1:10:2, :\right]'
    assert latex(Y[:5, 1:9:2]) == r'Y\left[:5, 1:9:2\right]'
    assert latex(Y[:5, 1:10:2]) == r'Y\left[:5, 1::2\right]'
    assert latex(Y[5, :5:2]) == r'Y\left[5:6, :5:2\right]'
    assert latex(X[0:1, 0:1]) == r'X\left[:1, :1\right]'
    assert latex(X[0:1:2, 0:1:2]) == r'X\left[:1:2, :1:2\right]'
    assert latex((Y + Z)[2:, 2:]) == r'\left(Y + Z\right)\left[2:, 2:\right]'


def test_latex_RandomDomain():
    from sympy.stats import Normal, Die, Exponential, pspace, where
    from sympy.stats.rv import RandomDomain

    X = Normal('x1', 0, 1)
    assert latex(where(X > 0)) == r"\text{Domain: }0 < x_{1} \wedge x_{1} < \infty"

    D = Die('d1', 6)
    assert latex(where(D > 4)) == r"\text{Domain: }d_{1} = 5 \vee d_{1} = 6"

    A = Exponential('a', 1)
    B = Exponential('b', 1)
    assert latex(
        pspace(Tuple(A, B)).domain) == \
        r"\text{Domain: }0 \leq a \wedge 0 \leq b \wedge a < \infty \wedge b < \infty"

    assert latex(RandomDomain(FiniteSet(x), FiniteSet(1, 2))) == \
        r'\text{Domain: }\left\{x\right\}\text{ in }\left\{1, 2\right\}'

def test_PrettyPoly():
    from sympy.polys.domains import QQ
    F = QQ.frac_field(x, y)
    R = QQ[x, y]

    assert latex(F.convert(x/(x + y))) == latex(x/(x + y))
    assert latex(R.convert(x + y)) == latex(x + y)


def test_integral_transforms():
    x = Symbol("x")
    k = Symbol("k")
    f = Function("f")
    a = Symbol("a")
    b = Symbol("b")

    assert latex(MellinTransform(f(x), x, k)) == \
        r"\mathcal{M}_{x}\left[f{\left(x \right)}\right]\left(k\right)"
    assert latex(InverseMellinTransform(f(k), k, x, a, b)) == \
        r"\mathcal{M}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)"

    assert latex(LaplaceTransform(f(x), x, k)) == \
        r"\mathcal{L}_{x}\left[f{\left(x \right)}\right]\left(k\right)"
    assert latex(InverseLaplaceTransform(f(k), k, x, (a, b))) == \
        r"\mathcal{L}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)"

    assert latex(FourierTransform(f(x), x, k)) == \
        r"\mathcal{F}_{x}\left[f{\left(x \right)}\right]\left(k\right)"
    assert latex(InverseFourierTransform(f(k), k, x)) == \
        r"\mathcal{F}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)"

    assert latex(CosineTransform(f(x), x, k)) == \
        r"\mathcal{COS}_{x}\left[f{\left(x \right)}\right]\left(k\right)"
    assert latex(InverseCosineTransform(f(k), k, x)) == \
        r"\mathcal{COS}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)"

    assert latex(SineTransform(f(x), x, k)) == \
        r"\mathcal{SIN}_{x}\left[f{\left(x \right)}\right]\left(k\right)"
    assert latex(InverseSineTransform(f(k), k, x)) == \
        r"\mathcal{SIN}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)"


def test_PolynomialRingBase():
    from sympy.polys.domains import QQ
    assert latex(QQ.old_poly_ring(x, y)) == r"\mathbb{Q}\left[x, y\right]"
    assert latex(QQ.old_poly_ring(x, y, order="ilex")) == \
        r"S_<^{-1}\mathbb{Q}\left[x, y\right]"


def test_categories():
    from sympy.categories import (Object, IdentityMorphism,
                                  NamedMorphism, Category, Diagram,
                                  DiagramGrid)

    A1 = Object("A1")
    A2 = Object("A2")
    A3 = Object("A3")

    f1 = NamedMorphism(A1, A2, "f1")
    f2 = NamedMorphism(A2, A3, "f2")
    id_A1 = IdentityMorphism(A1)

    K1 = Category("K1")

    assert latex(A1) == "A_{1}"
    assert latex(f1) == "f_{1}:A_{1}\\rightarrow A_{2}"
    assert latex(id_A1) == "id:A_{1}\\rightarrow A_{1}"
    assert latex(f2*f1) == "f_{2}\\circ f_{1}:A_{1}\\rightarrow A_{3}"

    assert latex(K1) == r"\mathbf{K_{1}}"

    d = Diagram()
    assert latex(d) == r"\emptyset"

    d = Diagram({f1: "unique", f2: S.EmptySet})
    assert latex(d) == r"\left\{ f_{2}\circ f_{1}:A_{1}" \
        r"\rightarrow A_{3} : \emptyset, \  id:A_{1}\rightarrow " \
        r"A_{1} : \emptyset, \  id:A_{2}\rightarrow A_{2} : " \
        r"\emptyset, \  id:A_{3}\rightarrow A_{3} : \emptyset, " \
        r"\  f_{1}:A_{1}\rightarrow A_{2} : \left\{unique\right\}, " \
        r"\  f_{2}:A_{2}\rightarrow A_{3} : \emptyset\right\}"

    d = Diagram({f1: "unique", f2: S.EmptySet}, {f2 * f1: "unique"})
    assert latex(d) == r"\left\{ f_{2}\circ f_{1}:A_{1}" \
        r"\rightarrow A_{3} : \emptyset, \  id:A_{1}\rightarrow " \
        r"A_{1} : \emptyset, \  id:A_{2}\rightarrow A_{2} : " \
        r"\emptyset, \  id:A_{3}\rightarrow A_{3} : \emptyset, " \
        r"\  f_{1}:A_{1}\rightarrow A_{2} : \left\{unique\right\}," \
        r" \  f_{2}:A_{2}\rightarrow A_{3} : \emptyset\right\}" \
        r"\Longrightarrow \left\{ f_{2}\circ f_{1}:A_{1}" \
        r"\rightarrow A_{3} : \left\{unique\right\}\right\}"

