from sympy import MatAdd, MatMul, Array from sympy.algebras.quaternion import Quaternion from sympy.calculus.accumulationbounds import AccumBounds from sympy.combinatorics.permutations import Cycle, Permutation, AppliedPermutation from sympy.concrete.products import Product from sympy.concrete.summations import Sum from sympy.core.containers import Tuple, Dict from sympy.core.expr import UnevaluatedExpr from sympy.core.function import (Derivative, Function, Lambda, Subs, diff) from sympy.core.mod import Mod from sympy.core.mul import Mul from sympy.core.numbers import (AlgebraicNumber, Float, I, Integer, Rational, oo, pi) from sympy.core.parameters import evaluate from sympy.core.power import Pow from sympy.core.relational import Eq, Ne from sympy.core.singleton import S from sympy.core.symbol import (Symbol, Wild, symbols) from sympy.functions.combinatorial.factorials import (FallingFactorial, RisingFactorial, binomial, factorial, factorial2, subfactorial) from sympy.functions.combinatorial.numbers import (bernoulli, bell, catalan, euler, genocchi, lucas, fibonacci, tribonacci, divisor_sigma, udivisor_sigma, mobius, primenu, primeomega, totient, reduced_totient) from sympy.functions.elementary.complexes import (Abs, arg, conjugate, im, polar_lift, re) from sympy.functions.elementary.exponential import (LambertW, exp, log) from sympy.functions.elementary.hyperbolic import (asinh, coth) from sympy.functions.elementary.integers import (ceiling, floor, frac) from sympy.functions.elementary.miscellaneous import (Max, Min, root, sqrt) from sympy.functions.elementary.piecewise import Piecewise from sympy.functions.elementary.trigonometric import (acsc, asin, cos, cot, sin, tan) from sympy.functions.special.beta_functions import beta from sympy.functions.special.delta_functions import (DiracDelta, Heaviside) from sympy.functions.special.elliptic_integrals import (elliptic_e, elliptic_f, elliptic_k, elliptic_pi) from sympy.functions.special.error_functions import (Chi, Ci, Ei, Shi, Si, expint) from sympy.functions.special.gamma_functions import (gamma, uppergamma) from sympy.functions.special.hyper import (hyper, meijerg) from sympy.functions.special.mathieu_functions import (mathieuc, mathieucprime, mathieus, mathieusprime) from sympy.functions.special.polynomials import (assoc_laguerre, assoc_legendre, chebyshevt, chebyshevu, gegenbauer, hermite, jacobi, laguerre, legendre) from sympy.functions.special.singularity_functions import SingularityFunction from sympy.functions.special.spherical_harmonics import (Ynm, Znm) from sympy.functions.special.tensor_functions import (KroneckerDelta, LeviCivita) from sympy.functions.special.zeta_functions import (dirichlet_eta, lerchphi, polylog, stieltjes, zeta) from sympy.integrals.integrals import Integral from sympy.integrals.transforms import (CosineTransform, FourierTransform, InverseCosineTransform, InverseFourierTransform, InverseLaplaceTransform, InverseMellinTransform, InverseSineTransform, LaplaceTransform, MellinTransform, SineTransform) from sympy.logic import Implies from sympy.logic.boolalg import (And, Or, Xor, Equivalent, false, Not, true) from sympy.matrices.dense import Matrix from sympy.matrices.expressions.kronecker import KroneckerProduct from sympy.matrices.expressions.matexpr import MatrixSymbol from sympy.matrices.expressions.permutation import PermutationMatrix from sympy.matrices.expressions.slice import MatrixSlice from sympy.physics.control.lti import TransferFunction, Series, Parallel, Feedback, TransferFunctionMatrix, MIMOSeries, MIMOParallel, MIMOFeedback from sympy.physics.quantum import Commutator, Operator from sympy.physics.quantum.trace import Tr from sympy.physics.units import meter, gibibyte, gram, microgram, second, milli, micro from sympy.polys.domains.integerring import ZZ from sympy.polys.fields import field from sympy.polys.polytools import Poly from sympy.polys.rings import ring from sympy.polys.rootoftools import (RootSum, rootof) from sympy.series.formal import fps from sympy.series.fourier import fourier_series from sympy.series.limits import Limit from sympy.series.order import Order from sympy.series.sequences import (SeqAdd, SeqFormula, SeqMul, SeqPer) from sympy.sets.conditionset import ConditionSet from sympy.sets.contains import Contains from sympy.sets.fancysets import (ComplexRegion, ImageSet, Range) from sympy.sets.ordinals import Ordinal, OrdinalOmega, OmegaPower from sympy.sets.powerset import PowerSet from sympy.sets.sets import (FiniteSet, Interval, Union, Intersection, Complement, SymmetricDifference, ProductSet) from sympy.sets.setexpr import SetExpr from sympy.stats.crv_types import Normal from sympy.stats.symbolic_probability import (Covariance, Expectation, Probability, Variance) from sympy.tensor.array import (ImmutableDenseNDimArray, ImmutableSparseNDimArray, MutableSparseNDimArray, MutableDenseNDimArray, tensorproduct) from sympy.tensor.array.expressions.array_expressions import ArraySymbol, ArrayElement from sympy.tensor.indexed import (Idx, Indexed, IndexedBase) from sympy.tensor.toperators import PartialDerivative from sympy.vector import CoordSys3D, Cross, Curl, Dot, Divergence, Gradient, Laplacian from sympy.testing.pytest import (XFAIL, raises, _both_exp_pow, warns_deprecated_sympy) from sympy.printing.latex import (latex, translate, greek_letters_set, tex_greek_dictionary, multiline_latex, latex_escape, LatexPrinter) import sympy as sym from sympy.abc import mu, tau class lowergamma(sym.lowergamma): pass # testing notation inheritance by a subclass with same name x, y, z, t, w, a, b, c, s, p = symbols('x y z t w a b c s p') 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)) == r"foo(x)" class R(Abs): def _latex(self, printer): return "foo" assert latex(R(x)) == r"foo" def test_latex_basic(): assert latex(1 + x) == r"x + 1" assert latex(x**2) == r"x^{2}" assert latex(x**(1 + x)) == r"x^{x + 1}" assert latex(x**3 + x + 1 + x**2) == r"x^{3} + x^{2} + x + 1" assert latex(2*x*y) == r"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(x**S.Half**5) == r"\sqrt[32]{x}" assert latex(Mul(S.Half, x**2, -5, evaluate=False)) == r"\frac{1}{2} x^{2} \left(-5\right)" assert latex(Mul(S.Half, x**2, 5, evaluate=False)) == r"\frac{1}{2} x^{2} \cdot 5" assert latex(Mul(-5, -5, evaluate=False)) == r"\left(-5\right) \left(-5\right)" assert latex(Mul(5, -5, evaluate=False)) == r"5 \left(-5\right)" assert