diff --git "a/.venv/lib/python3.13/site-packages/sympy/printing/tests/test_mathml.py" "b/.venv/lib/python3.13/site-packages/sympy/printing/tests/test_mathml.py" new file mode 100644--- /dev/null +++ "b/.venv/lib/python3.13/site-packages/sympy/printing/tests/test_mathml.py" @@ -0,0 +1,2048 @@ +from sympy.calculus.accumulationbounds import AccumBounds +from sympy.concrete.summations import Sum +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.function import Derivative, Lambda, diff, Function +from sympy.core.numbers import (zoo, Float, Integer, I, oo, pi, E, + Rational) +from sympy.core.relational import Lt, Ge, Ne, Eq +from sympy.core.singleton import S +from sympy.core.symbol import symbols, Symbol +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import (factorial2, + binomial, factorial) +from sympy.functions.combinatorial.numbers import (lucas, bell, + catalan, euler, tribonacci, fibonacci, bernoulli, primenu, primeomega, + totient, reduced_totient) +from sympy.functions.elementary.complexes import re, im, conjugate, Abs +from sympy.functions.elementary.exponential import exp, LambertW, log +from sympy.functions.elementary.hyperbolic import (tanh, acoth, atanh, + coth, asinh, acsch, asech, acosh, csch, sinh, cosh, sech) +from sympy.functions.elementary.integers import ceiling, floor +from sympy.functions.elementary.miscellaneous import Max, Min +from sympy.functions.elementary.trigonometric import (csc, sec, tan, + atan, sin, asec, cot, cos, acot, acsc, asin, acos) +from sympy.functions.special.delta_functions import Heaviside +from sympy.functions.special.elliptic_integrals import (elliptic_pi, + elliptic_f, elliptic_k, elliptic_e) +from sympy.functions.special.error_functions import (fresnelc, + fresnels, Ei, expint) +from sympy.functions.special.gamma_functions import (gamma, uppergamma, + lowergamma) +from sympy.functions.special.mathieu_functions import (mathieusprime, + mathieus, mathieucprime, mathieuc) +from sympy.functions.special.polynomials import (jacobi, chebyshevu, + chebyshevt, hermite, assoc_legendre, gegenbauer, assoc_laguerre, + legendre, laguerre) +from sympy.functions.special.singularity_functions import SingularityFunction +from sympy.functions.special.zeta_functions import (polylog, stieltjes, + lerchphi, dirichlet_eta, zeta) +from sympy.integrals.integrals import Integral +from sympy.logic.boolalg import (Xor, Or, false, true, And, Equivalent, + Implies, Not) +from sympy.matrices.dense import Matrix +from sympy.matrices.expressions.determinant import Determinant +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.physics.quantum import (ComplexSpace, FockSpace, hbar, + HilbertSpace, Dagger) +from sympy.printing.mathml import (MathMLPresentationPrinter, + MathMLPrinter, MathMLContentPrinter, mathml) +from sympy.series.limits import Limit +from sympy.sets.contains import Contains +from sympy.sets.fancysets import Range +from sympy.sets.sets import (Interval, Union, SymmetricDifference, + Complement, FiniteSet, Intersection, ProductSet) +from sympy.stats.rv import RandomSymbol +from sympy.tensor.indexed import IndexedBase +from sympy.vector import (Divergence, CoordSys3D, Cross, Curl, Dot, + Laplacian, Gradient) +from sympy.testing.pytest import raises, XFAIL + +x, y, z, a, b, c, d, e, n = symbols('x:z a:e n') +mp = MathMLContentPrinter() +mpp = MathMLPresentationPrinter() + + +def test_mathml_printer(): + m = MathMLPrinter() + assert m.doprint(1+x) == mp.doprint(1+x) + + +def test_content_printmethod(): + assert mp.doprint(1 + x) == 'x1' + + +def test_content_mathml_core(): + mml_1 = mp._print(1 + x) + assert mml_1.nodeName == 'apply' + nodes = mml_1.childNodes + assert len(nodes) == 3 + assert nodes[0].nodeName == 'plus' + assert nodes[0].hasChildNodes() is False + assert nodes[0].nodeValue is None + assert nodes[1].nodeName in ['cn', 'ci'] + if nodes[1].nodeName == 'cn': + assert nodes[1].childNodes[0].nodeValue == '1' + assert nodes[2].childNodes[0].nodeValue == 'x' + else: + assert nodes[1].childNodes[0].nodeValue == 'x' + assert nodes[2].childNodes[0].nodeValue == '1' + + mml_2 = mp._print(x**2) + assert mml_2.nodeName == 'apply' + nodes = mml_2.childNodes + assert nodes[1].childNodes[0].nodeValue == 'x' + assert nodes[2].childNodes[0].nodeValue == '2' + + mml_3 = mp._print(2*x) + assert mml_3.nodeName == 'apply' + nodes = mml_3.childNodes + assert nodes[0].nodeName == 'times' + assert nodes[1].childNodes[0].nodeValue == '2' + assert nodes[2].childNodes[0].nodeValue == 'x' + + mml = mp._print(Float(1.0, 2)*x) + assert mml.nodeName == 'apply' + nodes = mml.childNodes + assert nodes[0].nodeName == 'times' + assert nodes[1].childNodes[0].nodeValue == '1.0' + assert nodes[2].childNodes[0].nodeValue == 'x' + + +def test_content_mathml_functions(): + mml_1 = mp._print(sin(x)) + assert mml_1.nodeName == 'apply' + assert mml_1.childNodes[0].nodeName == 'sin' + assert mml_1.childNodes[1].nodeName == 'ci' + + mml_2 = mp._print(diff(sin(x), x, evaluate=False)) + assert mml_2.nodeName == 'apply' + assert mml_2.childNodes[0].nodeName == 'diff' + assert mml_2.childNodes[1].nodeName == 'bvar' + assert mml_2.childNodes[1].childNodes[ + 0].nodeName == 'ci' # below bvar there's x/ci> + + mml_3 = mp._print(diff(cos(x*y), x, evaluate=False)) + assert mml_3.nodeName == 'apply' + assert mml_3.childNodes[0].nodeName == 'partialdiff' + assert mml_3.childNodes[1].nodeName == 'bvar' + assert mml_3.childNodes[1].childNodes[ + 0].nodeName == 'ci' # below bvar there's x/ci> + + mml_4 = mp._print(Lambda((x, y), x * y)) + assert mml_4.nodeName == 'lambda' + assert mml_4.childNodes[0].nodeName == 'bvar' + assert mml_4.childNodes[0].childNodes[ + 0].nodeName == 'ci' # below bvar there's x/ci> + assert mml_4.childNodes[1].nodeName == 'bvar' + assert mml_4.childNodes[1].childNodes[ + 0].nodeName == 'ci' # below bvar there's y/ci> + assert mml_4.childNodes[2].nodeName == 'apply' + + +def test_content_mathml_limits(): + # XXX No unevaluated limits + lim_fun = sin(x)/x + mml_1 = mp._print(Limit(lim_fun, x, 0)) + assert mml_1.childNodes[0].nodeName == 'limit' + assert mml_1.childNodes[1].nodeName == 'bvar' + assert mml_1.childNodes[2].nodeName == 'lowlimit' + assert mml_1.childNodes[3].toxml() == mp._print(lim_fun).toxml() + + +def test_content_mathml_integrals(): + integrand = x + mml_1 = mp._print(Integral(integrand, (x, 0, 1))) + assert mml_1.childNodes[0].nodeName == 'int' + assert mml_1.childNodes[1].nodeName == 'bvar' + assert mml_1.childNodes[2].nodeName == 'lowlimit' + assert mml_1.childNodes[3].nodeName == 'uplimit' + assert mml_1.childNodes[4].toxml() == mp._print(integrand).toxml() + + +def test_content_mathml_matrices(): + A = Matrix([1, 2, 3]) + B = Matrix([[0, 5, 4], [2, 3, 1], [9, 7, 9]]) + mll_1 = mp._print(A) + assert mll_1.childNodes[0].nodeName == 'matrixrow' + assert mll_1.childNodes[0].childNodes[0].nodeName == 'cn' + assert mll_1.childNodes[0].childNodes[0].childNodes[0].nodeValue == '1' + assert mll_1.childNodes[1].nodeName == 'matrixrow' + assert