    # A linear diagram.
    A = Object("A")
    B = Object("B")
    C = Object("C")
    f = NamedMorphism(A, B, "f")
    g = NamedMorphism(B, C, "g")
    d = Diagram([f, g])
    grid = DiagramGrid(d)

    assert latex(grid) == "\\begin{array}{cc}\n" \
        "A & B \\\\\n" \
        " & C \n" \
        "\\end{array}\n"


def test_Modules():
    from sympy.polys.domains import QQ
    from sympy.polys.agca import homomorphism

    R = QQ.old_poly_ring(x, y)
    F = R.free_module(2)
    M = F.submodule([x, y], [1, x**2])

    assert latex(F) == r"{\mathbb{Q}\left[x, y\right]}^{2}"
    assert latex(M) == \
        r"\left\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangle"

    I = R.ideal(x**2, y)
    assert latex(I) == r"\left\langle {x^{2}},{y} \right\rangle"

    Q = F / M
    assert latex(Q) == \
        r"\frac{{\mathbb{Q}\left[x, y\right]}^{2}}{\left\langle {\left[ {x},"\
        r"{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangle}"
    assert latex(Q.submodule([1, x**3/2], [2, y])) == \
        r"\left\langle {{\left[ {1},{\frac{x^{3}}{2}} \right]} + {\left"\
        r"\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} "\
        r"\right\rangle}},{{\left[ {2},{y} \right]} + {\left\langle {\left[ "\
        r"{x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangle}} \right\rangle"

    h = homomorphism(QQ.old_poly_ring(x).free_module(2),
                     QQ.old_poly_ring(x).free_module(2), [0, 0])

    assert latex(h) == \
        r"{\left[\begin{matrix}0 & 0\\0 & 0\end{matrix}\right]} : "\
        r"{{\mathbb{Q}\left[x\right]}^{2}} \to {{\mathbb{Q}\left[x\right]}^{2}}"


def test_QuotientRing():
    from sympy.polys.domains import QQ
    R = QQ.old_poly_ring(x)/[x**2 + 1]

    assert latex(R) == \
        r"\frac{\mathbb{Q}\left[x\right]}{\left\langle {x^{2} + 1} \right\rangle}"
    assert latex(R.one) == r"{1} + {\left\langle {x^{2} + 1} \right\rangle}"


def test_Tr():
    #TODO: Handle indices
    A, B = symbols('A B', commutative=False)
    t = Tr(A*B)
    assert latex(t) == r'\operatorname{tr}\left(A B\right)'


def test_Adjoint():
    from sympy.matrices import MatrixSymbol, Adjoint, Inverse, Transpose
    X = MatrixSymbol('X', 2, 2)
    Y = MatrixSymbol('Y', 2, 2)
    assert latex(Adjoint(X)) == r'X^{\dagger}'
    assert latex(Adjoint(X + Y)) == r'\left(X + Y\right)^{\dagger}'
    assert latex(Adjoint(X) + Adjoint(Y)) == r'X^{\dagger} + Y^{\dagger}'
    assert latex(Adjoint(X*Y)) == r'\left(X Y\right)^{\dagger}'
    assert latex(Adjoint(Y)*Adjoint(X)) == r'Y^{\dagger} X^{\dagger}'
    assert latex(Adjoint(X**2)) == r'\left(X^{2}\right)^{\dagger}'
    assert latex(Adjoint(X)**2) == r'\left(X^{\dagger}\right)^{2}'
    assert latex(Adjoint(Inverse(X))) == r'\left(X^{-1}\right)^{\dagger}'
    assert latex(Inverse(Adjoint(X))) == r'\left(X^{\dagger}\right)^{-1}'
    assert latex(Adjoint(Transpose(X))) == r'\left(X^{T}\right)^{\dagger}'
    assert latex(Transpose(Adjoint(X))) == r'\left(X^{\dagger}\right)^{T}'
    assert latex(Transpose(Adjoint(X) + Y)) == r'\left(X^{\dagger} + Y\right)^{T}'


def test_Transpose():
    from sympy.matrices import Transpose, MatPow, HadamardPower
    X = MatrixSymbol('X', 2, 2)
    Y = MatrixSymbol('Y', 2, 2)
    assert latex(Transpose(X)) == r'X^{T}'
    assert latex(Transpose(X + Y)) == r'\left(X + Y\right)^{T}'

    assert latex(Transpose(HadamardPower(X, 2))) == \
        r'\left(X^{\circ {2}}\right)^{T}'
    assert latex(HadamardPower(Transpose(X), 2)) == \
        r'\left(X^{T}\right)^{\circ {2}}'
    assert latex(Transpose(MatPow(X, 2))) == \
        r'\left(X^{2}\right)^{T}'
    assert latex(MatPow(Transpose(X), 2)) == \
        r'\left(X^{T}\right)^{2}'


def test_Hadamard():
    from sympy.matrices import MatrixSymbol, HadamardProduct, HadamardPower
    from sympy.matrices.expressions import MatAdd, MatMul, MatPow
    X = MatrixSymbol('X', 2, 2)
    Y = MatrixSymbol('Y', 2, 2)
    assert latex(HadamardProduct(X, Y*Y)) == r'X \circ Y^{2}'
    assert latex(HadamardProduct(X, Y)*Y) == r'\left(X \circ Y\right) Y'

    assert latex(HadamardPower(X, 2)) == r'X^{\circ {2}}'
    assert latex(HadamardPower(X, -1)) == r'X^{\circ \left({-1}\right)}'
    assert latex(HadamardPower(MatAdd(X, Y), 2)) == \
        r'\left(X + Y\right)^{\circ {2}}'
    assert latex(HadamardPower(MatMul(X, Y), 2)) == \
        r'\left(X Y\right)^{\circ {2}}'