latex(Mul(S.Half, -5, S.Half, evaluate=False)) == r"\frac{1}{2} \left(-5\right) \frac{1}{2}" assert latex(Mul(5, I, 5, evaluate=False)) == r"5 i 5" assert latex(Mul(5, I, -5, evaluate=False)) == r"5 i \left(-5\right)" assert latex(Mul(Pow(x, 2), S.Half*x + 1)) == r"x^{2} \left(\frac{x}{2} + 1\right)" assert latex(Mul(Pow(x, 3), Rational(2, 3)*x + 1)) == r"x^{3} \left(\frac{2 x}{3} + 1\right)" assert latex(Mul(Pow(x, 11), 2*x + 1)) == r"x^{11} \left(2 x + 1\right)" assert latex(Mul(0, 1, evaluate=False)) == r'0 \cdot 1' assert latex(Mul(1, 0, evaluate=False)) == r'1 \cdot 0' assert latex(Mul(1, 1, evaluate=False)) == r'1 \cdot 1' assert latex(Mul(-1, 1, evaluate=False)) == r'\left(-1\right) 1' assert latex(Mul(1, 1, 1, evaluate=False)) == r'1 \cdot 1 \cdot 1' assert latex(Mul(1, 2, evaluate=False)) == r'1 \cdot 2' assert latex(Mul(1, S.Half, evaluate=False)) == r'1 \cdot \frac{1}{2}' assert latex(Mul(1, 1, S.Half, evaluate=False)) == \ r'1 \cdot 1 \cdot \frac{1}{2}' assert latex(Mul(1, 1, 2, 3, x, evaluate=False)) == \ r'1 \cdot 1 \cdot 2 \cdot 3 x' assert latex(Mul(1, -1, evaluate=False)) == r'1 \left(-1\right)' assert latex(Mul(4, 3, 2, 1, 0, y, x, evaluate=False)) == \ r'4 \cdot 3 \cdot 2 \cdot 1 \cdot 0 y x' assert latex(Mul(4, 3, 2, 1+z, 0, y, x, evaluate=False)) == \ r'4 \cdot 3 \cdot 2 \left(z + 1\right) 0 y x' assert latex(Mul(Rational(2, 3), Rational(5, 7), evaluate=False)) == \ r'\frac{2}{3} \cdot \frac{5}{7}' assert latex(1/x) == r"\frac{1}{x}" assert latex(1/x, fold_short_frac=True) == r"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) == r"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) == r"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(AlgebraicNumber(sqrt(2))) == r"\sqrt{2}" assert latex(AlgebraicNumber(sqrt(2), [3, -7])) == r"-7 + 3 \sqrt{2}" assert latex(AlgebraicNumber(sqrt(2), alias='alpha')) == r"\alpha" assert latex(AlgebraicNumber(sqrt(2), [3, -7], alias='alpha')) == \ r"3 \alpha - 7" assert latex(AlgebraicNumber(2**(S(1)/3), [1, 3, -7], alias='beta')) == \ r"\beta^{2} + 3 \beta - 7" k = ZZ.cyclotomic_field(5) assert latex(k.ext.field_element([1, 2, 3, 4])) == \ r"\zeta^{3} + 2 \zeta^{2} + 3 \zeta + 4" assert latex(k.ext.field_element([1, 2, 3, 4]), order='old') == \ r"4 + 3 \zeta + 2 \zeta^{2} + \zeta^{3}" assert latex(k.primes_above(19)[0]) == \ r"\left(19, \zeta^{2} + 5 \zeta + 1\right)" assert latex(k.primes_above(19)[0], order='old') == \ r"\left(19, 1 + 5 \zeta + \zeta^{2}\right)" assert latex(k.primes_above(7)[0]) == r"\left(7\right)" 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" assert latex(Pow(Rational(1, 3), -1, evaluate=False)) == r"\frac{1}{\frac{1}{3}}" assert latex(Pow(Rational(1, 3), -2, evaluate=False)) == r"\frac{1}{(\frac{1}{3})^{2}}" assert latex(Pow(Integer(1)/100, -1, evaluate=False)) == r"\frac{1}{\frac{1}{100}}" 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}" assert latex(SingularityFunction(x, 4, 5)**3) == \ r"{\left({\langle x - 4 \rangle}^{5}\right)}^{3}" assert latex(SingularityFunction(x, -3, 4)**3) == \ r"{\left({\langle x + 3 \rangle}^{4}\right)}^{3}" assert latex(SingularityFunction(x, 0, 4)**3) == \ r"{\left({\langle x \rangle}^{4}\right)}^{3}" assert latex(SingularityFunction(x, a, n)**3) == \ r"{\left({\langle - a + x \rangle}^{n}\right)}^{3}" assert latex(SingularityFunction(x, 4, -2)**3) == \ r"{\left({\langle x - 4 \rangle}^{-2}\right)}^{3}" assert latex((SingularityFunction(x, 4, -1)**3)**3) == \ r"{\left({\langle x - 4 \rangle}^{-1}\right)}^{9}" 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)" with warns_deprecated_sympy(): old_print_cyclic = Permutation.print_cyclic Permutation.print_cyclic = False assert latex(Permutation(0, 1)(2, 3)) == \ r"\begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 2 \end{pmatrix}" Permutation.print_cyclic = old_print_cyclic 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(\left(3 \mathbf{{x}_{A}}\right)\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(\left(x\right)\mathbf{\hat{i}_{A}}\right)' assert latex(Curl(3*A.x*A.j)) == \ r"\nabla\times \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)" assert latex(Curl(3*A.x*A.j+A.i)) == \ r"\nabla\times \left(\mathbf{\hat{i}_{A}} + \left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)" assert latex(Curl(3*x*A.x*A.j)) == \ r"\nabla\times \left(\left(3 \mathbf{{x}_{A}} x\right)\mathbf{\hat{j}_{A}}\right)" assert latex(x*Curl(3*A.x*A.j)) == \ r"x \left(\nabla\times \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)\right)" assert latex(Divergence(3*A.x*A.j+A.i)) == \ r"\nabla\cdot \left(\mathbf{\hat{i}_{A}} + \left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)" assert latex(Divergence(3*A.x*A.j)) == \ r"\nabla\cdot \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)" assert latex(x*Divergence(3*A.x*A.j)) == \ r"x \left(\nabla\cdot \left(\left(3 \mathbf{{x}_{A}}\right)\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(\left(3 \mathbf{{x}_{A}}\right)\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(\left(x\right)\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"\Delta \mathbf{{x}_{A}}" assert latex(Laplacian(A.x + 3*A.y)) == \ r"\Delta \left(\mathbf{{x}_{A}} + 3 \mathbf{{y}_{A}}\right)" assert latex(x*Laplacian(A.x)) == r"x \left(\Delta \mathbf{{x}_{A}}\right)" assert latex(Laplacian(x*A.x)) == r"\Delta \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) == r"\mathrm{T}" assert latex(TAU) == r"\tau" assert latex(taU) == r"\tau" # Check that all capitalized greek letters are handled explicitly capitalized_letters = {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^{\mathrm{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}" @_both_exp_pow def test_latex_functions(): assert latex(exp(x)) == r"e^{x}" assert latex(exp(1) + exp(2)) == r"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, evaluate=False)) == r'\operatorname{B}\left(x, x\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" a_1 = Function('a_1') assert latex(a_1) == r"a_{1}" assert latex(a_1(x)) == r"a_{1}{\left(x \right)}" assert latex(Function('a_1')) == r"a_{1}" # Issue #16925 # multi letter function names # > simple assert latex(Function('ab')) == r"\operatorname{ab}" assert latex(Function('ab1')) == r"\operatorname{ab}_{1}" assert latex(Function('ab12')) == r"\operatorname{ab}_{12}" assert latex(Function('ab_1')) == r"\operatorname{ab}_{1}" assert latex(Function('ab_12')) == r"\operatorname{ab}_{12}" assert