mll_1.childNodes[1].childNodes[0].nodeName == 'cn' + assert mll_1.childNodes[1].childNodes[0].childNodes[0].nodeValue == '2' + assert mll_1.childNodes[2].nodeName == 'matrixrow' + assert mll_1.childNodes[2].childNodes[0].nodeName == 'cn' + assert mll_1.childNodes[2].childNodes[0].childNodes[0].nodeValue == '3' + mll_2 = mp._print(B) + assert mll_2.childNodes[0].nodeName == 'matrixrow' + assert mll_2.childNodes[0].childNodes[0].nodeName == 'cn' + assert mll_2.childNodes[0].childNodes[0].childNodes[0].nodeValue == '0' + assert mll_2.childNodes[0].childNodes[1].nodeName == 'cn' + assert mll_2.childNodes[0].childNodes[1].childNodes[0].nodeValue == '5' + assert mll_2.childNodes[0].childNodes[2].nodeName == 'cn' + assert mll_2.childNodes[0].childNodes[2].childNodes[0].nodeValue == '4' + assert mll_2.childNodes[1].nodeName == 'matrixrow' + assert mll_2.childNodes[1].childNodes[0].nodeName == 'cn' + assert mll_2.childNodes[1].childNodes[0].childNodes[0].nodeValue == '2' + assert mll_2.childNodes[1].childNodes[1].nodeName == 'cn' + assert mll_2.childNodes[1].childNodes[1].childNodes[0].nodeValue == '3' + assert mll_2.childNodes[1].childNodes[2].nodeName == 'cn' + assert mll_2.childNodes[1].childNodes[2].childNodes[0].nodeValue == '1' + assert mll_2.childNodes[2].nodeName == 'matrixrow' + assert mll_2.childNodes[2].childNodes[0].nodeName == 'cn' + assert mll_2.childNodes[2].childNodes[0].childNodes[0].nodeValue == '9' + assert mll_2.childNodes[2].childNodes[1].nodeName == 'cn' + assert mll_2.childNodes[2].childNodes[1].childNodes[0].nodeValue == '7' + assert mll_2.childNodes[2].childNodes[2].nodeName == 'cn' + assert mll_2.childNodes[2].childNodes[2].childNodes[0].nodeValue == '9' + + +def test_content_mathml_sums(): + summand = x + mml_1 = mp._print(Sum(summand, (x, 1, 10))) + assert mml_1.childNodes[0].nodeName == 'sum' + assert mml_1.childNodes[1].nodeName == 'bvar' + assert mml_1.childNodes[2].nodeName == 'lowlimit' + assert mml_1.childNodes[3].nodeName == 'uplimit' + assert mml_1.childNodes[4].toxml() == mp._print(summand).toxml() + + +def test_content_mathml_tuples(): + mml_1 = mp._print([2]) + assert mml_1.nodeName == 'list' + assert mml_1.childNodes[0].nodeName == 'cn' + assert len(mml_1.childNodes) == 1 + + mml_2 = mp._print([2, Integer(1)]) + assert mml_2.nodeName == 'list' + assert mml_2.childNodes[0].nodeName == 'cn' + assert mml_2.childNodes[1].nodeName == 'cn' + assert len(mml_2.childNodes) == 2 + + +def test_content_mathml_add(): + mml = mp._print(x**5 - x**4 + x) + assert mml.childNodes[0].nodeName == 'plus' + assert mml.childNodes[1].childNodes[0].nodeName == 'minus' + assert mml.childNodes[1].childNodes[1].nodeName == 'apply' + + +def test_content_mathml_Rational(): + mml_1 = mp._print(Rational(1, 1)) + """should just return a number""" + assert mml_1.nodeName == 'cn' + + mml_2 = mp._print(Rational(2, 5)) + assert mml_2.childNodes[0].nodeName == 'divide' + + +def test_content_mathml_constants(): + mml = mp._print(I) + assert mml.nodeName == 'imaginaryi' + + mml = mp._print(E) + assert mml.nodeName == 'exponentiale' + + mml = mp._print(oo) + assert mml.nodeName == 'infinity' + + mml = mp._print(pi) + assert mml.nodeName == 'pi' + + assert mathml(hbar) == '' + assert mathml(S.TribonacciConstant) == '' + assert mathml(S.GoldenRatio) == 'φ' + mml = mathml(S.EulerGamma) + assert mml == '' + + mml = mathml(S.EmptySet) + assert mml == '' + + mml = mathml(S.true) + assert mml == '' + + mml = mathml(S.false) + assert mml == '' + + mml = mathml(S.NaN) + assert mml == '' + + +def test_content_mathml_trig(): + mml = mp._print(sin(x)) + assert mml.childNodes[0].nodeName == 'sin' + + mml = mp._print(cos(x)) + assert mml.childNodes[0].nodeName == 'cos' + + mml = mp._print(tan(x)) + assert mml.childNodes[0].nodeName == 'tan' + + mml = mp._print(cot(x)) + assert mml.childNodes[0].nodeName == 'cot' + + mml = mp._print(csc(x)) + assert mml.childNodes[0].nodeName == 'csc' + + mml = mp._print(sec(x)) + assert mml.childNodes[0].nodeName == 'sec' + + mml = mp._print(asin(x)) + assert mml.childNodes[0].nodeName == 'arcsin' + + mml = mp._print(acos(x)) + assert mml.childNodes[0].nodeName == 'arccos' + + mml = mp._print(atan(x)) + assert mml.childNodes[0].nodeName == 'arctan' + + mml = mp._print(acot(x)) + assert mml.childNodes[0].nodeName == 'arccot' + + mml = mp._print(acsc(x)) + assert mml.childNodes[0].nodeName == 'arccsc' + + mml = mp._print(asec(x)) + assert mml.childNodes[0].nodeName == 'arcsec' + + mml = mp._print(sinh(x)) + assert mml.childNodes[0].nodeName == 'sinh' + + mml = mp._print(cosh(x)) + assert mml.childNodes[0].nodeName == 'cosh' + + mml = mp._print(tanh(x)) + assert mml.childNodes[0].nodeName == 'tanh' + + mml = mp._print(coth(x)) + assert mml.childNodes[0].nodeName == 'coth' + + mml = mp._print(csch(x)) + assert mml.childNodes[0].nodeName == 'csch' + + mml = mp._print(sech(x)) + assert mml.childNodes[0].nodeName == 'sech' + + mml = mp._print(asinh(x)) + assert mml.childNodes[0].nodeName == 'arcsinh' + + mml = mp._print(atanh(x)) + assert mml.childNodes[0].nodeName == 'arctanh' + + mml = mp._print(acosh(x)) + assert mml.childNodes[0].nodeName == 'arccosh' + + mml = mp._print(acoth(x)) + assert mml.childNodes[0].nodeName == 'arccoth' + + mml = mp._print(acsch(x)) + assert mml.childNodes[0].nodeName == 'arccsch' + + mml = mp._print(asech(x)) + assert mml.childNodes[0].nodeName == 'arcsech' + + +def test_content_mathml_relational(): + mml_1 = mp._print(Eq(x, 1)) + assert mml_1.nodeName == 'apply' + assert mml_1.childNodes[0].nodeName == 'eq' + assert mml_1.childNodes[1].nodeName == 'ci' + assert mml_1.childNodes[1].childNodes[0].nodeValue == 'x' + assert mml_1.childNodes[2].nodeName == 'cn' + assert mml_1.childNodes[2].childNodes[0].nodeValue == '1' + + mml_2 = mp._print(Ne(1, x)) + assert mml_2.nodeName == 'apply' + assert mml_2.childNodes[0].nodeName == 'neq' + assert mml_2.childNodes[1].nodeName == 'cn' + assert mml_2.childNodes[1].childNodes[0].nodeValue == '1' + assert mml_2.childNodes[2].nodeName == 'ci' + assert mml_2.childNodes[2].childNodes[0].nodeValue == 'x' + + mml_3 = mp._print(Ge(1, x)) + assert mml_3.nodeName == 'apply' + assert mml_3.childNodes[0].nodeName == 'geq' + assert mml_3.childNodes[1].nodeName == 'cn' + assert mml_3.childNodes[1].childNodes[0].nodeValue == '1' + assert mml_3.childNodes[2].nodeName == 'ci' + assert mml_3.childNodes[2].childNodes[0].nodeValue == 'x' + + mml_4 = mp._print(Lt(1, x)) + assert mml_4.nodeName == 'apply' + assert mml_4.childNodes[0].nodeName == 'lt' + assert mml_4.childNodes[1].nodeName == 'cn' + assert mml_4.childNodes[1].childNodes[0].nodeValue == '1' + assert mml_4.childNodes[2].nodeName == 'ci' + assert mml_4.childNodes[2].childNodes[0].nodeValue == 'x' + + +def test_content_symbol(): + mml = mp._print(x) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeValue == 'x' + del mml + + mml = mp._print(Symbol("x^2")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msup' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeValue == '2' + del mml + + mml = mp._print(Symbol("x__2")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msup' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeValue == '2' + del mml + + mml = mp._print(Symbol("x_2")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msub' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeValue == '2' + del mml + + mml = mp._print(Symbol("x^3_2")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msubsup' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeValue == '2' + assert mml.childNodes[0].childNodes[2].