    assert latex(HadamardPower(MatPow(X, -1), -1)) == \
        r'\left(X^{-1}\right)^{\circ \left({-1}\right)}'
    assert latex(MatPow(HadamardPower(X, -1), -1)) == \
        r'\left(X^{\circ \left({-1}\right)}\right)^{-1}'

    assert latex(HadamardPower(X, n+1)) == \
        r'X^{\circ \left({n + 1}\right)}'


def test_ElementwiseApplyFunction():
    from sympy.matrices import MatrixSymbol
    X = MatrixSymbol('X', 2, 2)
    expr = (X.T*X).applyfunc(sin)
    assert latex(expr) == r"{\left( d \mapsto \sin{\left(d \right)} \right)}_{\circ}\left({X^{T} X}\right)"
    expr = X.applyfunc(Lambda(x, 1/x))
    assert latex(expr) == r'{\left( d \mapsto \frac{1}{d} \right)}_{\circ}\left({X}\right)'


def test_ZeroMatrix():
    from sympy import ZeroMatrix
    assert latex(ZeroMatrix(1, 1), mat_symbol_style='plain') == r"\mathbb{0}"
    assert latex(ZeroMatrix(1, 1), mat_symbol_style='bold') == r"\mathbf{0}"


def test_OneMatrix():
    from sympy import OneMatrix
    assert latex(OneMatrix(3, 4), mat_symbol_style='plain') == r"\mathbb{1}"
    assert latex(OneMatrix(3, 4), mat_symbol_style='bold') == r"\mathbf{1}"


def test_Identity():
    from sympy import Identity
    assert latex(Identity(1), mat_symbol_style='plain') == r"\mathbb{I}"
    assert latex(Identity(1), mat_symbol_style='bold') == r"\mathbf{I}"


def test_boolean_args_order():
    syms = symbols('a:f')

    expr = And(*syms)
    assert latex(expr) == 'a \\wedge b \\wedge c \\wedge d \\wedge e \\wedge f'

    expr = Or(*syms)
    assert latex(expr) == 'a \\vee b \\vee c \\vee d \\vee e \\vee f'

    expr = Equivalent(*syms)
    assert latex(expr) == \
        'a \\Leftrightarrow b \\Leftrightarrow c \\Leftrightarrow d \\Leftrightarrow e \\Leftrightarrow f'

    expr = Xor(*syms)
    assert latex(expr) == \
        'a \\veebar b \\veebar c \\veebar d \\veebar e \\veebar f'


def test_imaginary():
    i = sqrt(-1)
    assert latex(i) == r'i'


def test_builtins_without_args():
    assert latex(sin) == r'\sin'
    assert latex(cos) == r'\cos'
    assert latex(tan) == r'\tan'
    assert latex(log) == r'\log'
    assert latex(Ei) == r'\operatorname{Ei}'
    assert latex(zeta) == r'\zeta'


def test_latex_greek_functions():
    # bug because capital greeks that have roman equivalents should not use
    # \Alpha, \Beta, \Eta, etc.
    s = Function('Alpha')
    assert latex(s) == r'A'
    assert latex(s(x)) == r'A{\left(x \right)}'
    s = Function('Beta')
    assert latex(s) == r'B'
    s = Function('Eta')
    assert latex(s) == r'H'
    assert latex(s(x)) == r'H{\left(x \right)}'

    # bug because sympy.core.numbers.Pi is special
    p = Function('Pi')
    # assert latex(p(x)) == r'\Pi{\left(x \right)}'
    assert latex(p) == r'\Pi'

    # bug because not all greeks are included
    c = Function('chi')
    assert latex(c(x)) == r'\chi{\left(x \right)}'
    assert latex(c) == r'\chi'


def test_translate():
    s = 'Alpha'
    assert translate(s) == 'A'
    s = 'Beta'
    assert translate(s) == 'B'
    s = 'Eta'
    assert translate(s) == 'H'
    s = 'omicron'
    assert translate(s) == 'o'
    s = 'Pi'
    assert translate(s) == r'\Pi'
    s = 'pi'
    assert translate(s) == r'\pi'
    s = 'LamdaHatDOT'
    assert translate(s) == r'\dot{\hat{\Lambda}}'


def test_other_symbols():
    from sympy.printing.latex import other_symbols
    for s in other_symbols:
        assert latex(symbols(s)) == "\\"+s