latex(Function('ab_c')) == r"\operatorname{ab}_{c}" assert latex(Function('ab_cd')) == r"\operatorname{ab}_{cd}" # > with argument assert latex(Function('ab')(Symbol('x'))) == r"\operatorname{ab}{\left(x \right)}" assert latex(Function('ab1')(Symbol('x'))) == r"\operatorname{ab}_{1}{\left(x \right)}" assert latex(Function('ab12')(Symbol('x'))) == r"\operatorname{ab}_{12}{\left(x \right)}" assert latex(Function('ab_1')(Symbol('x'))) == r"\operatorname{ab}_{1}{\left(x \right)}" assert latex(Function('ab_c')(Symbol('x'))) == r"\operatorname{ab}_{c}{\left(x \right)}" assert latex(Function('ab_cd')(Symbol('x'))) == r"\operatorname{ab}_{cd}{\left(x \right)}" # > with power # does not work on functions without brackets # > with argument and power combined assert latex(Function('ab')()**2) == r"\operatorname{ab}^{2}{\left( \right)}" assert latex(Function('ab1')()**2) == r"\operatorname{ab}_{1}^{2}{\left( \right)}" assert latex(Function('ab12')()**2) == r"\operatorname{ab}_{12}^{2}{\left( \right)}" assert latex(Function('ab_1')()**2) == r"\operatorname{ab}_{1}^{2}{\left( \right)}" assert latex(Function('ab_12')()**2) == r"\operatorname{ab}_{12}^{2}{\left( \right)}" assert latex(Function('ab')(Symbol('x'))**2) == r"\operatorname{ab}^{2}{\left(x \right)}" assert latex(Function('ab1')(Symbol('x'))**2) == r"\operatorname{ab}_{1}^{2}{\left(x \right)}" assert latex(Function('ab12')(Symbol('x'))**2) == r"\operatorname{ab}_{12}^{2}{\left(x \right)}" assert latex(Function('ab_1')(Symbol('x'))**2) == r"\operatorname{ab}_{1}^{2}{\left(x \right)}" assert latex(Function('ab_12')(Symbol('x'))**2) == \ r"\operatorname{ab}_{12}^{2}{\left(x \right)}" # single letter function names # > simple assert latex(Function('a')) == r"a" assert latex(Function('a1')) == r"a_{1}" assert latex(Function('a12')) == r"a_{12}" assert latex(Function('a_1')) == r"a_{1}" assert latex(Function('a_12')) == r"a_{12}" # > with argument assert latex(Function('a')()) == r"a{\left( \right)}" assert latex(Function('a1')()) == r"a_{1}{\left( \right)}" assert latex(Function('a12')()) == r"a_{12}{\left( \right)}" assert latex(Function('a_1')()) == r"a_{1}{\left( \right)}" assert latex(Function('a_12')()) == r"a_{12}{\left( \right)}" # > with power # does not work on functions without brackets # > with argument and power combined assert latex(Function('a')()**2) == r"a^{2}{\left( \right)}" assert latex(Function('a1')()**2) == r"a_{1}^{2}{\left( \right)}" assert latex(Function('a12')()**2) == r"a_{12}^{2}{\left( \right)}" assert latex(Function('a_1')()**2) == r"a_{1}^{2}{\left( \right)}" assert latex(Function('a_12')()**2) == r"a_{12}^{2}{\left( \right)}" assert latex(Function('a')(Symbol('x'))**2) == r"a^{2}{\left(x \right)}" assert latex(Function('a1')(Symbol('x'))**2) == r"a_{1}^{2}{\left(x \right)}" assert latex(Function('a12')(Symbol('x'))**2) == r"a_{12}^{2}{\left(x \right)}" assert latex(Function('a_1')(Symbol('x'))**2) == r"a_{1}^{2}{\left(x \right)}" assert latex(Function('a_12')(Symbol('x'))**2) == r"a_{12}^{2}{\left(x \right)}" assert latex(Function('a')()**32) == r"a^{32}{\left( \right)}" assert latex(Function('a1')()**32) == r"a_{1}^{32}{\left( \right)}" assert latex(Function('a12')()**32) == r"a_{12}^{32}{\left( \right)}" assert latex(Function('a_1')()**32) == r"a_{1}^{32}{\left( \right)}" assert latex(Function('a_12')()**32) == r"a_{12}^{32}{\left( \right)}" assert latex(Function('a')(Symbol('x'))**32) == r"a^{32}{\left(x \right)}" assert latex(Function('a1')(Symbol('x'))**32) == r"a_{1}^{32}{\left(x \right)}" assert latex(Function('a12')(Symbol('x'))**32) == r"a_{12}^{32}{\left(x \right)}" assert latex(Function('a_1')(Symbol('x'))**32) == r"a_{1}^{32}{\left(x \right)}" assert latex(Function('a_12')(Symbol('x'))**32) == r"a_{12}^{32}{\left(x \right)}" assert latex(Function('a')()**a) == r"a^{a}{\left( \right)}" assert latex(Function('a1')()**a) == r"a_{1}^{a}{\left( \right)}" assert latex(Function('a12')()**a) == r"a_{12}^{a}{\left( \right)}" assert latex(Function('a_1')()**a) == r"a_{1}^{a}{\left( \right)}" assert latex(Function('a_12')()**a) == r"a_{12}^{a}{\left( \right)}" assert latex(Function('a')(Symbol('x'))**a) == r"a^{a}{\left(x \right)}" assert latex(Function('a1')(Symbol('x'))**a) == r"a_{1}^{a}{\left(x \right)}" assert latex(Function('a12')(Symbol('x'))**a) == r"a_{12}^{a}{\left(x \right)}" assert latex(Function('a_1')(Symbol('x'))**a) == r"a_{1}^{a}{\left(x \right)}" assert latex(Function('a_12')(Symbol('x'))**a) == r"a_{12}^{a}{\left(x \right)}" ab = Symbol('ab') assert latex(Function('a')()**ab) == r"a^{ab}{\left( \right)}" assert latex(Function('a1')()**ab) == r"a_{1}^{ab}{\left( \right)}" assert latex(Function('a12')()**ab) == r"a_{12}^{ab}{\left( \right)}" assert latex(Function('a_1')()**ab) == r"a_{1}^{ab}{\left( \right)}" assert latex(Function('a_12')()**ab) == r"a_{12}^{ab}{\left( \right)}" assert latex(Function('a')(Symbol('x'))**ab) == r"a^{ab}{\left(x \right)}" assert latex(Function('a1')(Symbol('x'))**ab) == r"a_{1}^{ab}{\left(x \right)}" assert latex(Function('a12')(Symbol('x'))**ab) == r"a_{12}^{ab}{\left(x \right)}" assert latex(Function('a_1')(Symbol('x'))**ab) == r"a_{1}^{ab}{\left(x \right)}" assert latex(Function('a_12')(Symbol('x'))**ab) == r"a_{12}^{ab}{\left(x \right)}" assert latex(Function('a^12')(x)) == R"a^{12}{\left(x \right)}" assert latex(Function('a^12')(x) ** ab) == R"\left(a^{12}\right)^{ab}{\left(x \right)}" assert latex(Function('a__12')(x)) == R"a^{12}{\left(x \right)}" assert latex(Function('a__12')(x) ** ab) == R"\left(a^{12}\right)^{ab}{\left(x \right)}" assert latex(Function('a_1__1_2')(x)) == R"a^{1}_{1 2}{\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{arsinh}{\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(LambertW(n) * LambertW(n)) == r"W^{2}\left(n\right)" assert latex(Pow(LambertW(n), 2)) == r"W^{2}\left(n\right)" assert latex(LambertW(n)**k) == r"W^{k}\left(n\right)" assert latex(LambertW(n, k)**p) == r"W^{p}_{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(7, x + 1)) == r'7 \bmod \left(x + 1\right)' assert latex(Mod(2 * x, 7)) == r'2 x \bmod 7' assert latex(Mod(7, 2 * x)) == r'7 \bmod 2 x' 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)' assert latex(Mod(7, 2 * x)**n) == r'\left(7 \bmod 2 x\right)^{n}' # 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.