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[2].childNodes[0].nodeValue == '3' + del mml + + mml = mp._print(Symbol("x__3_2")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msubsup' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeValue == '2' + assert mml.childNodes[0].childNodes[2].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[2].childNodes[0].nodeValue == '3' + del mml + + mml = mp._print(Symbol("x_2_a")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msub' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mrow' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].childNodes[ + 0].nodeValue == '2' + assert mml.childNodes[0].childNodes[1].childNodes[1].nodeName == 'mml:mo' + assert mml.childNodes[0].childNodes[1].childNodes[1].childNodes[ + 0].nodeValue == ' ' + assert mml.childNodes[0].childNodes[1].childNodes[2].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[2].childNodes[ + 0].nodeValue == 'a' + del mml + + mml = mp._print(Symbol("x^2^a")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msup' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mrow' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].childNodes[ + 0].nodeValue == '2' + assert mml.childNodes[0].childNodes[1].childNodes[1].nodeName == 'mml:mo' + assert mml.childNodes[0].childNodes[1].childNodes[1].childNodes[ + 0].nodeValue == ' ' + assert mml.childNodes[0].childNodes[1].childNodes[2].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[2].childNodes[ + 0].nodeValue == 'a' + del mml + + mml = mp._print(Symbol("x__2__a")) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeName == 'mml:msup' + assert mml.childNodes[0].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].nodeName == 'mml:mrow' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[0].childNodes[ + 0].nodeValue == '2' + assert mml.childNodes[0].childNodes[1].childNodes[1].nodeName == 'mml:mo' + assert mml.childNodes[0].childNodes[1].childNodes[1].childNodes[ + 0].nodeValue == ' ' + assert mml.childNodes[0].childNodes[1].childNodes[2].nodeName == 'mml:mi' + assert mml.childNodes[0].childNodes[1].childNodes[2].childNodes[ + 0].nodeValue == 'a' + del mml + + +def test_content_mathml_greek(): + mml = mp._print(Symbol('alpha')) + assert mml.nodeName == 'ci' + assert mml.childNodes[0].nodeValue == '\N{GREEK SMALL LETTER ALPHA}' + + assert mp.doprint(Symbol('alpha')) == 'α' + assert mp.doprint(Symbol('beta')) == 'β' + assert mp.doprint(Symbol('gamma')) == 'γ' + assert mp.doprint(Symbol('delta')) == 'δ' + assert mp.doprint(Symbol('epsilon')) == 'ε' + assert mp.doprint(Symbol('zeta')) == 'ζ' + assert mp.doprint(Symbol('eta')) == 'η' + assert mp.doprint(Symbol('theta')) == 'θ' + assert mp.doprint(Symbol('iota')) == 'ι' + assert mp.doprint(Symbol('kappa')) == 'κ' + assert mp.doprint(Symbol('lambda')) == 'λ' + assert mp.doprint(Symbol('mu')) == 'μ' + assert mp.doprint(Symbol('nu')) == 'ν' + assert mp.doprint(Symbol('xi')) == 'ξ' + assert mp.doprint(Symbol('omicron')) == 'ο' + assert mp.doprint(Symbol('pi')) == 'π' + assert mp.doprint(Symbol('rho')) == 'ρ' + assert mp.doprint(Symbol('varsigma')) == 'ς' + assert mp.doprint(Symbol('sigma')) == 'σ' + assert mp.doprint(Symbol('tau')) == 'τ' + assert mp.doprint(Symbol('upsilon')) == 'υ' + assert mp.doprint(Symbol('phi')) == 'φ' + assert mp.doprint(Symbol('chi')) == 'χ' + assert mp.doprint(Symbol('psi')) == 'ψ' + assert mp.doprint(Symbol('omega')) == 'ω' + + assert mp.doprint(Symbol('Alpha')) == 'Α' + assert mp.doprint(Symbol('Beta')) == 'Β' + assert mp.doprint(Symbol('Gamma')) == 'Γ' + assert mp.doprint(Symbol('Delta')) == 'Δ' + assert mp.doprint(Symbol('Epsilon')) == 'Ε' + assert mp.doprint(Symbol('Zeta')) == 'Ζ' + assert mp.doprint(Symbol('Eta')) == 'Η' + assert mp.doprint(Symbol('Theta')) == 'Θ' + assert mp.doprint(Symbol('Iota')) == 'Ι' + assert mp.doprint(Symbol('Kappa')) == 'Κ' + assert mp.doprint(Symbol('Lambda')) == 'Λ' + assert mp.doprint(Symbol('Mu')) == 'Μ' + assert mp.doprint(Symbol('Nu')) == 'Ν' + assert mp.doprint(Symbol('Xi')) == 'Ξ' + assert mp.doprint(Symbol('Omicron')) == 'Ο' + assert mp.doprint(Symbol('Pi')) == 'Π' + assert mp.doprint(Symbol('Rho')) == 'Ρ' + assert mp.doprint(Symbol('Sigma')) == 'Σ' + assert mp.doprint(Symbol('Tau')) == 'Τ' + assert mp.doprint(Symbol('Upsilon')) == 'Υ' + assert mp.doprint(Symbol('Phi')) == 'Φ' + assert mp.doprint(Symbol('Chi')) == 'Χ' + assert mp.doprint(Symbol('Psi')) == 'Ψ' + assert mp.doprint(Symbol('Omega')) == 'Ω' + + +def test_content_mathml_order(): + expr = x**3 + x**2*y + 3*x*y**3 + y**4 + + mp = MathMLContentPrinter({'order': 'lex'}) + mml = mp._print(expr) + + assert mml.childNodes[1].childNodes[0].nodeName == 'power' + assert mml.childNodes[1].childNodes[1].childNodes[0].data == 'x' + assert mml.childNodes[1].childNodes[2].childNodes[0].data == '3' + + assert mml.childNodes[4].childNodes[0].nodeName == 'power' + assert mml.childNodes[4].childNodes[1].childNodes[0].data == 'y' + assert mml.childNodes[4].childNodes[2].childNodes[0].data == '4' + + mp = MathMLContentPrinter({'order': 'rev-lex'}) + mml = mp._print(expr) + + assert mml.childNodes[1].childNodes[0].nodeName == 'power' + assert mml.childNodes[1].childNodes[1].childNodes[0].data == 'y' + assert mml.childNodes[1].childNodes[2].childNodes[0].data == '4' + + assert mml.childNodes[4].childNodes[0].nodeName == 'power' + assert mml.childNodes[4].childNodes[1].childNodes[0].data == 'x' + assert mml.childNodes[4].childNodes[2].childNodes[0].data == '3' + + +def test_content_settings(): + raises(TypeError, lambda: mathml(x, method="garbage")) + + +def test_content_mathml_logic(): + assert mathml(And(x, y)) == 'xy' + assert mathml(Or(x, y)) == 'xy' + assert mathml(Xor(x, y)) == 'xy' + assert mathml(Implies(x, y)) == 'xy' + assert mathml(Not(x)) == 'x' + + +def test_content_finite_sets(): + assert mathml(FiniteSet(a)) == 'a' + assert mathml(FiniteSet(a, b)) == 'ab' + assert mathml(FiniteSet(FiniteSet(a, b), c)) == \ + 'cab' + + 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) + # XXX ProductSet does not support evaluate keyword + P1 = ProductSet(A, B) + P2 = ProductSet(C, D) + + assert mathml(U1) == \ + 'ab' + assert mathml(I1) == \ + 'ab' \ + '' + assert mathml(C1) == \ + 'ab' + assert mathml(P1) == \ + 'ab' \ + '' + + assert mathml(Intersection(A, U2, evaluate=False)) == \ + 'a' \ + 'cd' + assert mathml(Intersection(U1, U2, evaluate=False)) == \ + 'a' \ + 'bc' \ + 'd' + + # XXX Does the parenthesis appear