def test_modifiers():
    # Test each modifier individually in the simplest case
    # (with funny capitalizations)
    assert latex(symbols("xMathring")) == r"\mathring{x}"
    assert latex(symbols("xCheck")) == r"\check{x}"
    assert latex(symbols("xBreve")) == r"\breve{x}"
    assert latex(symbols("xAcute")) == r"\acute{x}"
    assert latex(symbols("xGrave")) == r"\grave{x}"
    assert latex(symbols("xTilde")) == r"\tilde{x}"
    assert latex(symbols("xPrime")) == r"{x}'"
    assert latex(symbols("xddDDot")) == r"\ddddot{x}"
    assert latex(symbols("xDdDot")) == r"\dddot{x}"
    assert latex(symbols("xDDot")) == r"\ddot{x}"
    assert latex(symbols("xBold")) == r"\boldsymbol{x}"
    assert latex(symbols("xnOrM")) == r"\left\|{x}\right\|"
    assert latex(symbols("xAVG")) == r"\left\langle{x}\right\rangle"
    assert latex(symbols("xHat")) == r"\hat{x}"
    assert latex(symbols("xDot")) == r"\dot{x}"
    assert latex(symbols("xBar")) == r"\bar{x}"
    assert latex(symbols("xVec")) == r"\vec{x}"
    assert latex(symbols("xAbs")) == r"\left|{x}\right|"
    assert latex(symbols("xMag")) == r"\left|{x}\right|"
    assert latex(symbols("xPrM")) == r"{x}'"
    assert latex(symbols("xBM")) == r"\boldsymbol{x}"
    # Test strings that are *only* the names of modifiers
    assert latex(symbols("Mathring")) == r"Mathring"
    assert latex(symbols("Check")) == r"Check"
    assert latex(symbols("Breve")) == r"Breve"
    assert latex(symbols("Acute")) == r"Acute"
    assert latex(symbols("Grave")) == r"Grave"
    assert latex(symbols("Tilde")) == r"Tilde"
    assert latex(symbols("Prime")) == r"Prime"
    assert latex(symbols("DDot")) == r"\dot{D}"
    assert latex(symbols("Bold")) == r"Bold"
    assert latex(symbols("NORm")) == r"NORm"
    assert latex(symbols("AVG")) == r"AVG"
    assert latex(symbols("Hat")) == r"Hat"
    assert latex(symbols("Dot")) == r"Dot"
    assert latex(symbols("Bar")) == r"Bar"
    assert latex(symbols("Vec")) == r"Vec"
    assert latex(symbols("Abs")) == r"Abs"
    assert latex(symbols("Mag")) == r"Mag"
    assert latex(symbols("PrM")) == r"PrM"
    assert latex(symbols("BM")) == r"BM"
    assert latex(symbols("hbar")) == r"\hbar"
    # Check a few combinations
    assert latex(symbols("xvecdot")) == r"\dot{\vec{x}}"
    assert latex(symbols("xDotVec")) == r"\vec{\dot{x}}"
    assert latex(symbols("xHATNorm")) == r"\left\|{\hat{x}}\right\|"
    # Check a couple big, ugly combinations
    assert latex(symbols('xMathringBm_yCheckPRM__zbreveAbs')) == \
        r"\boldsymbol{\mathring{x}}^{\left|{\breve{z}}\right|}_{{\check{y}}'}"
    assert latex(symbols('alphadothat_nVECDOT__tTildePrime')) == \
        r"\hat{\dot{\alpha}}^{{\tilde{t}}'}_{\dot{\vec{n}}}"


def test_greek_symbols():
    assert latex(Symbol('alpha'))   == r'\alpha'
    assert latex(Symbol('beta'))    == r'\beta'
    assert latex(Symbol('gamma'))   == r'\gamma'
    assert latex(Symbol('delta'))   == r'\delta'
    assert latex(Symbol('epsilon')) == r'\epsilon'
    assert latex(Symbol('zeta'))    == r'\zeta'
    assert latex(Symbol('eta'))     == r'\eta'
    assert latex(Symbol('theta'))   == r'\theta'
    assert latex(Symbol('iota'))    == r'\iota'
    assert latex(Symbol('kappa'))   == r'\kappa'
    assert latex(Symbol('lambda'))  == r'\lambda'
    assert latex(Symbol('mu'))      == r'\mu'
    assert latex(Symbol('nu'))      == r'\nu'
    assert latex(Symbol('xi'))      == r'\xi'
    assert latex(Symbol('omicron')) == r'o'
    assert latex(Symbol('pi'))      == r'\pi'
    assert latex(Symbol('rho'))     == r'\rho'
    assert latex(Symbol('sigma'))   == r'\sigma'
    assert latex(Symbol('tau'))     == r'\tau'
    assert latex(Symbol('upsilon')) == r'\upsilon'
    assert latex(Symbol('phi'))     == r'\phi'
    assert latex(Symbol('chi'))     == r'\chi'
    assert latex(Symbol('psi'))     == r'\psi'
    assert latex(Symbol('omega'))   == r'\omega'

    assert latex(Symbol('Alpha'))   == r'A'
    assert latex(Symbol('Beta'))    == r'B'
    assert latex(Symbol('Gamma'))   == r'\Gamma'
    assert latex(Symbol('Delta'))   == r'\Delta'
    assert latex(Symbol('Epsilon')) == r'E'
    assert latex(Symbol('Zeta'))    == r'Z'
    assert latex(Symbol('Eta'))     == r'H'
    assert latex(Symbol('Theta'))   == r'\Theta'
    assert latex(Symbol('Iota'))    == r'I'
    assert latex(Symbol('Kappa'))   == r'K'
    assert latex(Symbol('Lambda'))  == r'\Lambda'
    assert latex(Symbol('Mu'))      == r'M'
    assert latex(Symbol('Nu'))      == r'N'
    assert latex(Symbol('Xi'))      == r'\Xi'
    assert latex(Symbol('Omicron')) == r'O'
    assert latex(Symbol('Pi'))      == r'\Pi'
    assert latex(Symbol('Rho'))     == r'P'
    assert latex(Symbol('Sigma'))   == r'\Sigma'
    assert latex(Symbol('Tau'))     == r'T'
    assert latex(Symbol('Upsilon')) == r'\Upsilon'
    assert latex(Symbol('Phi'))     == r'\Phi'
    assert latex(Symbol('Chi'))     == r'X'
    assert latex(Symbol('Psi'))     == r'\Psi'
    assert latex(Symbol('Omega'))   == r'\Omega'

    assert latex(Symbol('varepsilon')) == r'\varepsilon'
    assert latex(Symbol('varkappa')) == r'\varkappa'
    assert latex(Symbol('varphi')) == r'\varphi'
    assert latex(Symbol('varpi')) == r'\varpi'
    assert latex(Symbol('varrho')) == r'\varrho'
    assert latex(Symbol('varsigma')) == r'\varsigma'
    assert latex(Symbol('vartheta')) == r'\vartheta'


def test_fancyset_symbols():
    assert latex(S.Rationals) == '\\mathbb{Q}'
    assert latex(S.Naturals) == '\\mathbb{N}'
    assert latex(S.Naturals0) == '\\mathbb{N}_0'
    assert latex(S.Integers) == '\\mathbb{Z}'
    assert latex(S.Reals) == '\\mathbb{R}'
    assert latex(S.Complexes) == '\\mathbb{C}'