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} 2, x ' \ 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 == r'\Psi_{0} \overline{\Psi_{0}}' assert indexed_latex == r'\overline{{\Psi}_{0}} {\Psi}_{0}' # Symbol('gamma') gives r'\gamma' interval = '\\mathrel{..}\\nobreak ' assert latex(Indexed('x1', Symbol('i'))) == r'{x_{1}}_{i}' assert latex(Indexed('x2', Idx('i'))) == r'{x_{2}}_{i}' assert latex(Indexed('x3', Idx('i', Symbol('N')))) == r'{x_{3}}_{{i}_{0'+interval+'N - 1}}' assert latex(Indexed('x3', Idx('i', Symbol('N')+1))) == r'{x_{3}}_{{i}_{0'+interval+'N}}' assert latex(Indexed('x4', Idx('i', (Symbol('a'),Symbol('b'))))) == r'{x_{4}}_{{i}_{a'+interval+'b}}' assert latex(IndexedBase('gamma')) == r'\gamma' assert latex(IndexedBase('a b')) == r'a b' assert latex(IndexedBase('a_b')) == r'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)}' # set diff operator assert latex(diff(f(x), x), diff_operator="rd") == r'\frac{\mathrm{d}}{\mathrm{d} x} 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" # set diff operator assert latex(Integral(x, x), diff_operator="rd") == r'\int x\, \mathrm{d}x' assert latex(Integral(x, (x, 0, 1)), diff_operator="rd") == r'\int\limits_{0}^{1} x\, \mathrm{d}x' 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'\text{Range}\left(a, b, c\right)' assert latex(Range(a, 10, 1)) == r'\text{Range}\left(a, 10\right)' assert latex(Range(0, b, 1)) == r'\text{Range}\left(b\right)' assert latex(Range(0, 10, c)) == r'\text{Range}\left(0, 10, c\right)' i = Symbol('i', integer=True) n = Symbol('n', negative=True, integer=True) p = Symbol('p', positive=True, integer=True) assert latex(Range(i, i + 3)) == r'\left\{i, i + 1, i + 2\right\}' assert latex(Range(-oo, n, 2)) == r'\left\{\ldots, n - 4, n - 2\right\}' assert latex(Range(p, oo)) == r'\left\{p, p + 1, \ldots\right\}' # The following will work if __iter__ is improved # assert latex(Range(-3, p + 7)) == r'\left\{-3, -2, \ldots, p + 6\right\}' # Must have integer assumptions assert latex(Range(a, a + 3)) == r'\text{Range}\left(a, a + 3\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_latex_powerset(): fset = FiniteSet(1, 2, 3) assert latex(PowerSet(fset)) == r'\mathcal{P}\left(\left\{1, 2, 3\right\}\right)' def test_latex_ordinals(): w = OrdinalOmega() assert latex(w) == r"\omega" wp = OmegaPower(2, 3) assert latex(wp) == r'3 \omega^{2}' assert latex(Ordinal(wp, OmegaPower(1, 1))) == r'3 \omega^{2} + \omega' assert latex(Ordinal(OmegaPower(2, 1), OmegaPower(1, 2))) == r'\omega^{2} + 2 \omega' 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)) == \ r'\left\{a\right\} \cap ' \ r'\left(\left\{c\right\} \cup \left\{d\right\}\right)' assert latex(Intersection(U1, U2, evaluate=False)) == \ r'\left(\left\{a\right\} \cup \left\{b\right\}\right) ' \ r'\cap \left(\left\{c\right\} \cup \left\{d\right\}\right)' assert latex(Intersection(C1, C2, evaluate=False)) == \ r'\left(\left\{a\right\} \setminus ' \ r'\left\{b\right\}\right) \cap \left(\left\{c\right\} ' \ r'\setminus \left\{d\right\}\right)' assert latex(Intersection(D1, D2, evaluate=False)) == \ r'\left(\left\{a\right\} \triangle ' \ r'\left\{b\right\}\right) \cap \left(\left\{c\right\} ' \ r'\triangle \left\{d\right\}\right)' assert latex(Intersection(P1, P2, evaluate=False)) == \ r'\left(\left\{a\right\} \times \left\{b\right\}\right) ' \ r'\cap \left(\left\{c\right\} \times ' \ r'\left\{d\right\}\right)' assert latex(Union(A, I2, evaluate=False)) == \ r'\left\{a\right\} \cup ' \ r'\left(\left\{c\right\} \cap \left\{d\right\}\right)' assert latex(Union(I1, I2, evaluate=False)) == \ r'\left(\left\{a\right\} \cap \left\{b\right\}\right) ' \ r'\cup \left(\left\{c\right\} \cap \left\{d\right\}\right)' assert latex(Union(C1, C2, evaluate=False)) == \ r'\left(\left\{a\right\} \setminus ' \ r'\left\{b\right\}\right) \cup \left(\left\{c\right\} ' \ r'\setminus \left\{d\right\}\right)' assert latex(Union(D1, D2, evaluate=False)) == \ r'\left(\left\{a\right\} \triangle ' \ r'\left\{b\right\}\right) \cup \left(\left\{c\right\} ' \ r'\triangle \left\{d\right\}\right)' assert latex(Union(P1, P2, evaluate=False)) == \ r'\left(\left\{a\right\} \times \left\{b\right\}\right) ' \ r'\cup \left(\left\{c\right\} \times ' \ r'\left\{d\right\}\right)' assert latex(Complement(A, C2, evaluate=False)) == \ r'\left\{a\right\} \setminus \left(\left\{c\right\} ' \ r'\setminus \left\{d\right\}\right)' assert latex(Complement(U1, U2, evaluate=False)) == \ r'\left(\left\{a\right\} \cup \left\{b\right\}\right) ' \ r'\setminus \left(\left\{c\right\} \cup ' \ r'\left\{d\right\}\right)' assert latex(Complement(I1, I2, evaluate=False)) == \ r'\left(\left\{a\right\} \cap \left\{b\right\}\right) ' \ r'\setminus \left(\left\{c\right\} \cap ' \ r'\left\{d\right\}\right)' assert latex(Complement(D1, D2, evaluate=False)) == \ r'\left(\left\{a\right\} \triangle ' \ r'\left\{b\right\}\right) \setminus ' \ r'\left(\left\{c\right\} \triangle \left\{d\right\}\right)' assert latex(Complement(P1, P2, evaluate=False)) == \ r'\left(\left\{a\right\} \times \left\{b\right\}\right) '\ r'\setminus \left(\left\{c\right\} \times '\ r'\left\{d\right\}\right)' assert latex(SymmetricDifference(A, D2, evaluate=False)) == \ r'\left\{a\right\} \triangle \left(\left\{c\right\} ' \ r'\triangle \left\{d\right\}\right)' assert latex(SymmetricDifference(U1, U2, evaluate=False)) == \ r'\left(\left\{a\right\} \cup \left\{b\right\}\right) ' \ r'\triangle \left(\left\{c\right\} \cup ' \ r'\left\{d\right\}\right)' assert latex(SymmetricDifference(I1, I2, evaluate=False)) == \ r'\left(\left\{a\right\} \cap \left\{b\right\}\right) ' \ r'\triangle \left(\left\{c\right\} \cap ' \ r'\left\{d\right\}\right)' assert latex(SymmetricDifference(C1, C2, evaluate=False)) == \ r'\left(\left\{a\right\} \setminus ' \ r'\left\{b\right\}\right) \triangle ' \ r'\left(\left\{c\right\} \setminus \left\{d\right\}\right)' assert latex(SymmetricDifference(P1, P2, evaluate=False)) == \ r'\left(\left\{a\right\} \times \left\{b\right\}\right) ' \ r'\triangle \left(\left\{c\right\} \times ' \ r'\left\{d\right\}\right)' # XXX This can be incorrect since cartesian product is not associative assert latex(ProductSet(A, P2).flatten()) == \ r'\left\{a\right\} \times \left\{c\right\} \times ' \ r'\left\{d\right\}' assert latex(ProductSet(U1, U2)) == \ r'\left(\left\{a\right\} \cup \left\{b\right\}\right) ' \ r'\times \left(\left\{c\right\} \cup ' \ r'\left\{d\right\}\right)' assert latex(ProductSet(I1, I2)) == \ r'\left(\left\{a\right\} \cap \left\{b\right\}\right) ' \ r'\times \left(\left\{c\right\} \cap ' \ r'\left\{d\right\}\right)' assert latex(ProductSet(C1, C2)) == \ r'\left(\left\{a\right\} \setminus ' \ r'\left\{b\right\}\right) \times \left(\left\{c\right\} ' \ r'\setminus \left\{d\right\}\right)' assert latex(ProductSet(D1, D2)) == \ r'\left(\left\{a\right\} \triangle ' \ r'\left\{b\right\}\right) \times \left(\left\{c\right\} ' \ r'\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}\; \middle|\; 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\; \middle|\; 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\; \middle|\; \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\; \middle|\; x \in \mathbb{R} \wedge x^{2} = 1 \right\}" assert latex(ConditionSet(x, Eq(x**2, 1), S.UniversalSet)) == \ r"\left\{x\; \middle|\; x^{2} = 1 \right\}" def test_latex_ComplexRegion(): assert latex(ComplexRegion(Interval(3, 5)*Interval(4, 6))) == \ r"\left\{x + y i\; \middle|\; 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)\; \middle|\; 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(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)) == r"8 \sqrt{2} \tau^{\frac{7}{2}}" assert latex((2*mu)**Rational(7, 2), mode='equation*') == \ r"\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}" assert latex((2*mu)**Rational(7, 2), mode='equation', itex=True) == \ r"$$8 \sqrt{2} \mu^{\frac{7}{2}}$$" 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_NumberSymbols(): assert latex(S.Catalan) == "G" assert latex(S.EulerGamma) == r"\gamma" assert latex(S.Exp1) == "e" assert latex(S.GoldenRatio) == r"\phi" assert latex(S.Pi) == r"\pi" assert latex(S.TribonacciConstant) == r"\text{TribonacciConstant}" def test_latex_rational(): # tests issue 3973 assert latex(-Rational(1, 2)) == r"- \frac{1}{2}" assert latex(Rational(-1, 2)) == r"- \frac{1}{2}" assert latex(Rational(1, -2)) == r"- \frac{1}{2}" assert latex(-Rational(-1, 2)) == r"\frac{1}{2}" assert latex(-Rational(1, 2)*x) == r"- \frac{x}{2}" assert latex(-Rational(1, 2)*x + Rational(-2, 3)*y) == \ r"- \frac{x}{2} - \frac{2 y}{3}" def test_latex_inverse(): # tests issue 4129 assert latex(1/x) == r"\frac{1}{x}" assert latex(1/(x + y)) == r"\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) == r'x + y' assert latex(expr, mode='plain') == r'x + y' assert latex(expr, mode='inline') == r'$x + y$' assert latex( expr, mode='equation*') == r'\begin{equation*}x + y\end{equation*}' assert latex( expr, mode='equation') == r'\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) == r"\begin{cases} x & \text{for}\: x < 1 \\x^{2} &" \ r" \text{otherwise} \end{cases}" assert latex(p, itex=True) == \ r"\begin{cases} x & \text{for}\: x \lt 1 \\x^{2} &" \ r" \text{otherwise} \end{cases}" p = Piecewise((x, x < 0), (0, x >= 0)) assert latex(p) == r'\begin{cases} x & \text{for}\: x < 0 \\0 &' \ r' \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))) == \ r'\begin{cases} x & ' \ r'\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) == r"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) == \ r'\left[\begin{matrix}\frac{1}{x} & y\\z & w\end{matrix}\right]' assert latex(M1) == \ r"\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') == r"4 \times 4^{x}" assert latex(4*4**x, mul_symbol='dot') == r"4 \cdot 4^{x}" assert latex(4*4**x, mul_symbol='ldot') == r"4 \,.\, 4^{x}" assert latex(4*x, mul_symbol='times') == r"4 \times x" assert latex(4*x, mul_symbol='dot') == r"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 r'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 r'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) == r"A B C^{-1}" assert latex(C**-1*A*B) == r"C^{-1} A B" assert latex(A*C**-1*B) == r"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') == r"x^{3} + x^{2} y + 3 x y^{3} + y^{4}" assert latex( expr, order='rev-lex') == r"y^{4} + 3 x y^{3} + x^{2} y + x^{3}" assert latex(expr, order='none') == r"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)) == \ r'\operatorname{Poly}{\left( a x^{5} + x^{4} + b x^{3} + 2 x^{2} + c'\ r' x + 3, x, domain=\mathbb{Z}\left[a, b, c\right] \right)}' assert latex(Poly([a, 1, b+c, 2, 3], x)) == \ r'\operatorname{Poly}{\left( a x^{4} + x^{3} + \left(b + c\right) '\ r'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))) == \ r'\operatorname{Poly}{\left( a x^{3} + x^{2}y - b xy^{2} - xy - '\ r'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(genocchi(n)) == r"G_{n}" assert latex(genocchi(n, x)) == r"G_{n}\left(x\right)" assert latex(genocchi(n)**2) == r"G_{n}^{2}" assert latex(genocchi(n, x)**2) == r"G_{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)" assert latex(mobius(n)) == r"\mu\left(n\right)" assert latex(mobius(n)**2) == r"\mu^{2}\left(n\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) == r"x" assert latex(x, symbol_names={x: "x_i"}) == r"x_i" assert latex(x + y, symbol_names={x: "x_i"}) == r"x_i + y" assert latex(x**2, symbol_names={x: "x_i"}) == r"x_i^{2}" assert latex(x + y, symbol_names={x: "x_i", y: "y_j"}) == r"x_i + y_j" def test_matAdd(): C = MatrixSymbol('C', 5, 5) B = MatrixSymbol('B', 5, 5) n = symbols("n") h = MatrixSymbol("h", 1, 1) assert latex(C - 2*B) in [r'- 2 B + C', r'C -2 B'] assert latex(C + 2*B) in [r'2 B + C', r'C + 2 B'] assert latex(B - 2*C) in [r'B - 2 C', r'- 2 C + B'] assert latex(B + 2*C) in [r'B + 2 C', r'2 C + B'] assert latex(n * h - (-h + h.T) * (h + h.T)) == 'n h - \\left(- h + h^{T}\\right) \\left(h + h^{T}\\right)' assert latex(MatAdd(MatAdd(h, h), MatAdd(h, h))) == '\\left(h + h\\right) + \\left(h + h\\right)' assert latex(MatMul(MatMul(h, h), MatMul(h, h))) == '\\left(h h\\right) \\left(h h\\right)' def test_matMul(): A = MatrixSymbol('A', 5, 5) B = MatrixSymbol('B', 5, 5) x = Symbol('x') assert latex(2*A) == r'2 A' assert latex(2*x*A) == r'2 x A' assert latex(-2*A) == r'- 2 A' assert latex(1.5*A) == r'1.5 A' assert latex(sqrt(2)*A) == r'\sqrt{2} A' assert latex(-sqrt(2)*A) == r'- \sqrt{2} A' assert latex(2*sqrt(2)*x*A) == r'2 \sqrt{2} x A' assert latex(-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\} \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) == r"A_{1}" assert latex(f1) == r"f_{1}:A_{1}\rightarrow A_{2}" assert latex(id_A1) == r"id:A_{1}\rightarrow A_{1}" assert latex(f2*f1) == r"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) == r"\begin{array}{cc}" + "\n" \ r"A & B \\" + "\n" \ r" & C " + "\n" \ r"\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_Determinant(): from sympy.matrices import Determinant, Inverse, BlockMatrix, OneMatrix, ZeroMatrix m = Matrix(((1, 2), (3, 4))) assert latex(Determinant(m)) == '\\left|{\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}}\\right|' assert latex(Determinant(Inverse(m))) == \ '\\left|{\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right]^{-1}}\\right|' X = MatrixSymbol('X', 2, 2) assert latex(Determinant(X)) == '\\left|{X}\\right|' assert latex(Determinant(X + m)) == \ '\\left|{\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right] + X}\\right|' assert latex(Determinant(BlockMatrix(((OneMatrix(2, 2), X), (m, ZeroMatrix(2, 2)))))) == \ '\\left|{\\begin{matrix}1 & X\\\\\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right] & 0\\end{matrix}}\\right|' def test_Adjoint(): from sympy.matrices import 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}' m = Matrix(((1, 2), (3, 4))) assert latex(Adjoint(m)) == '\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right]^{\\dagger}' assert latex(Adjoint(m+X)) == \ '\\left(\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right] + X\\right)^{\\dagger}' from sympy.matrices import BlockMatrix, OneMatrix, ZeroMatrix assert latex(Adjoint(BlockMatrix(((OneMatrix(2, 2), X), (m, ZeroMatrix(2, 2)))))) == \ '\\left[\\begin{matrix}1 & X\\\\\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right] & 0\\end{matrix}\\right]^{\\dagger}' # Issue 20959 Mx = MatrixSymbol('M^x', 2, 2) assert latex(Adjoint(Mx)) == r'\left(M^{x}\right)^{\dagger}' # adjoint style assert latex(Adjoint(X), adjoint_style="star") == r'X^{\ast}' assert latex(Adjoint(X + Y), adjoint_style="hermitian") == r'\left(X + Y\right)^{\mathsf{H}}' assert latex(Adjoint(X) + Adjoint(Y), adjoint_style="dagger") == r'X^{\dagger} + Y^{\dagger}' assert latex(Adjoint(Y)*Adjoint(X)) == r'Y^{\dagger} X^{\dagger}' assert latex(Adjoint(X**2), adjoint_style="star") == r'\left(X^{2}\right)^{\ast}' assert latex(Adjoint(X)**2, adjoint_style="hermitian") == r'\left(X^{\mathsf{H}}\right)^{2}' 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}' m = Matrix(((1, 2), (3, 4))) assert latex(Transpose(m)) == '\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right]^{T}' assert latex(Transpose(m+X)) == \ '\\left(\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right] + X\\right)^{T}' from sympy.matrices import BlockMatrix, OneMatrix, ZeroMatrix assert latex(Transpose(BlockMatrix(((OneMatrix(2, 2), X), (m, ZeroMatrix(2, 2)))))) == \ '\\left[\\begin{matrix}1 & X\\\\\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right] & 0\\end{matrix}\\right]^{T}' # Issue 20959 Mx = MatrixSymbol('M^x', 2, 2) assert latex(Transpose(Mx)) == r'\left(M^{x}\right)^{T}' def test_Hadamard(): from sympy.matrices import 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_MatPow(): from sympy.matrices.expressions import MatPow X = MatrixSymbol('X', 2, 2) Y = MatrixSymbol('Y', 2, 2) assert latex(MatPow(X, 2)) == 'X^{2}' assert latex(MatPow(X*X, 2)) == '\\left(X^{2}\\right)^{2}' assert latex(MatPow(X*Y, 2)) == '\\left(X Y\\right)^{2}' assert latex(MatPow(X + Y, 2)) == '\\left(X + Y\\right)^{2}' assert latex(MatPow(X + X, 2)) == '\\left(2 X\\right)^{2}' # Issue 20959 Mx = MatrixSymbol('M^x', 2, 2) assert latex(MatPow(Mx, 2)) == r'\left(M^{x}\right)^{2}' def test_ElementwiseApplyFunction(): 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( x \mapsto \frac{1}{x} \right)}_{\circ}\left({X}\right)' def test_ZeroMatrix(): from sympy.matrices.expressions.special import ZeroMatrix assert latex(ZeroMatrix(1, 1), mat_symbol_style='plain') == r"0" assert latex(ZeroMatrix(1, 1), mat_symbol_style='bold') == r"\mathbf{0}" def test_OneMatrix(): from sympy.matrices.expressions.special import OneMatrix assert latex(OneMatrix(3, 4), mat_symbol_style='plain') == r"1" assert latex(OneMatrix(3, 4), mat_symbol_style='bold') == r"\mathbf{1}" def test_Identity(): from sympy.matrices.expressions.special 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_latex_DFT_IDFT(): from sympy.matrices.expressions.fourier import DFT, IDFT assert latex(DFT(13)) == r"\text{DFT}_{13}" assert latex(IDFT(x)) == r"\text{IDFT}_{x}" def test_boolean_args_order(): syms = symbols('a:f') expr = And(*syms) assert latex(expr) == r'a \wedge b \wedge c \wedge d \wedge e \wedge f' expr = Or(*syms) assert latex(expr) == r'a \vee b \vee c \vee d \vee e \vee f' expr = Equivalent(*syms) assert latex(expr) == \ r'a \Leftrightarrow b \Leftrightarrow c \Leftrightarrow d \Leftrightarrow e \Leftrightarrow f' expr = Xor(*syms) assert latex(expr) == \ r'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'\mathrm{A}' assert latex(s(x)) == r'\mathrm{A}{\left(x \right)}' s = Function('Beta') assert latex(s) == r'\mathrm{B}' s = Function('Eta') assert latex(s) == r'\mathrm{H}' assert latex(s(x)) == r'\mathrm{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) == r'\mathrm{A}' s = 'Beta' assert translate(s) == r'\mathrm{B}' s = 'Eta' assert translate(s) == r'\mathrm{H}' s = 'omicron' assert translate(s) == r'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)) == r"" "\\" + 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'\mathrm{A}' assert latex(Symbol('Beta')) == r'\mathrm{B}' assert latex(Symbol('Gamma')) == r'\Gamma' assert latex(Symbol('Delta')) == r'\Delta' assert latex(Symbol('Epsilon')) == r'\mathrm{E}' assert latex(Symbol('Zeta')) == r'\mathrm{Z}' assert latex(Symbol('Eta')) == r'\mathrm{H}' assert latex(Symbol('Theta')) == r'\Theta' assert latex(Symbol('Iota')) == r'\mathrm{I}' assert latex(Symbol('Kappa')) == r'\mathrm{K}' assert latex(Symbol('Lambda')) == r'\Lambda' assert latex(Symbol('Mu')) == r'\mathrm{M}' assert latex(Symbol('Nu')) == r'\mathrm{N}' assert latex(Symbol('Xi')) == r'\Xi' assert latex(Symbol('Omicron')) == r'\mathrm{O}' assert latex(Symbol('Pi')) == r'\Pi' assert latex(Symbol('Rho')) == r'\mathrm{P}' assert latex(Symbol('Sigma')) == r'\Sigma' assert latex(Symbol('Tau')) == r'\mathrm{T}' assert latex(Symbol('Upsilon')) == r'\Upsilon' assert latex(Symbol('Phi')) == r'\Phi' assert latex(Symbol('Chi')) == r'\mathrm{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) == r'\mathbb{Q}' assert latex(S.Naturals) == r'\mathbb{N}' assert latex(S.Naturals0) == r'\mathbb{N}_0' assert latex(S.Integers) == r'\mathbb{Z}' assert latex(S.Reals) == r'\mathbb{R}' assert latex(S.Complexes) == r'\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}' # Issue 