correctly for these examples in mathjax? + assert mathml(Intersection(C1, C2, evaluate=False)) == \ + 'a' \ + 'bc' \ + 'd' + assert mathml(Intersection(P1, P2, evaluate=False)) == \ + 'a' \ + 'b' \ + 'cd' + + assert mathml(Union(A, I2, evaluate=False)) == \ + 'a' \ + 'cd' + assert mathml(Union(I1, I2, evaluate=False)) == \ + 'a' \ + 'bc' \ + 'd' + assert mathml(Union(C1, C2, evaluate=False)) == \ + 'a' \ + 'bc' \ + 'd' + assert mathml(Union(P1, P2, evaluate=False)) == \ + 'a' \ + 'b' \ + 'cd' + + assert mathml(Complement(A, C2, evaluate=False)) == \ + 'a' \ + 'cd' + assert mathml(Complement(U1, U2, evaluate=False)) == \ + 'a' \ + 'bc' \ + 'd' + assert mathml(Complement(I1, I2, evaluate=False)) == \ + 'a' \ + 'bc' \ + 'd' + assert mathml(Complement(P1, P2, evaluate=False)) == \ + 'a' \ + 'b' \ + 'cd' + + assert mathml(ProductSet(A, P2)) == \ + 'a' \ + 'c' \ + 'd' + assert mathml(ProductSet(U1, U2)) == \ + 'a' \ + 'bc' \ + 'd' + assert mathml(ProductSet(I1, I2)) == \ + 'a' \ + 'b' \ + 'cd' + assert mathml(ProductSet(C1, C2)) == \ + 'a' \ + 'b' \ + 'cd' + + +def test_presentation_printmethod(): + assert mpp.doprint(1 + x) == 'x+1' + assert mpp.doprint(x**2) == 'x2' + assert mpp.doprint(x**-1) == '1x' + assert mpp.doprint(x**-2) == \ + '1x2' + assert mpp.doprint(2*x) == \ + '2⁢x' + + +def test_presentation_mathml_core(): + mml_1 = mpp._print(1 + x) + assert mml_1.nodeName == 'mrow' + nodes = mml_1.childNodes + assert len(nodes) == 3 + assert nodes[0].nodeName in ['mi', 'mn'] + assert nodes[1].nodeName == 'mo' + if nodes[0].nodeName == 'mn': + assert nodes[0].childNodes[0].nodeValue == '1' + assert nodes[2].childNodes[0].nodeValue == 'x' + else: + assert nodes[0].childNodes[0].nodeValue == 'x' + assert nodes[2].childNodes[0].nodeValue == '1' + + mml_2 = mpp._print(x**2) + assert mml_2.nodeName == 'msup' + nodes = mml_2.childNodes + assert nodes[0].childNodes[0].nodeValue == 'x' + assert nodes[1].childNodes[0].nodeValue == '2' + + mml_3 = mpp._print(2*x) + assert mml_3.nodeName == 'mrow' + nodes = mml_3.childNodes + assert nodes[0].childNodes[0].nodeValue == '2' + assert nodes[1].childNodes[0].nodeValue == '⁢' + assert nodes[2].childNodes[0].nodeValue == 'x' + + mml = mpp._print(Float(1.0, 2)*x) + assert mml.nodeName == 'mrow' + nodes = mml.childNodes + assert nodes[0].childNodes[0].nodeValue == '1.0' + assert nodes[1].childNodes[0].nodeValue == '⁢' + assert nodes[2].childNodes[0].nodeValue == 'x' + + +def test_presentation_mathml_functions(): + mml_1 = mpp._print(sin(x)) + assert mml_1.childNodes[0].childNodes[0 + ].nodeValue == 'sin' + assert mml_1.childNodes[1].childNodes[1 + ].childNodes[0].nodeValue == 'x' + + mml_2 = mpp._print(diff(sin(x), x, evaluate=False)) + assert mml_2.nodeName == 'mrow' + assert mml_2.childNodes[0].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == 'ⅆ' + assert mml_2.childNodes[1].childNodes[1 + ].nodeName == 'mrow' + assert mml_2.childNodes[0].childNodes[1 + ].childNodes[0].childNodes[0].nodeValue == 'ⅆ' + + mml_3 = mpp._print(diff(cos(x*y), x, evaluate=False)) + assert mml_3.childNodes[0].nodeName == 'mfrac' + assert mml_3.childNodes[0].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == '∂' + assert mml_3.childNodes[1].childNodes[0 + ].childNodes[0].nodeValue == 'cos' + + +def test_print_derivative(): + f = Function('f') + d = Derivative(f(x, y, z), x, z, x, z, z, y) + assert mathml(d) == \ + 'yz2xzxxyz' + assert mathml(d, printer='presentation') == \ + '∂6∂y∂2z∂x∂z∂xf(x,y,z)' + + +def test_presentation_mathml_limits(): + lim_fun = sin(x)/x + mml_1 = mpp._print(Limit(lim_fun, x, 0)) + assert mml_1.childNodes[0].nodeName == 'munder' + assert mml_1.childNodes[0].childNodes[0 + ].childNodes[0].nodeValue == 'lim' + assert mml_1.childNodes[0].childNodes[1 + ].childNodes[0].childNodes[0 + ].nodeValue == 'x' + assert mml_1.childNodes[0].childNodes[1 + ].childNodes[1].childNodes[0 + ].nodeValue == '→' + assert mml_1.childNodes[0].childNodes[1 + ].childNodes[2].childNodes[0 + ].nodeValue == '0' + + +def test_presentation_mathml_integrals(): + assert mpp.doprint(Integral(x, (x, 0, 1))) == \ + '∫01'\ + 'xⅆx' + assert mpp.doprint(Integral(log(x), x)) == \ + '∫log(x' \ + ')ⅆx' + assert mpp.doprint(Integral(x*y, x, y)) == \ + '∬x⁢'\ + 'yⅆyⅆx' + z, w = symbols('z w') + assert mpp.doprint(Integral(x*y*z, x, y, z)) == \ + '∭x⁢'\ + 'y⁢zⅆ'\ + 'zⅆyⅆx' + assert mpp.doprint(Integral(x*y*z*w, x, y, z, w)) == \ + '∫∫∫'\ + '∫w⁢'\ + 'x⁢y'\ + '⁢zⅆw'\ + 'ⅆzⅆyⅆx' + assert mpp.doprint(Integral(x, x, y, (z, 0, 1))) == \ + '∫01'\ + '∫∫xⅆz'\ + 'ⅆyⅆx' + assert mpp.doprint(Integral(x, (x, 0))) == \ + '∫0xⅆ'\ + 'x' + + +def test_presentation_mathml_matrices(): + A = Matrix([1, 2, 3]) + B = Matrix([[0, 5, 4], [2, 3, 1], [9, 7, 9]]) + mll_1 = mpp._print(A) + assert mll_1.childNodes[1].nodeName == 'mtable' + assert mll_1.childNodes[1].childNodes[0].nodeName == 'mtr' + assert len(mll_1.childNodes[1].childNodes) == 3 + assert mll_1.childNodes[1].childNodes[0].childNodes[0].nodeName == 'mtd' + assert len(mll_1.childNodes[1].childNodes[0].childNodes) == 1 + assert mll_1.childNodes[1].childNodes[0].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == '1' + assert mll_1.childNodes[1].childNodes[1].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == '2' + assert mll_1.childNodes[1].childNodes[2].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == '3' + mll_2 = mpp._print(B) + assert mll_2.childNodes[1].nodeName == 'mtable' + assert mll_2.childNodes[1].childNodes[0].nodeName == 'mtr' + assert len(mll_2.childNodes[1].childNodes) == 3 + assert mll_2.childNodes[1].childNodes[0].childNodes[0].nodeName == 'mtd' + assert len(mll_2.childNodes[1].childNodes[0].childNodes) == 3 + assert mll_2.childNodes[1].childNodes[0].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == '0' + assert mll_2.childNodes[1].childNodes[0].childNodes[1 + ].childNodes[0].childNodes[0].nodeValue == '5' + assert mll_2.childNodes[1].childNodes[0].childNodes[2 + ].childNodes[0].childNodes[0].nodeValue == '4' + assert mll_2.childNodes[1].childNodes[1].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == '2' + assert mll_2.childNodes[1].childNodes[1].childNodes[1 + ].childNodes[0].childNodes[0].nodeValue == '3' + assert mll_2.childNodes[1].childNodes[1].childNodes[2 + ].childNodes[0].childNodes[0].nodeValue == '1' + assert mll_2.childNodes[1].childNodes[2].childNodes[0 + ].childNodes[0].childNodes[0].nodeValue == '9' + assert mll_2.childNodes[1].childNodes[2].childNodes[1 + ].childNodes[0].childNodes[0].nodeValue == '7' + assert mll_2.childNodes[1].childNodes[2].childNodes[2 + ].childNodes[0].childNodes[0].nodeValue == '9' + + +def test_presentation_mathml_sums(): + mml_1 = mpp._print(Sum(x, (x, 1, 10))) + assert mml_1.childNodes[0].nodeName == 'munderover' + assert len(mml_1.childNodes[0].childNodes) == 3 + assert mml_1.childNodes[0].childNodes[0].childNodes[0 + ].nodeValue == '∑' + assert len(mml_1.childNodes[0].childNodes[1].childNodes) == 3 + assert mml_1.childNodes[0].childNodes[2].childNodes[0 + ].nodeValue == '10' + assert mml_1.childNodes[1].childNodes[0].nodeValue == 'x' + + assert mpp.doprint(Sum(x, (x, 1, 10))) == \ + '∑x=110x' + assert mpp.doprint(Sum(x + y, (x, 1, 10))) == \ + '∑x=110(x+y)' + + +def test_presentation_mathml_add(): + mml = mpp._print(x**5 - x**4 + x) + assert len(mml.childNodes) == 5 + assert mml.childNodes[0].childNodes[0].childNodes[0 + ].