@XFAIL
def test_builtin_without_args_mismatched_names():
    assert latex(CosineTransform) == r'\mathcal{COS}'


def test_builtin_no_args():
    assert latex(Chi) == r'\operatorname{Chi}'
    assert latex(beta) == r'\operatorname{B}'
    assert latex(gamma) == r'\Gamma'
    assert latex(KroneckerDelta) == r'\delta'
    assert latex(DiracDelta) == r'\delta'
    assert latex(lowergamma) == r'\gamma'


def test_issue_6853():
    p = Function('Pi')
    assert latex(p(x)) == r"\Pi{\left(x \right)}"


def test_Mul():
    e = Mul(-2, x + 1, evaluate=False)
    assert latex(e) == r'- 2 \left(x + 1\right)'
    e = Mul(2, x + 1, evaluate=False)
    assert latex(e) == r'2 \left(x + 1\right)'
    e = Mul(S.Half, x + 1, evaluate=False)
    assert latex(e) == r'\frac{x + 1}{2}'
    e = Mul(y, x + 1, evaluate=False)
    assert latex(e) == r'y \left(x + 1\right)'
    e = Mul(-y, x + 1, evaluate=False)
    assert latex(e) == r'- y \left(x + 1\right)'
    e = Mul(-2, x + 1)
    assert latex(e) == r'- 2 x - 2'
    e = Mul(2, x + 1)
    assert latex(e) == r'2 x + 2'


def test_Pow():
    e = Pow(2, 2, evaluate=False)
    assert latex(e) == r'2^{2}'
    assert latex(x**(Rational(-1, 3))) == r'\frac{1}{\sqrt[3]{x}}'
    x2 = Symbol(r'x^2')
    assert latex(x2**2) == r'\left(x^{2}\right)^{2}'


def test_issue_7180():
    assert latex(Equivalent(x, y)) == r"x \Leftrightarrow y"
    assert latex(Not(Equivalent(x, y))) == r"x \not\Leftrightarrow y"


def test_issue_8409():
    assert latex(S.Half**n) == r"\left(\frac{1}{2}\right)^{n}"


def test_issue_8470():
    from sympy.parsing.sympy_parser import parse_expr
    e = parse_expr("-B*A", evaluate=False)
    assert latex(e) == r"A \left(- B\right)"


def test_issue_15439():
    x = MatrixSymbol('x', 2, 2)
    y = MatrixSymbol('y', 2, 2)
    assert latex((x * y).subs(y, -y)) == r"x \left(- y\right)"
    assert latex((x * y).subs(y, -2*y)) == r"x \left(- 2 y\right)"
    assert latex((x * y).subs(x, -x)) == r"- x y"


def test_issue_2934():
    assert latex(Symbol(r'\frac{a_1}{b_1}')) == '\\frac{a_1}{b_1}'


def test_issue_10489():
    latexSymbolWithBrace = 'C_{x_{0}}'
    s = Symbol(latexSymbolWithBrace)
    assert latex(s) == latexSymbolWithBrace
    assert latex(cos(s)) == r'\cos{\left(C_{x_{0}} \right)}'


def test_issue_12886():
    m__1, l__1 = symbols('m__1, l__1')
    assert latex(m__1**2 + l__1**2) == \
        r'\left(l^{1}\right)^{2} + \left(m^{1}\right)^{2}'


def test_issue_13559():
    from sympy.parsing.sympy_parser import parse_expr
    expr = parse_expr('5/1', evaluate=False)
    assert latex(expr) == r"\frac{5}{1}"


def test_issue_13651():
    expr = c + Mul(-1, a + b, evaluate=False)
    assert latex(expr) == r"c - \left(a + b\right)"


def test_latex_UnevaluatedExpr():
    x = symbols("x")
    he = UnevaluatedExpr(1/x)
    assert latex(he) == latex(1/x) == r"\frac{1}{x}"
    assert latex(he**2) == r"\left(\frac{1}{x}\right)^{2}"
    assert latex(he + 1) == r"1 + \frac{1}{x}"
    assert latex(x*he) == r"x \frac{1}{x}"


def test_MatrixElement_printing():
    # test cases for issue #11821
    A = MatrixSymbol("A", 1, 3)
    B = MatrixSymbol("B", 1, 3)
    C = MatrixSymbol("C", 1, 3)

    assert latex(A[0, 0]) == r"A_{0, 0}"
    assert latex(3 * A[0, 0]) == r"3 A_{0, 0}"

    F = C[0, 0].subs(C, A - B)
    assert latex(F) == r"\left(A - B\right)_{0, 0}"

    i, j, k = symbols("i j k")
    M = MatrixSymbol("M", k, k)
    N = MatrixSymbol("N", k, k)
    assert latex((M*N)[i, j]) == \
        r'\sum_{i_{1}=0}^{k - 1} M_{i, i_{1}} N_{i_{1}, j}'


def test_MatrixSymbol_printing():
    # test cases for issue #14237
    A = MatrixSymbol("A", 3, 3)
    B = MatrixSymbol("B", 3, 3)
    C = MatrixSymbol("C", 3, 3)

    assert latex(-A) == r"- A"
    assert latex(A - A*B - B) == r"A - A B - B"
    assert latex(-A*B - A*B*C - B) == r"- A B - A B C - B"


def test_KroneckerProduct_printing():
    A = MatrixSymbol('A', 3, 3)
    B = MatrixSymbol('B', 2, 2)
    assert latex(KroneckerProduct(A, B)) == r'A \otimes B'


def test_Quaternion_latex_printing():
    q = Quaternion(x, y, z, t)
    assert latex(q) == "x + y i + z j + t k"
    q = Quaternion(x, y, z, x*t)
    assert latex(q) == "x + y i + z j + t x k"
    q = Quaternion(x, y, z, x + t)
    assert latex(q) == r"x + y i + z j + \left(t + x\right) k"


def test_TensorProduct_printing():
    from sympy.tensor.functions import TensorProduct
    A = MatrixSymbol("A", 3, 3)
    B = MatrixSymbol("B", 3, 3)
    assert latex(TensorProduct(A, B)) == r"A \otimes B"