11011 assert latex(S('1.453e4500')**x) == r'{1.453 \cdot 10^{4500}}^{x}' 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"\left(- x\right) y" def test_issue_2934(): assert latex(Symbol(r'\frac{a_1}{b_1}')) == r'\frac{a_1}{b_1}' def test_issue_10489(): latexSymbolWithBrace = r'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}' X_a = MatrixSymbol('X_a', 3, 3) assert latex(X_a[0, 0]) == r"{X_{a}}_{0,0}" 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_Series_printing(): tf1 = TransferFunction(x*y**2 - z, y**3 - t**3, y) tf2 = TransferFunction(x - y, x + y, y) tf3 = TransferFunction(t*x**2 - t**w*x + w, t - y, y) assert latex(Series(tf1, tf2)) == \ r'\left(\frac{x y^{2} - z}{- t^{3} + y^{3}}\right) \left(\frac{x - y}{x + y}\right)' assert latex(Series(tf1, tf2, tf3)) == \ r'\left(\frac{x y^{2} - z}{- t^{3} + y^{3}}\right) \left(\frac{x - y}{x + y}\right) \left(\frac{t x^{2} - t^{w} x + w}{t - y}\right)' assert latex(Series(-tf2, tf1)) == \ r'\left(\frac{- x + y}{x + y}\right) \left(\frac{x y^{2} - z}{- t^{3} + y^{3}}\right)' M_1 = Matrix([[5/s], [5/(2*s)]]) T_1 = TransferFunctionMatrix.from_Matrix(M_1, s) M_2 = Matrix([[5, 6*s**3]]) T_2 = TransferFunctionMatrix.from_Matrix(M_2, s) # Brackets assert latex(T_1*(T_2 + T_2)) == \ r'\left[\begin{matrix}\frac{5}{s}\\\frac{5}{2 s}\end{matrix}\right]_\tau\cdot\left(\left[\begin{matrix}\frac{5}{1} &' \ r' \frac{6 s^{3}}{1}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{5}{1} & \frac{6 s^{3}}{1}\end{matrix}\right]_\tau\right)' \ == latex(MIMOSeries(MIMOParallel(T_2, T_2), T_1)) # No Brackets M_3 = Matrix([[5, 6], [6, 5/s]]) T_3 = TransferFunctionMatrix.from_Matrix(M_3, s) assert latex(T_1*T_2 + T_3) == r'\left[\begin{matrix}\frac{5}{s}\\\frac{5}{2 s}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}' \ r'\frac{5}{1} & \frac{6 s^{3}}{1}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{5}{1} & \frac{6}{1}\\\frac{6}{1} & ' \ r'\frac{5}{s}\end{matrix}\right]_\tau' == latex(MIMOParallel(MIMOSeries(T_2, T_1), T_3)) def test_TransferFunction_printing(): tf1 = TransferFunction(x - 1, x + 1, x) assert latex(tf1) == r"\frac{x - 1}{x + 1}" tf2 = TransferFunction(x + 1, 2 - y, x) assert latex(tf2) == r"\frac{x + 1}{2 - y}" tf3 = TransferFunction(y, y**2 + 2*y + 3, y) assert latex(tf3) == r"\frac{y}{y^{2} + 2 y + 3}" def test_Parallel_printing(): tf1 = TransferFunction(x*y**2 - z, y**3 - t**3, y) tf2 = TransferFunction(x - y, x + y, y) assert latex(Parallel(tf1, tf2)) == \ r'\frac{x y^{2} - z}{- t^{3} + y^{3}} + \frac{x - y}{x + y}' assert latex(Parallel(-tf2, tf1)) == \ r'\frac{- x + y}{x + y} + \frac{x y^{2} - z}{- t^{3} + y^{3}}' M_1 = Matrix([[5, 6], [6, 5/s]]) T_1 = TransferFunctionMatrix.from_Matrix(M_1, s) M_2 = Matrix([[5/s, 6], [6, 5/(s - 1)]]) T_2 = TransferFunctionMatrix.from_Matrix(M_2, s) M_3 = Matrix([[6, 5/(s*(s - 1))], [5, 6]]) T_3 = TransferFunctionMatrix.from_Matrix(M_3, s) assert latex(T_1 + T_2 + T_3) == r'\left[\begin{matrix}\frac{5}{1} & \frac{6}{1}\\\frac{6}{1} & \frac{5}{s}\end{matrix}\right]' \ r'_\tau + \left[\begin{matrix}\frac{5}{s} & \frac{6}{1}\\\frac{6}{1} & \frac{5}{s - 1}\end{matrix}\right]_\tau + \left[\begin{matrix}' \ r'\frac{6}{1} & \frac{5}{s \left(s - 1\right)}\\\frac{5}{1} & \frac{6}{1}\end{matrix}\right]_\tau' \ == latex(MIMOParallel(T_1, T_2, T_3)) == latex(MIMOParallel(T_1, MIMOParallel(T_2, T_3))) == latex(MIMOParallel(MIMOParallel(T_1, T_2), T_3)) def test_TransferFunctionMatrix_printing(): tf1 = TransferFunction(p, p + x, p) tf2 = TransferFunction(-s + p, p + s, p) tf3 = TransferFunction(p, y**2 + 2*y + 3, p) assert latex(TransferFunctionMatrix([[tf1], [tf2]])) == \ r'\left[\begin{matrix}\frac{p}{p + x}\\\frac{p - s}{p + s}\end{matrix}\right]_\tau' assert latex(TransferFunctionMatrix([[tf1, tf2], [tf3, -tf1]])) == \ r'\left[\begin{matrix}\frac{p}{p + x} & \frac{p - s}{p + s}\\\frac{p}{y^{2} + 2 y + 3} & \frac{\left(-1\right) p}{p + x}\end{matrix}\right]_\tau' def test_Feedback_printing(): tf1 = TransferFunction(p, p + x, p) tf2 = TransferFunction(-s + p, p + s, p) # Negative Feedback (Default) assert latex(Feedback(tf1, tf2)) == \ r'\frac{\frac{p}{p + x}}{\frac{1}{1} + \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}' assert latex(Feedback(tf1*tf2, TransferFunction(1, 1, p))) == \ r'\frac{\left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}{\frac{1}{1} + \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}' # Positive Feedback assert latex(Feedback(tf1, tf2, 1)) == \ r'\frac{\frac{p}{p + x}}{\frac{1}{1} - \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}' assert latex(Feedback(tf1*tf2, sign=1)) == \ r'\frac{\left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}{\frac{1}{1} - \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}' def test_MIMOFeedback_printing(): tf1 = TransferFunction(1, s, s) tf2 = TransferFunction(s, s**2 - 1, s) tf3 = TransferFunction(s, s - 1, s) tf4 = TransferFunction(s**2, s**2 - 1, s) tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf3, tf4]]) tfm_2 = TransferFunctionMatrix([[tf4, tf3], [tf2, tf1]]) # Negative Feedback (Default) assert latex(MIMOFeedback(tfm_1, tfm_2)) == \ r'\left(I_{\tau} + \left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\cdot\left[' \ r'\begin{matrix}\frac{s^{2}}{s^{2} - 1} & \frac{s}{s - 1}\\\frac{s}{s^{2} - 1} & \frac{1}{s}\end{matrix}\right]_\tau\right)^{-1} \cdot \left[\begin{matrix}' \ r'\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau' # Positive Feedback assert latex(MIMOFeedback(tfm_1*tfm_2, tfm_1, 1)) == \ r'\left(I_{\tau} - \left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\cdot\left' \ r'[\begin{matrix}\frac{s^{2}}{s^{2} - 1} & \frac{s}{s - 1}\\\frac{s}{s^{2} - 1} & \frac{1}{s}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}' \ r'\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\right)^{-1} \cdot \left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}' \ r'\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}\frac{s^{2}}{s^{2} - 1} & \frac{s}{s - 1}\\\frac{s}{s^{2} - 1}' \ r' & \frac{1}{s}\end{matrix}\right]_\tau' def test_Quaternion_latex_printing(): q = Quaternion(x, y, z, t) assert latex(q) == r"x + y i + z j + t k" q = Quaternion(x, y, z, x*t) assert latex(q) == r"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_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) == r"{}^{i}" assert latex(-i) == r"{}_{i}" expr = A(i) assert