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].childNodes[0 + ].nodeValue == '5' + assert mml.childNodes[1].childNodes[0].nodeValue == '-' + assert mml.childNodes[2].childNodes[0].childNodes[0 + ].nodeValue == 'x' + assert mml.childNodes[2].childNodes[1].childNodes[0 + ].nodeValue == '4' + assert mml.childNodes[3].childNodes[0].nodeValue == '+' + assert mml.childNodes[4].childNodes[0].nodeValue == 'x' + + +def test_presentation_mathml_Rational(): + mml_1 = mpp._print(Rational(1, 1)) + assert mml_1.nodeName == 'mn' + + mml_2 = mpp._print(Rational(2, 5)) + assert mml_2.nodeName == 'mfrac' + assert mml_2.childNodes[0].childNodes[0].nodeValue == '2' + assert mml_2.childNodes[1].childNodes[0].nodeValue == '5' + + +def test_presentation_mathml_constants(): + mml = mpp._print(I) + assert mml.childNodes[0].nodeValue == 'ⅈ' + + mml = mpp._print(E) + assert mml.childNodes[0].nodeValue == 'ⅇ' + + mml = mpp._print(oo) + assert mml.childNodes[0].nodeValue == '∞' + + mml = mpp._print(pi) + assert mml.childNodes[0].nodeValue == 'π' + + assert mathml(hbar, printer='presentation') == 'ℏ' + assert mathml(S.TribonacciConstant, printer='presentation' + ) == 'TribonacciConstant' + assert mathml(S.EulerGamma, printer='presentation' + ) == 'γ' + assert mathml(S.GoldenRatio, printer='presentation' + ) == 'Φ' + + assert mathml(zoo, printer='presentation') == \ + '∞~' + + assert mathml(S.NaN, printer='presentation') == 'NaN' + +def test_presentation_mathml_trig(): + mml = mpp._print(sin(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'sin' + + mml = mpp._print(cos(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'cos' + + mml = mpp._print(tan(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'tan' + + mml = mpp._print(asin(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'arcsin' + + mml = mpp._print(acos(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'arccos' + + mml = mpp._print(atan(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'arctan' + + mml = mpp._print(sinh(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'sinh' + + mml = mpp._print(cosh(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'cosh' + + mml = mpp._print(tanh(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'tanh' + + mml = mpp._print(asinh(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'arcsinh' + + mml = mpp._print(atanh(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'arctanh' + + mml = mpp._print(acosh(x)) + assert mml.childNodes[0].childNodes[0].nodeValue == 'arccosh' + + +def test_presentation_mathml_relational(): + mml_1 = mpp._print(Eq(x, 1)) + assert len(mml_1.childNodes) == 3 + assert mml_1.childNodes[0].nodeName == 'mi' + assert mml_1.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml_1.childNodes[1].nodeName == 'mo' + assert mml_1.childNodes[1].childNodes[0].nodeValue == '=' + assert mml_1.childNodes[2].nodeName == 'mn' + assert mml_1.childNodes[2].childNodes[0].nodeValue == '1' + + mml_2 = mpp._print(Ne(1, x)) + assert len(mml_2.childNodes) == 3 + assert mml_2.childNodes[0].nodeName == 'mn' + assert mml_2.childNodes[0].childNodes[0].nodeValue == '1' + assert mml_2.childNodes[1].nodeName == 'mo' + assert mml_2.childNodes[1].childNodes[0].nodeValue == '≠' + assert mml_2.childNodes[2].nodeName == 'mi' + assert mml_2.childNodes[2].childNodes[0].nodeValue == 'x' + + mml_3 = mpp._print(Ge(1, x)) + assert len(mml_3.childNodes) == 3 + assert mml_3.childNodes[0].nodeName == 'mn' + assert mml_3.childNodes[0].childNodes[0].nodeValue == '1' + assert mml_3.childNodes[1].nodeName == 'mo' + assert mml_3.childNodes[1].childNodes[0].nodeValue == '≥' + assert mml_3.childNodes[2].nodeName == 'mi' + assert mml_3.childNodes[2].childNodes[0].nodeValue == 'x' + + mml_4 = mpp._print(Lt(1, x)) + assert len(mml_4.childNodes) == 3 + assert mml_4.childNodes[0].nodeName == 'mn' + assert mml_4.childNodes[0].childNodes[0].nodeValue == '1' + assert mml_4.childNodes[1].nodeName == 'mo' + assert mml_4.childNodes[1].childNodes[0].nodeValue == '<' + assert mml_4.childNodes[2].nodeName == 'mi' + assert mml_4.childNodes[2].childNodes[0].nodeValue == 'x' + + +def test_presentation_symbol(): + mml = mpp._print(x) + assert mml.nodeName == 'mi' + assert mml.childNodes[0].nodeValue == 'x' + del mml + + mml = mpp._print(Symbol("x^2")) + assert mml.nodeName == 'msup' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].nodeValue == '2' + del mml + + mml = mpp._print(Symbol("x__2")) + assert mml.nodeName == 'msup' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].nodeValue == '2' + del mml + + mml = mpp._print(Symbol("x_2")) + assert mml.nodeName == 'msub' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].nodeValue == '2' + del mml + + mml = mpp._print(Symbol("x^3_2")) + assert mml.nodeName == 'msubsup' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].nodeValue == '2' + assert mml.childNodes[2].nodeName == 'mi' + assert mml.childNodes[2].childNodes[0].nodeValue == '3' + del mml + + mml = mpp._print(Symbol("x__3_2")) + assert mml.nodeName == 'msubsup' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].nodeValue == '2' + assert mml.childNodes[2].nodeName == 'mi' + assert mml.childNodes[2].childNodes[0].nodeValue == '3' + del mml + + mml = mpp._print(Symbol("x_2_a")) + assert mml.nodeName == 'msub' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mrow' + assert mml.childNodes[1].childNodes[0].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].childNodes[0].nodeValue == '2' + assert mml.childNodes[1].childNodes[1].nodeName == 'mo' + assert mml.childNodes[1].childNodes[1].childNodes[0].nodeValue == ' ' + assert mml.childNodes[1].childNodes[2].nodeName == 'mi' + assert mml.childNodes[1].childNodes[2].childNodes[0].nodeValue == 'a' + del mml + + mml = mpp._print(Symbol("x^2^a")) + assert mml.nodeName == 'msup' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mrow' + assert mml.childNodes[1].childNodes[0].