def test_WedgeProduct_printing():
    from sympy.diffgeom.rn import R2
    from sympy.diffgeom import WedgeProduct
    wp = WedgeProduct(R2.dx, R2.dy)
    assert latex(wp) == r"\operatorname{d}x \wedge \operatorname{d}y"


def test_issue_14041():
    import sympy.physics.mechanics as me

    A_frame = me.ReferenceFrame('A')
    thetad, phid = me.dynamicsymbols('theta, phi', 1)
    L = Symbol('L')

    assert latex(L*(phid + thetad)**2*A_frame.x) == \
        r"L \left(\dot{\phi} + \dot{\theta}\right)^{2}\mathbf{\hat{a}_x}"
    assert latex((phid + thetad)**2*A_frame.x) == \
        r"\left(\dot{\phi} + \dot{\theta}\right)^{2}\mathbf{\hat{a}_x}"
    assert latex((phid*thetad)**a*A_frame.x) == \
        r"\left(\dot{\phi} \dot{\theta}\right)^{a}\mathbf{\hat{a}_x}"


def test_issue_9216():
    expr_1 = Pow(1, -1, evaluate=False)
    assert latex(expr_1) == r"1^{-1}"

    expr_2 = Pow(1, Pow(1, -1, evaluate=False), evaluate=False)
    assert latex(expr_2) == r"1^{1^{-1}}"

    expr_3 = Pow(3, -2, evaluate=False)
    assert latex(expr_3) == r"\frac{1}{9}"

    expr_4 = Pow(1, -2, evaluate=False)
    assert latex(expr_4) == r"1^{-2}"


def test_latex_printer_tensor():
    from sympy.tensor.tensor import TensorIndexType, tensor_indices, TensorHead, tensor_heads
    L = TensorIndexType("L")
    i, j, k, l = tensor_indices("i j k l", L)
    i0 = tensor_indices("i_0", L)
    A, B, C, D = tensor_heads("A B C D", [L])
    H = TensorHead("H", [L, L])
    K = TensorHead("K", [L, L, L, L])

    assert latex(i) == "{}^{i}"
    assert latex(-i) == "{}_{i}"

    expr = A(i)
    assert latex(expr) == "A{}^{i}"

    expr = A(i0)
    assert latex(expr) == "A{}^{i_{0}}"

    expr = A(-i)
    assert latex(expr) == "A{}_{i}"

    expr = -3*A(i)
    assert latex(expr) == r"-3A{}^{i}"

    expr = K(i, j, -k, -i0)
    assert latex(expr) == "K{}^{ij}{}_{ki_{0}}"

    expr = K(i, -j, -k, i0)
    assert latex(expr) == "K{}^{i}{}_{jk}{}^{i_{0}}"

    expr = K(i, -j, k, -i0)
    assert latex(expr) == "K{}^{i}{}_{j}{}^{k}{}_{i_{0}}"

    expr = H(i, -j)
    assert latex(expr) == "H{}^{i}{}_{j}"

    expr = H(i, j)
    assert latex(expr) == "H{}^{ij}"

    expr = H(-i, -j)
    assert latex(expr) == "H{}_{ij}"

    expr = (1+x)*A(i)
    assert latex(expr) == r"\left(x + 1\right)A{}^{i}"

    expr = H(i, -i)
    assert latex(expr) == "H{}^{L_{0}}{}_{L_{0}}"

    expr = H(i, -j)*A(j)*B(k)
    assert latex(expr) == "H{}^{i}{}_{L_{0}}A{}^{L_{0}}B{}^{k}"

    expr = A(i) + 3*B(i)
    assert latex(expr) == "3B{}^{i} + A{}^{i}"

    # Test ``TensorElement``:
    from sympy.tensor.tensor import TensorElement

    expr = TensorElement(K(i, j, k, l), {i: 3, k: 2})
    assert latex(expr) == 'K{}^{i=3,j,k=2,l}'

    expr = TensorElement(K(i, j, k, l), {i: 3})
    assert latex(expr) == 'K{}^{i=3,jkl}'

    expr = TensorElement(K(i, -j, k, l), {i: 3, k: 2})
    assert latex(expr) == 'K{}^{i=3}{}_{j}{}^{k=2,l}'

    expr = TensorElement(K(i, -j, k, -l), {i: 3, k: 2})
    assert latex(expr) == 'K{}^{i=3}{}_{j}{}^{k=2}{}_{l}'

    expr = TensorElement(K(i, j, -k, -l), {i: 3, -k: 2})
    assert latex(expr) == 'K{}^{i=3,j}{}_{k=2,l}'

    expr = TensorElement(K(i, j, -k, -l), {i: 3})
    assert latex(expr) == 'K{}^{i=3,j}{}_{kl}'

    expr = PartialDerivative(A(i), A(i))
    assert latex(expr) == r"\frac{\partial}{\partial {A{}^{L_{0}}}}{A{}^{L_{0}}}"

    expr = PartialDerivative(A(-i), A(-j))
    assert latex(expr) == r"\frac{\partial}{\partial {A{}_{j}}}{A{}_{i}}"

    expr = PartialDerivative(K(i, j, -k, -l), A(m), A(-n))
    assert latex(expr) == r"\frac{\partial^{2}}{\partial {A{}^{m}} \partial {A{}_{n}}}{K{}^{ij}{}_{kl}}"

    expr = PartialDerivative(B(-i) + A(-i), A(-j), A(-n))
    assert latex(expr) == r"\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(A{}_{i} + B{}_{i}\right)}"

    expr = PartialDerivative(3*A(-i), A(-j), A(-n))
    assert latex(expr) == r"\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(3A{}_{i}\right)}"