latex(expr) == r"A{}^{i}" expr = A(i0) assert latex(expr) == r"A{}^{i_{0}}" expr = A(-i) assert latex(expr) == r"A{}_{i}" expr = -3*A(i) assert latex(expr) == r"-3A{}^{i}" expr = K(i, j, -k, -i0) assert latex(expr) == r"K{}^{ij}{}_{ki_{0}}" expr = K(i, -j, -k, i0) assert latex(expr) == r"K{}^{i}{}_{jk}{}^{i_{0}}" expr = K(i, -j, k, -i0) assert latex(expr) == r"K{}^{i}{}_{j}{}^{k}{}_{i_{0}}" expr = H(i, -j) assert latex(expr) == r"H{}^{i}{}_{j}" expr = H(i, j) assert latex(expr) == r"H{}^{ij}" expr = H(-i, -j) assert latex(expr) == r"H{}_{ij}" expr = (1+x)*A(i) assert latex(expr) == r"\left(x + 1\right)A{}^{i}" expr = H(i, -i) assert latex(expr) == r"H{}^{L_{0}}{}_{L_{0}}" expr = H(i, -j)*A(j)*B(k) assert latex(expr) == r"H{}^{i}{}_{L_{0}}A{}^{L_{0}}B{}^{k}" expr = A(i) + 3*B(i) assert latex(expr) == r"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) == r'K{}^{i=3,j,k=2,l}' expr = TensorElement(K(i, j, k, l), {i: 3}) assert latex(expr) == r'K{}^{i=3,jkl}' expr = TensorElement(K(i, -j, k, l), {i: 3, k: 2}) assert latex(expr) == r'K{}^{i=3}{}_{j}{}^{k=2,l}' expr = TensorElement(K(i, -j, k, -l), {i: 3, k: 2}) assert latex(expr) == r'K{}^{i=3}{}_{j}{}^{k=2}{}_{l}' expr = TensorElement(K(i, j, -k, -l), {i: 3, -k: 2}) assert latex(expr) == r'K{}^{i=3,j}{}_{k=2,l}' expr = TensorElement(K(i, j, -k, -l), {i: 3}) assert latex(expr) == r'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(): 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)\; \middle|\; \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_latex_symbolic_probability(): mu = symbols("mu") sigma = symbols("sigma", positive=True) X = Normal("X", mu, sigma) assert latex(Expectation(X)) == r'\operatorname{E}\left[X\right]' assert latex(Variance(X)) == r'\operatorname{Var}\left(X\right)' assert latex(Probability(X > 0)) == r'\operatorname{P}\left(X > 0\right)' Y = Normal("Y", mu, sigma) assert latex(Covariance(X, Y)) == r'\operatorname{Cov}\left(X, Y\right)' def test_trace(): # Issue 15303 from sympy.matrices.expressions.trace 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.core.basic import Basic from sympy.core.expr import 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'\operatorname{UnimplementedExpr}\left(x\right)' assert latex(unimplemented_expr(x**2)) == \ r'\operatorname{UnimplementedExpr}\left(x^{2}\right)' assert latex(unimplemented_expr_sup_sub(x)) == \ r'\operatorname{UnimplementedExpr^{1}_{x}}\left(x\right)' def test_MatrixSymbol_bold(): # Issue #15871 from sympy.matrices.expressions.trace 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_issue_21758(): from sympy.functions.elementary.piecewise import piecewise_fold from sympy.series.fourier import FourierSeries x = Symbol('x') k, n = symbols('k n') fo = FourierSeries(x, (x, -pi, pi), (0, SeqFormula(0, (k, 1, oo)), SeqFormula( Piecewise((-2*pi*cos(n*pi)/n + 2*sin(n*pi)/n**2, (n > -oo) & (n < oo) & Ne(n, 0)), (0, True))*sin(n*x)/pi, (n, 1, oo)))) assert latex(piecewise_fold(fo)) == '\\begin{cases} 2 \\sin{\\left(x \\right)}' \ ' - \\sin{\\left(2 x \\right)} + \\frac{2 \\sin{\\left(3 x \\right)}}{3} +' \ ' \\ldots & \\text{for}\\: n > -\\infty \\wedge n < \\infty \\wedge ' \ 'n \\neq 0 \\\\0 & \\text{otherwise} \\end{cases}' assert latex(FourierSeries(x, (x, -pi, pi), (0, SeqFormula(0, (k, 1, oo)), SeqFormula(0, (n, 1, oo))))) == '0' def test_imaginary_unit(): assert latex(1 + I) == r'1 + i' assert latex(1 + I, imaginary_unit='i') == r'1 + i' assert latex(1 + I, imaginary_unit='j') == r'1 + j' assert latex(1 + I, imaginary_unit='foo') == r'1 + foo' assert latex(I, imaginary_unit="ti") == r'\text{i}' assert latex(I, imaginary_unit="tj") == r'\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 x,y = symbols('x y', real=True) 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, [x, y]) assert latex(rect) == r'\text{rect}^{\text{P}}_{\text{M}}' b = BaseScalarField(rect, 0) assert latex(b) == r'\mathbf{x}' 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}}' assert latex(4*micro*gram/second) == r'\frac{4 \mu \text{g}}{\text{s}}' assert latex(5*milli*meter) == r'5 \text{m} \text{m}' assert latex(milli) == r'\text{m}' 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{,}8 \cdot 10^{-7}') 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')) def test_Str(): from sympy.core.symbol import Str assert str(Str('x')) == r'x' def test_latex_escape(): assert latex_escape(r"~^\&%$#_{}") == "".join([ r'\textasciitilde', r'\textasciicircum', r'\textbackslash', r'\&', r'\%', r'\$', r'\#', r'\_', r'\{', r'\}', ]) def test_emptyPrinter(): class MyObject: def __repr__(self): return "" # unknown objects are monospaced assert latex(MyObject()) == r"\mathtt{\text{}}" # even if they are nested within other objects assert latex((MyObject(),)) == r"\left( \mathtt{\text{}},\right)" def test_global_settings(): import inspect # settings should be visible in the signature of `latex` assert inspect.signature(latex).parameters['imaginary_unit'].default == r'i' assert latex(I) == r'i' try: # but changing the defaults... LatexPrinter.set_global_settings(imaginary_unit='j') # ... should change the signature assert inspect.signature(latex).parameters['imaginary_unit'].default == r'j' assert latex(I) == r'j' finally: # there's no public API to undo this, but we need to make sure we do # so as not to impact other tests del LatexPrinter._global_settings['imaginary_unit'] # check we really did undo it assert inspect.signature(latex).parameters['imaginary_unit'].default == r'i' assert latex(I) == r'i' def test_pickleable(): # this tests that the _PrintFunction instance is pickleable import pickle assert pickle.loads(pickle.dumps(latex)) is latex def test_printing_latex_array_expressions(): assert latex(ArraySymbol("A", (2, 3, 4))) == "A" assert latex(ArrayElement("A", (2, 1/(1-x), 0))) == "{{A}_{2, \\frac{1}{1 - x}, 0}}" M = MatrixSymbol("M", 3, 3) N = MatrixSymbol("N", 3, 3) assert latex(ArrayElement(M*N, [x, 0])) == "{{\\left(M N\\right)}_{x, 0}}" def test_Array(): arr = Array(range(10)) assert latex(arr) == r'\left[\begin{matrix}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\end{matrix}\right]' arr = Array(range(11)) # fill the empty argument with a bunch of 'c' to avoid latex errors assert latex(arr) == r'\left[\begin{array}{ccccccccccc}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array}\right]' def test_latex_with_unevaluated(): with evaluate(False): assert latex(a * a) == r"a a"