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].childNodes[0].nodeValue == '2' + assert mml.childNodes[1].childNodes[1].nodeName == 'mo' + assert mml.childNodes[1].childNodes[1].childNodes[0].nodeValue == ' ' + assert mml.childNodes[1].childNodes[2].nodeName == 'mi' + assert mml.childNodes[1].childNodes[2].childNodes[0].nodeValue == 'a' + del mml + + mml = mpp._print(Symbol("x__2__a")) + assert mml.nodeName == 'msup' + assert mml.childNodes[0].nodeName == 'mi' + assert mml.childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[1].nodeName == 'mrow' + assert mml.childNodes[1].childNodes[0].nodeName == 'mi' + assert mml.childNodes[1].childNodes[0].childNodes[0].nodeValue == '2' + assert mml.childNodes[1].childNodes[1].nodeName == 'mo' + assert mml.childNodes[1].childNodes[1].childNodes[0].nodeValue == ' ' + assert mml.childNodes[1].childNodes[2].nodeName == 'mi' + assert mml.childNodes[1].childNodes[2].childNodes[0].nodeValue == 'a' + del mml + + +def test_presentation_mathml_greek(): + mml = mpp._print(Symbol('alpha')) + assert mml.nodeName == 'mi' + assert mml.childNodes[0].nodeValue == '\N{GREEK SMALL LETTER ALPHA}' + + assert mpp.doprint(Symbol('alpha')) == 'α' + assert mpp.doprint(Symbol('beta')) == 'β' + assert mpp.doprint(Symbol('gamma')) == 'γ' + assert mpp.doprint(Symbol('delta')) == 'δ' + assert mpp.doprint(Symbol('epsilon')) == 'ε' + assert mpp.doprint(Symbol('zeta')) == 'ζ' + assert mpp.doprint(Symbol('eta')) == 'η' + assert mpp.doprint(Symbol('theta')) == 'θ' + assert mpp.doprint(Symbol('iota')) == 'ι' + assert mpp.doprint(Symbol('kappa')) == 'κ' + assert mpp.doprint(Symbol('lambda')) == 'λ' + assert mpp.doprint(Symbol('mu')) == 'μ' + assert mpp.doprint(Symbol('nu')) == 'ν' + assert mpp.doprint(Symbol('xi')) == 'ξ' + assert mpp.doprint(Symbol('omicron')) == 'ο' + assert mpp.doprint(Symbol('pi')) == 'π' + assert mpp.doprint(Symbol('rho')) == 'ρ' + assert mpp.doprint(Symbol('varsigma')) == 'ς' + assert mpp.doprint(Symbol('sigma')) == 'σ' + assert mpp.doprint(Symbol('tau')) == 'τ' + assert mpp.doprint(Symbol('upsilon')) == 'υ' + assert mpp.doprint(Symbol('phi')) == 'φ' + assert mpp.doprint(Symbol('chi')) == 'χ' + assert mpp.doprint(Symbol('psi')) == 'ψ' + assert mpp.doprint(Symbol('omega')) == 'ω' + + assert mpp.doprint(Symbol('Alpha')) == 'Α' + assert mpp.doprint(Symbol('Beta')) == 'Β' + assert mpp.doprint(Symbol('Gamma')) == 'Γ' + assert mpp.doprint(Symbol('Delta')) == 'Δ' + assert mpp.doprint(Symbol('Epsilon')) == 'Ε' + assert mpp.doprint(Symbol('Zeta')) == 'Ζ' + assert mpp.doprint(Symbol('Eta')) == 'Η' + assert mpp.doprint(Symbol('Theta')) == 'Θ' + assert mpp.doprint(Symbol('Iota')) == 'Ι' + assert mpp.doprint(Symbol('Kappa')) == 'Κ' + assert mpp.doprint(Symbol('Lambda')) == 'Λ' + assert mpp.doprint(Symbol('Mu')) == 'Μ' + assert mpp.doprint(Symbol('Nu')) == 'Ν' + assert mpp.doprint(Symbol('Xi')) == 'Ξ' + assert mpp.doprint(Symbol('Omicron')) == 'Ο' + assert mpp.doprint(Symbol('Pi')) == 'Π' + assert mpp.doprint(Symbol('Rho')) == 'Ρ' + assert mpp.doprint(Symbol('Sigma')) == 'Σ' + assert mpp.doprint(Symbol('Tau')) == 'Τ' + assert mpp.doprint(Symbol('Upsilon')) == 'Υ' + assert mpp.doprint(Symbol('Phi')) == 'Φ' + assert mpp.doprint(Symbol('Chi')) == 'Χ' + assert mpp.doprint(Symbol('Psi')) == 'Ψ' + assert mpp.doprint(Symbol('Omega')) == 'Ω' + + +def test_presentation_mathml_order(): + expr = x**3 + x**2*y + 3*x*y**3 + y**4 + + mp = MathMLPresentationPrinter({'order': 'lex'}) + mml = mp._print(expr) + assert mml.childNodes[0].nodeName == 'msup' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeValue == '3' + + assert mml.childNodes[6].nodeName == 'msup' + assert mml.childNodes[6].childNodes[0].childNodes[0].nodeValue == 'y' + assert mml.childNodes[6].childNodes[1].childNodes[0].nodeValue == '4' + + mp = MathMLPresentationPrinter({'order': 'rev-lex'}) + mml = mp._print(expr) + + assert mml.childNodes[0].nodeName == 'msup' + assert mml.childNodes[0].childNodes[0].childNodes[0].nodeValue == 'y' + assert mml.childNodes[0].childNodes[1].childNodes[0].nodeValue == '4' + + assert mml.childNodes[6].nodeName == 'msup' + assert mml.childNodes[6].childNodes[0].childNodes[0].nodeValue == 'x' + assert mml.childNodes[6].childNodes[1].childNodes[0].nodeValue == '3' + + +def test_print_intervals(): + a = Symbol('a', real=True) + assert mpp.doprint(Interval(0, a)) == \ + '[0,a]' + assert mpp.doprint(Interval(0, a, False, False)) == \ + '[0,a]' + assert mpp.doprint(Interval(0, a, True, False)) == \ + '(0,a]' + assert mpp.doprint(Interval(0, a, False, True)) == \ + '[0,a)' + assert mpp.doprint(Interval(0, a, True, True)) == \ + '(0,a)' + + +def test_print_tuples(): + assert mpp.doprint(Tuple(0,)) == \ + '(0)' + assert mpp.doprint(Tuple(0, a)) == \ + '(0,a)' + assert mpp.doprint(Tuple(0, a, a)) == \ + '(0,a,a)' + assert mpp.doprint(Tuple(0, 1, 2, 3, 4)) == \ + '(0,1,2,3,4)' + assert mpp.doprint(Tuple(0, 1, Tuple(2, 3, 4))) == \ + '(0,1,(2,3'\ + ',4))' + + +def test_print_re_im(): + assert mpp.doprint(re(x)) == \ + 'ℜ(x)' + assert mpp.doprint(im(x)) == \ + 'ℑ(x)' + assert mpp.doprint(re(x + 1, evaluate=False)) == \ + 'ℜ(x+1)' + assert mpp.doprint(im(x + 1, evaluate=False)) == \ + 'ℑ(x+1)' + + +def test_print_Abs(): + assert mpp.doprint(Abs(x)) == \ + '|x|' + assert mpp.doprint(Abs(x + 1)) == \ + '|x+1|' + + +def test_print_Determinant(): + assert mpp.doprint(Determinant(Matrix([[1, 2], [3, 4]]))) == \ + '|[1234]|' + + +def test_presentation_settings(): + raises(TypeError, lambda: mathml(x, printer='presentation', + method="garbage")) + + +def test_print_domains(): + from sympy.sets import Integers, Naturals, Naturals0, Reals, Complexes + + assert mpp.doprint(Complexes) == 'ℂ' + assert mpp.doprint(Integers) == 'ℤ' + assert mpp.doprint(Naturals) == 'ℕ' + assert mpp.doprint(Naturals0) == \ + 'ℕ0' + assert mpp.doprint(Reals) == 'ℝ' + + +def test_print_expression_with_minus(): + assert mpp.doprint(-x) == '-x' + assert mpp.doprint(-x/y) == \ + '-xy' + assert mpp.doprint(-Rational(1, 2)) == \ + '-12' + + +def test_print_AssocOp(): + from sympy.core.operations import AssocOp + + class TestAssocOp(AssocOp): + identity = 0 + + expr = TestAssocOp(1, 2) + assert mpp.doprint(expr) == \ + 'testassocop12' + + +def test_print_basic(): + expr = Basic(S(1), S(2)) + assert mpp.doprint(expr) == \ + 'basic(1,2)' + assert mp.doprint(expr) == '12' + + +def test_mat_delim_print(): + expr = Matrix([[1, 2], [3, 4]]) + assert mathml(expr, printer='presentation', mat_delim='[') == \ + '[1'\ + '234'\ + ']' + assert mathml(expr, printer='presentation', mat_delim='(') == \ + '(12'\ + '34)' + assert mathml(expr, printer='presentation', mat_delim='') == \ + '12'\ + '34' + + +def test_ln_notation_print(): + expr = log(x) + assert mathml(expr, printer='presentation') == \ + 'log(x)' + assert mathml(expr, printer='presentation', ln_notation=False) == \ + 'log(x)' + assert mathml(expr, printer='presentation', ln_notation=True) == \ + 'ln(x)' + + +def test_mul_symbol_print(): + expr = x * y + assert mathml(expr, printer='presentation') == \ + 'x⁢y' + assert mathml(expr, printer='presentation', mul_symbol=None) == \ + 'x⁢y' + assert mathml(expr, printer='presentation', mul_symbol='dot') == \ + 'x·y' + assert mathml(expr, printer='presentation', mul_symbol='ldot') == \ + 'x․y' + assert mathml(expr, printer='presentation', mul_symbol='times') == \ + 'x×y' + + +def test_print_lerchphi(): + assert mpp.doprint(lerchphi(1, 2, 3)) == \ + 'Φ(1,2,3)' + + +def test_print_polylog(): + assert mp.doprint(polylog(x, y)) == \ + 'xy' + assert mpp.doprint(polylog(x, y)) == \ + 'Lix(y)' + + +def test_print_set_frozenset(): + f = frozenset({1, 5, 3}) + assert mpp.doprint(f) == \ + '{1,3,5}' + s = set({1, 2, 3}) + assert mpp.doprint(s) == \ + '{1,2,3}' + + +def