def test_multiline_latex():
    a, b, c, d, e, f = symbols('a b c d e f')
    expr = -a + 2*b -3*c +4*d -5*e
    expected = r"\begin{eqnarray}" + "\n"\
    r"f & = &- a \nonumber\\" + "\n"\
    r"& & + 2 b \nonumber\\" + "\n"\
    r"& & - 3 c \nonumber\\" + "\n"\
    r"& & + 4 d \nonumber\\" + "\n"\
    r"& & - 5 e " + "\n"\
    r"\end{eqnarray}"
    assert multiline_latex(f, expr, environment="eqnarray") == expected

    expected2 = r'\begin{eqnarray}' + '\n'\
    r'f & = &- a + 2 b \nonumber\\' + '\n'\
    r'& & - 3 c + 4 d \nonumber\\' + '\n'\
    r'& & - 5 e ' + '\n'\
    r'\end{eqnarray}'

    assert multiline_latex(f, expr, 2, environment="eqnarray") == expected2

    expected3 = r'\begin{eqnarray}' + '\n'\
    r'f & = &- a + 2 b - 3 c \nonumber\\'+ '\n'\
    r'& & + 4 d - 5 e ' + '\n'\
    r'\end{eqnarray}'

    assert multiline_latex(f, expr, 3, environment="eqnarray") == expected3

    expected3dots = r'\begin{eqnarray}' + '\n'\
    r'f & = &- a + 2 b - 3 c \dots\nonumber\\'+ '\n'\
    r'& & + 4 d - 5 e ' + '\n'\
    r'\end{eqnarray}'

    assert multiline_latex(f, expr, 3, environment="eqnarray", use_dots=True) == expected3dots

    expected3align = r'\begin{align*}' + '\n'\
    r'f = &- a + 2 b - 3 c \\'+ '\n'\
    r'& + 4 d - 5 e ' + '\n'\
    r'\end{align*}'

    assert multiline_latex(f, expr, 3) == expected3align
    assert multiline_latex(f, expr, 3, environment='align*') == expected3align

    expected2ieee = r'\begin{IEEEeqnarray}{rCl}' + '\n'\
    r'f & = &- a + 2 b \nonumber\\' + '\n'\
    r'& & - 3 c + 4 d \nonumber\\' + '\n'\
    r'& & - 5 e ' + '\n'\
    r'\end{IEEEeqnarray}'

    assert multiline_latex(f, expr, 2, environment="IEEEeqnarray") == expected2ieee

    raises(ValueError, lambda: multiline_latex(f, expr, environment="foo"))

def test_issue_15353():
    from sympy import ConditionSet, Tuple, S, sin, cos
    a, x = symbols('a x')
    # Obtained from nonlinsolve([(sin(a*x)),cos(a*x)],[x,a])
    sol = ConditionSet(
        Tuple(x, a), Eq(sin(a*x), 0) & Eq(cos(a*x), 0), S.Complexes**2)
    assert latex(sol) == \
        r'\left\{\left( x, \  a\right) \mid \left( x, \  a\right) \in ' \
        r'\mathbb{C}^{2} \wedge \sin{\left(a x \right)} = 0 \wedge ' \
        r'\cos{\left(a x \right)} = 0 \right\}'


def test_trace():
    # Issue 15303
    from sympy import trace
    A = MatrixSymbol("A", 2, 2)
    assert latex(trace(A)) == r"\operatorname{tr}\left(A \right)"
    assert latex(trace(A**2)) == r"\operatorname{tr}\left(A^{2} \right)"


def test_print_basic():
    # Issue 15303
    from sympy import Basic, Expr

    # dummy class for testing printing where the function is not
    # implemented in latex.py
    class UnimplementedExpr(Expr):
        def __new__(cls, e):
            return Basic.__new__(cls, e)

    # dummy function for testing
    def unimplemented_expr(expr):
        return UnimplementedExpr(expr).doit()

    # override class name to use superscript / subscript
    def unimplemented_expr_sup_sub(expr):
        result = UnimplementedExpr(expr)
        result.__class__.__name__ = 'UnimplementedExpr_x^1'
        return result

    assert latex(unimplemented_expr(x)) == r'UnimplementedExpr\left(x\right)'
    assert latex(unimplemented_expr(x**2)) == \
        r'UnimplementedExpr\left(x^{2}\right)'
    assert latex(unimplemented_expr_sup_sub(x)) == \
        r'UnimplementedExpr^{1}_{x}\left(x\right)'


def test_MatrixSymbol_bold():
    # Issue #15871
    from sympy import trace
    A = MatrixSymbol("A", 2, 2)
    assert latex(trace(A), mat_symbol_style='bold') == \
        r"\operatorname{tr}\left(\mathbf{A} \right)"
    assert latex(trace(A), mat_symbol_style='plain') == \
        r"\operatorname{tr}\left(A \right)"

    A = MatrixSymbol("A", 3, 3)
    B = MatrixSymbol("B", 3, 3)
    C = MatrixSymbol("C", 3, 3)

    assert latex(-A, mat_symbol_style='bold') == r"- \mathbf{A}"
    assert latex(A - A*B - B, mat_symbol_style='bold') == \
        r"\mathbf{A} - \mathbf{A} \mathbf{B} - \mathbf{B}"
    assert latex(-A*B - A*B*C - B, mat_symbol_style='bold') == \
        r"- \mathbf{A} \mathbf{B} - \mathbf{A} \mathbf{B} \mathbf{C} - \mathbf{B}"

    A_k = MatrixSymbol("A_k", 3, 3)
    assert latex(A_k, mat_symbol_style='bold') == r"\mathbf{A}_{k}"

    A = MatrixSymbol(r"\nabla_k", 3, 3)
    assert latex(A, mat_symbol_style='bold') == r"\mathbf{\nabla}_{k}"

def test_AppliedPermutation():
    p = Permutation(0, 1, 2)
    x = Symbol('x')
    assert latex(AppliedPermutation(p, x)) == \
        r'\sigma_{\left( 0\; 1\; 2\right)}(x)'


def test_PermutationMatrix():
    p = Permutation(0, 1, 2)
    assert latex(PermutationMatrix(p)) == r'P_{\left( 0\; 1\; 2\right)}'
    p = Permutation(0, 3)(1, 2)
    assert latex(PermutationMatrix(p)) == \
        r'P_{\left( 0\; 3\right)\left( 1\; 2\right)}'


def test_imaginary_unit():
    assert latex(1 + I) == '1 + i'
    assert latex(1 + I, imaginary_unit='i') == '1 + i'
    assert latex(1 + I, imaginary_unit='j') == '1 + j'
    assert latex(1 + I, imaginary_unit='foo') == '1 + foo'
    assert latex(I, imaginary_unit="ti") == '\\text{i}'
    assert latex(I, imaginary_unit="tj") == '\\text{j}'


def test_text_re_im():
    assert latex(im(x), gothic_re_im=True) ==  r'\Im{\left(x\right)}'
    assert latex(im(x), gothic_re_im=False) ==  r'\operatorname{im}{\left(x\right)}'
    assert latex(re(x), gothic_re_im=True) ==  r'\Re{\left(x\right)}'
    assert latex(re(x), gothic_re_im=False) ==  r'\operatorname{re}{\left(x\right)}'


def test_latex_diffgeom():
    from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential
    from sympy.diffgeom.rn import R2
    m = Manifold('M', 2)
    assert latex(m) == r'\text{M}'
    p = Patch('P', m)
    assert latex(p) == r'\text{P}_{\text{M}}'
    rect = CoordSystem('rect', p)
    assert latex(rect) == r'\text{rect}^{\text{P}}_{\text{M}}'
    b = BaseScalarField(rect, 0)
    assert latex(b) ==  r'\mathbf{rect_{0}}'

    g = Function('g')
    s_field = g(R2.x, R2.y)
    assert latex(Differential(s_field)) == \
        r'\operatorname{d}\left(g{\left(\mathbf{x},\mathbf{y} \right)}\right)'


def test_unit_printing():
    assert latex(5*meter) == r'5 \text{m}'
    assert latex(3*gibibyte) == r'3 \text{gibibyte}'
    assert latex(4*microgram/second) == r'\frac{4 \mu\text{g}}{\text{s}}'


def test_issue_17092():
    x_star = Symbol('x^*')
    assert latex(Derivative(x_star, x_star,2)) == r'\frac{d^{2}}{d \left(x^{*}\right)^{2}} x^{*}'


def test_latex_decimal_separator():

    x, y, z, t = symbols('x y z t')
    k, m, n = symbols('k m n', integer=True)
    f, g, h = symbols('f g h', cls=Function)

    # comma decimal_separator
    assert(latex([1, 2.3, 4.5], decimal_separator='comma') == r'\left[ 1; \  2{,}3; \  4{,}5\right]')
    assert(latex(FiniteSet(1, 2.3, 4.5), decimal_separator='comma') == r'\left\{1; 2{,}3; 4{,}5\right\}')
    assert(latex((1, 2.3, 4.6), decimal_separator = 'comma') == r'\left( 1; \  2{,}3; \  4{,}6\right)')
    assert(latex((1,), decimal_separator='comma') == r'\left( 1;\right)')

    # period decimal_separator
    assert(latex([1, 2.3, 4.5], decimal_separator='period') == r'\left[ 1, \  2.3, \  4.5\right]' )
    assert(latex(FiniteSet(1, 2.3, 4.5), decimal_separator='period') == r'\left\{1, 2.3, 4.5\right\}')
    assert(latex((1, 2.3, 4.6), decimal_separator = 'period') == r'\left( 1, \  2.3, \  4.6\right)')
    assert(latex((1,), decimal_separator='period') == r'\left( 1,\right)')

    # default decimal_separator
    assert(latex([1, 2.3, 4.5]) == r'\left[ 1, \  2.3, \  4.5\right]')
    assert(latex(FiniteSet(1, 2.3, 4.5)) == r'\left\{1, 2.3, 4.5\right\}')
    assert(latex((1, 2.3, 4.6)) == r'\left( 1, \  2.3, \  4.6\right)')
    assert(latex((1,)) == r'\left( 1,\right)')

    assert(latex(Mul(3.4,5.3), decimal_separator = 'comma') ==r'18{,}02')
    assert(latex(3.4*5.3, decimal_separator = 'comma')==r'18{,}02')
    x = symbols('x')
    y = symbols('y')
    z = symbols('z')
    assert(latex(x*5.3 + 2**y**3.4 + 4.5 + z, decimal_separator = 'comma')== r'2^{y^{3{,}4}} + 5{,}3 x + z + 4{,}5')

    assert(latex(0.987, decimal_separator='comma') == r'0{,}987')
    assert(latex(S(0.987), decimal_separator='comma')== r'0{,}987')
    assert(latex(.3, decimal_separator='comma')== r'0{,}3')
    assert(latex(S(.3), decimal_separator='comma')== r'0{,}3')


    assert(latex(5.8*10**(-7), decimal_separator='comma') ==r'5{,}8e-07')
    assert(latex(S(5.7)*10**(-7), decimal_separator='comma')==r'5{,}7 \cdot 10^{-7}')
    assert(latex(S(5.7*10**(-7)), decimal_separator='comma')==r'5{,}7 \cdot 10^{-7}')

    x = symbols('x')
    assert(latex(1.2*x+3.4, decimal_separator='comma')==r'1{,}2 x + 3{,}4')
    assert(latex(FiniteSet(1, 2.3, 4.5), decimal_separator='period')==r'\left\{1, 2.3, 4.5\right\}')

    # Error Handling tests
    raises(ValueError, lambda: latex([1,2.3,4.5], decimal_separator='non_existing_decimal_separator_in_list'))
    raises(ValueError, lambda: latex(FiniteSet(1,2.3,4.5), decimal_separator='non_existing_decimal_separator_in_set'))
    raises(ValueError, lambda: latex((1,2.3,4.5), decimal_separator='non_existing_decimal_separator_in_tuple'))