test_print_FiniteSet(): + f1 = FiniteSet(x, 1, 3) + assert mpp.doprint(f1) == \ + '{1,3,x}' + + +def test_print_LambertW(): + assert mpp.doprint(LambertW(x)) == 'W(x)' + assert mpp.doprint(LambertW(x, y)) == 'W(x,y)' + + +def test_print_EmptySet(): + assert mpp.doprint(S.EmptySet) == '∅' + + +def test_print_UniversalSet(): + assert mpp.doprint(S.UniversalSet) == '𝕌' + + +def test_print_spaces(): + assert mpp.doprint(HilbertSpace()) == 'ℋ' + assert mpp.doprint(ComplexSpace(2)) == '𝒞2' + assert mpp.doprint(FockSpace()) == 'ℱ' + + +def test_print_constants(): + assert mpp.doprint(hbar) == 'ℏ' + assert mpp.doprint(S.TribonacciConstant) == 'TribonacciConstant' + assert mpp.doprint(S.GoldenRatio) == 'Φ' + assert mpp.doprint(S.EulerGamma) == 'γ' + + +def test_print_Contains(): + assert mpp.doprint(Contains(x, S.Naturals)) == \ + 'x∈ℕ' + + +def test_print_Dagger(): + x = symbols('x', commutative=False) + assert mpp.doprint(Dagger(x)) == 'x†' + + +def test_print_SetOp(): + f1 = FiniteSet(x, 1, 3) + f2 = FiniteSet(y, 2, 4) + + prntr = lambda x: mathml(x, printer='presentation') + + assert prntr(Union(f1, f2, evaluate=False)) == \ + '{1,3,x'\ + '}∪{2,'\ + '4,y}' + assert prntr(Intersection(f1, f2, evaluate=False)) == \ + '{1,3,x'\ + '}∩{2'\ + ',4,y}' + assert prntr(Complement(f1, f2, evaluate=False)) == \ + '{1,3,x'\ + '}∖{2'\ + ',4,y}' + assert prntr(SymmetricDifference(f1, f2, evaluate=False)) == \ + '{1,3,x'\ + '}∆{2'\ + ',4,y}' + + A = FiniteSet(a) + C = FiniteSet(c) + D = FiniteSet(d) + + U1 = Union(C, D, evaluate=False) + I1 = Intersection(C, D, evaluate=False) + C1 = Complement(C, D, evaluate=False) + D1 = SymmetricDifference(C, D, evaluate=False) + # XXX ProductSet does not support evaluate keyword + P1 = ProductSet(C, D) + + assert prntr(Union(A, I1, evaluate=False)) == \ + '{a}' \ + '∪({' \ + 'c}∩{' \ + 'd})' + assert prntr(Intersection(A, C1, evaluate=False)) == \ + '{a}' \ + '∩({' \ + 'c}∖{' \ + 'd})' + assert prntr(Complement(A, D1, evaluate=False)) == \ + '{a}' \ + '∖({' \ + 'c}∆{' \ + 'd})' + assert prntr(SymmetricDifference(A, P1, evaluate=False)) == \ + '{a}' \ + '∆({' \ + 'c}×{' \ + 'd})' + assert prntr(ProductSet(A, U1)) == \ + '{a}' \ + '×({' \ + 'c}∪{' \ + 'd})' + + +def test_print_logic(): + assert mpp.doprint(And(x, y)) == \ + 'x∧y' + assert mpp.doprint(Or(x, y)) == \ + 'x∨y' + assert mpp.doprint(Xor(x, y)) == \ + 'x⊻y' + assert mpp.doprint(Implies(x, y)) == \ + 'x⇒y' + assert mpp.doprint(Equivalent(x, y)) == \ + 'x⇔y' + + assert mpp.doprint(And(Eq(x, y), x > 4)) == \ + 'x=y∧'\ + 'x>4' + assert mpp.doprint(And(Eq(x, 3), y < 3, x > y + 1)) == \ + 'x=3∧'\ + 'x>y+1'\ + '∧y<3' + assert mpp.doprint(Or(Eq(x, y), x > 4)) == \ + 'x=y∨'\ + 'x>4' + assert mpp.doprint(And(Eq(x, 3), Or(y < 3, x > y + 1))) == \ + 'x=3'\ + '∧(x>'\ + 'y+1∨'\ + 'y<3)' + + assert mpp.doprint(Not(x)) == '¬x' + assert mpp.doprint(Not(And(x, y))) == \ + '¬(x∧y)' + + +def test_root_notation_print(): + assert mathml(x**(S.One/3), printer='presentation') == \ + 'x3' + assert mathml(x**(S.One/3), printer='presentation', root_notation=False) ==\ + 'x13' + assert mathml(x**(S.One/3), printer='content') == \ + '3x' + assert mathml(x**(S.One/3), printer='content', root_notation=False) == \ + 'x13' + assert mathml(x**(Rational(-1, 3)), printer='presentation') == \ + '1x3' + assert mathml(x**(Rational(-1, 3)), printer='presentation', root_notation=False) \ + == '1x13' + + +def test_fold_frac_powers_print(): + expr = x ** Rational(5, 2) + assert mathml(expr, printer='presentation') == \ + 'x52' + assert mathml(expr, printer='presentation', fold_frac_powers=True) == \ + 'x52' + assert mathml(expr, printer='presentation', fold_frac_powers=False) == \ + 'x52' + + +def test_fold_short_frac_print(): + expr = Rational(2, 5) + assert mathml(expr, printer='presentation') == \ + '25' + assert mathml(expr, printer='presentation', fold_short_frac=True) == \ + '25' + assert mathml(expr, printer='presentation', fold_short_frac=False) == \ + '25' + + +def test_print_factorials(): + assert mpp.doprint(factorial(x)) == 'x!' + assert mpp.doprint(factorial(x + 1)) == \ + '(x+1)!' + assert mpp.doprint(factorial2(x)) == 'x!!' + assert mpp.doprint(factorial2(x + 1)) == \ + '(x+1)!!' + assert mpp.doprint(binomial(x, y)) == \ + '(xy)' + assert mpp.doprint(binomial(4, x + y)) == \ + '(4x'\ + '+y)' + + +def test_print_floor(): + expr = floor(x) + assert mathml(expr, printer='presentation') == \ + '⌊x⌋' + + +def test_print_ceiling(): + expr = ceiling(x) + assert mathml(expr, printer='presentation') == \ + '⌈x⌉' + + +def test_print_Lambda(): + expr = Lambda(x, x+1) + assert mathml(expr, printer='presentation') == \ + '(x↦x+1)' + expr = Lambda((x, y), x + y) + assert mathml(expr, printer='presentation') == \ + '((x,y)↦x+y)' + + +def test_print_conjugate(): + assert mpp.doprint(conjugate(x)) == \ + 'x' + assert mpp.doprint(conjugate(x + 1)) == \ + 'x+1' + + +def test_print_AccumBounds(): + a = Symbol('a', real=True) + assert mpp.doprint(AccumBounds(0, 1)) == '⟨0,1⟩' + assert mpp.doprint(AccumBounds(0, a)) == '⟨0,a⟩' + assert mpp.doprint(AccumBounds(a + 1, a + 2)) == '⟨a+1,a+2⟩' + + +def test_print_Float(): + assert mpp.doprint(Float(1e100)) == '1.0·10100' + assert mpp.doprint(Float(1e-100)) == '1.0·10-100' + assert mpp.doprint(Float(-1e100)) == '-1.0·10100' + assert mpp.doprint(Float(1.0*oo)) == '∞' + assert mpp.doprint(Float(-1.0*oo)) == '-∞' + + +def test_print_different_functions(): + assert mpp.doprint(gamma(x)) == 'Γ(x)' + assert mpp.doprint(lowergamma(x, y)) == 'γ(x,y)' + assert mpp.doprint(uppergamma(x, y)) == 'Γ(x,y)' + assert mpp.doprint(zeta(x)) == 'ζ(x)' + assert mpp.doprint(zeta(x, y)) == 'ζ(x,y)' + assert mpp.doprint(dirichlet_eta(x)) == 'η(x)' + assert mpp.doprint(elliptic_k(x)) == 'Κ(x)' + assert mpp.doprint(totient(x)) == 'ϕ(x)' + assert mpp.doprint(reduced_totient(x)) == 'λ(x)' + assert mpp.doprint(primenu(x)) == 'ν(x)' + assert mpp.doprint(primeomega(x)) == 'Ω(x)' + assert mpp.doprint(fresnels(x)) == 'S(x)' + assert mpp.doprint(fresnelc(x)) == 'C(x)' + assert mpp.doprint(Heaviside(x)) == 'Θ(x,12)' + + +def test_mathml_builtins(): + assert mpp.doprint(None) == 'None' + assert mpp.doprint(true) == 'True' + assert mpp.doprint(false) == 'False' + + +def test_mathml_Range(): + assert mpp.doprint(Range(1, 51)) == \ + '{1,2,…,50}' + assert mpp.doprint(Range(1, 4)) == \ + '{1,2,3}' + assert mpp.doprint(Range(0, 3, 1)) == \ + '{0,1,2}' + assert mpp.doprint(Range(0, 30, 1)) == \ + '{0,1,…,29}' + assert mpp.doprint(Range(30, 1, -1)) == \ + '{30,29,…,2}' + assert mpp.doprint(Range(0, oo, 2)) == \ + '{0,2,…}' + assert mpp.doprint(Range(oo, -2, -2)) == \ + '{…,2,0}' + assert mpp.doprint(Range(-2, -oo, -1)) == \ + '{-2,-3,…}' + + +def test_print_exp(): + assert mpp.doprint(exp(x)) == \ + 'ⅇx' + assert mpp.doprint(exp(1) + exp(2)) == \ + 'ⅇ+ⅇ2' + + +def test_print_MinMax(): + assert mpp.doprint(Min(x, y)) == \ + 'min(x,y)' + assert mpp.doprint(Min(x, 2, x**3)) == \ + 'min(2,x,x3)' + assert mpp.doprint(Max(x, y)) == \ + 'max(x,y)' + assert mpp.doprint(Max(x, 2, x**3)) == \ + 'max(2,x,x3)' + + +def test_mathml_presentation_numbers(): + n = Symbol('n') + assert mathml(catalan(n), printer='presentation') == \ + 'Cn' + assert mathml(bernoulli(n), printer='presentation') == \ + 'Bn' + assert mathml(bell(n), printer='presentation') == \ + 'Bn' + assert mathml(euler(n), printer='presentation') == \ + 'En' + assert mathml(fibonacci(n), printer='presentation') == \ + 'Fn' + assert mathml(lucas(n), printer='presentation') == \ + 'Ln' + assert mathml(tribonacci(n), printer='presentation') == \ + 'Tn' + assert mathml(bernoulli(n, x), printer='presentation') == \ + mathml(bell(n, x), printer='presentation') == \ + 'Bn(x)' + assert mathml(euler(n, x), printer='presentation') == \ + 'En(x)' + assert mathml(fibonacci(n, x), printer='presentation') == \ + 'Fn(x)' + assert mathml(tribonacci(n, x), printer='presentation') == \ + 'Tn(x)' + + +def test_mathml_presentation_mathieu(): + assert mathml(mathieuc(x, y, z), printer='presentation') == \ + 'C(x,y,z)' + assert mathml(mathieus(x, y, z), printer='presentation') == \ + 'S(x,y,z)' + assert mathml(mathieucprime(x, y, z), printer='presentation') == \ + 'C′(x,y,z)' + assert mathml(mathieusprime(x, y, z), printer='presentation') == \ + 'S′(x,y,z)' + + +def test_mathml_presentation_stieltjes(): + assert mathml(stieltjes(n), printer='presentation') == \ + 'γn' + assert mathml(stieltjes(n, x), printer='presentation') == \ + 'γn(x)' + + +def test_print_matrix_symbol(): + A = MatrixSymbol('A', 1, 2) + assert mpp.doprint(A) == 'A' + assert mp.doprint(A) == 'A' + assert mathml(A, printer='presentation', mat_symbol_style="bold") == \ + 'A' + # No effect in content printer + assert mathml(A, mat_symbol_style="bold") == 'A' + + +def test_print_hadamard(): + from sympy.matrices.expressions import HadamardProduct + from sympy.matrices.expressions import Transpose + + X = MatrixSymbol('X', 2, 2) + Y = MatrixSymbol('Y', 2, 2) + + assert mathml(HadamardProduct(X, Y*Y), printer="presentation") == \ + '' \ + 'X' \ + '∘' \ + 'Y2' \ + '' + + assert mathml(HadamardProduct(X, Y)*Y, printer="presentation") == \ + '' \ + '(' \ + 'X∘Y' \ + ')' \ + '⁢Y' \ + '' + + assert mathml(HadamardProduct(X, Y, Y), printer="presentation") == \ + '' \ + 'X∘' \ + 'Y∘' \ + 'Y' \ + '' + + assert mathml( + Transpose(HadamardProduct(X, Y)), printer="presentation") == \ + '' \ + '(' \ + 'X∘Y' \ + ')' \ + 'T' \ + '' + + +def test_print_random_symbol(): + R = RandomSymbol(Symbol('R')) + assert mpp.doprint(R) == 'R' + assert mp.doprint(R) == 'R' + + +def test_print_IndexedBase(): + assert mathml(IndexedBase(a)[b], printer='presentation') == \ + 'ab' + assert mathml(IndexedBase(a)[b, c, d], printer='presentation') == \ + 'a(b,c,d)' + assert mathml(IndexedBase(a)[b]*IndexedBase(c)[d]*IndexedBase(e), + printer='presentation') == \ + 'ab⁢'\ + 'cd⁢e' + + +def test_print_Indexed(): + assert mathml(IndexedBase(a), printer='presentation') == 'a' + assert mathml(IndexedBase(a/b), printer='presentation') == \ + 'ab' + assert mathml(IndexedBase((a, b)), printer='presentation') == \ + '(a,b)' + +def test_print_MatrixElement(): + i, j = symbols('i j') + A = MatrixSymbol('A', i, j) + assert mathml(A[0,0],printer = 'presentation') == \ + 'A0,0' + assert mathml(A[i,j], printer = 'presentation') == \ + 'Ai,j' + assert mathml(A[i*j,0], printer = 'presentation') == \ + 'Ai⁢j,0' + + +def test_print_Vector(): + ACS = CoordSys3D('A') + assert mathml(Cross(ACS.i, ACS.j*ACS.x*3 + ACS.k), printer='presentation') == \ + 'i^'\ + 'A×('\ + '(3⁢'\ + 'xA'\ + ')⁢'\ + 'j^'\ + 'A+'\ + 'k^'\ + 'A)' + assert mathml(Cross(ACS.i, ACS.j), printer='presentation') == \ + 'i^'\ + 'A×'\ + 'j^'\ + 'A' + assert mathml(x*Cross(ACS.i, ACS.j), printer='presentation') == \ + 'x⁢('\ + 'i^'\ + 'A×'\ + 'j^'\ + 'A)' + assert mathml(Cross(x*ACS.i, ACS.j), printer='presentation') == \ + '-j'\ + '^A'\ + '×((x)'\ + '⁢i'\ + '^A'\ + ')' + assert mathml(Curl(3*ACS.x*ACS.j), printer='presentation') == \ + '∇×(('\ + '3⁢x'\ + 'A)⁢'\ + 'j^'\ + 'A)' + assert mathml(Curl(3*x*ACS.x*ACS.j), printer='presentation') == \ + '∇×(('\ + '3⁢x'\ + 'A⁢'\ + 'x)⁢'\ + 'j^'\ + 'A)' + assert mathml(x*Curl(3*ACS.x*ACS.j), printer='presentation') == \ + 'x⁢(∇'\ + '×((3'\ + '⁢x'\ + 'A)'\ + '⁢j'\ + '^A)'\ + ')' + assert mathml(Curl(3*x*ACS.x*ACS.j + ACS.i), printer='presentation') == \ + '∇×('\ + 'i^'\ + 'A+('\ + '3⁢x'\ + 'A⁢'\ + 'x)⁢'\ + 'j^'\ + 'A)' + assert mathml(Divergence(3*ACS.x*ACS.j), printer='presentation') == \ + '∇·(('\ + '3⁢x'\ + 'A)'\ + '⁢j'\ + '^A)' + assert mathml(x*Divergence(3*ACS.x*ACS.j), printer='presentation') == \ + 'x⁢(∇'\ + '·((3'\ + '⁢x'\ + 'A)'\ + '⁢j'\ + '^A'\ + '))' + assert mathml(Divergence(3*x*ACS.x*ACS.j + ACS.i), printer='presentation') == \ + '∇·('\ + 'i^'\ + 'A+('\ + '3⁢'\ + 'xA'\ + '⁢x)'\ + '⁢j'\ + '^A'\ + ')' + assert mathml(Dot(ACS.i, ACS.j*ACS.x*3+ACS.k), printer='presentation') == \ + 'i^'\ + 'A·('\ + '(3⁢'\ + 'xA'\ + ')⁢'\ + 'j^'\ + 'A+'\ + 'k^'\ + 'A)' + assert mathml(Dot(ACS.i, ACS.j), printer='presentation') == \ + 'i^'\ + 'A·'\ + 'j^'\ + 'A' + assert mathml(Dot(x*ACS.i, ACS.j), printer='presentation') == \ + 'j^'\ + 'A·('\ + '(x)⁢'\ + 'i^'\ + 'A)' + assert mathml(x*Dot(ACS.i, ACS.j), printer='presentation') == \ + 'x⁢('\ + 'i^'\ + 'A·'\ + 'j^'\ + 'A)' + assert mathml(Gradient(ACS.x), printer='presentation') == \ + '∇x'\ + 'A' + assert mathml(Gradient(ACS.x + 3*ACS.y), printer='presentation') == \ + '∇('\ + 'xA+3'\ + '⁢y'\ + 'A)' + assert mathml(x*Gradient(ACS.x), printer='presentation') == \ + 'x⁢(∇'\ + 'xA'\ + ')' + assert mathml(Gradient(x*ACS.x), printer='presentation') == \ + '∇('\ + 'xA⁢'\ + 'x)' + assert mathml(Cross(ACS.z, ACS.x), printer='presentation') == \ + '-x'\ + 'A×'\ + 'zA' + assert mathml(Laplacian(ACS.x), printer='presentation') == \ + '∆x'\ + 'A' + assert mathml(Laplacian(ACS.x + 3*ACS.y), printer='presentation') == \ + '∆('\ + 'xA+3'\ + '⁢y'\ + 'A)' + assert mathml(x*Laplacian(ACS.x), printer='presentation') == \ + 'x⁢(∆'\ + 'xA'\ + ')' + assert mathml(Laplacian(x*ACS.x), printer='presentation') == \ + '∆('\ + 'xA⁢'\ + 'x)' + +@XFAIL +def test_vector_cross_xfail(): + ACS = CoordSys3D('A') + assert mathml(Cross(ACS.x, ACS.z) + Cross(ACS.z, ACS.x), printer='presentation') == \ + '0^' + +def test_print_elliptic_f(): + assert mathml(elliptic_f(x, y), printer = 'presentation') == \ + '𝖥(x|y)' + assert mathml(elliptic_f(x/y, y), printer = 'presentation') == \ + '𝖥(xy|y)' + +def test_print_elliptic_e(): + assert mathml(elliptic_e(x), printer = 'presentation') == \ + '𝖤(x)' + assert mathml(elliptic_e(x, y), printer = 'presentation') == \ + '𝖤(x|y)' + +def test_print_elliptic_pi(): + assert mathml(elliptic_pi(x, y), printer = 'presentation') == \ + '𝛱(x|y)' + assert mathml(elliptic_pi(x, y, z), printer = 'presentation') == \ + '𝛱(x;y|z)' + +def test_print_Ei(): + assert mathml(Ei(x), printer = 'presentation') == \ + 'Ei(x)' + assert mathml(Ei(x**y), printer = 'presentation') == \ + 'Ei(xy)' + +def test_print_expint(): + assert mathml(expint(x, y), printer = 'presentation') == \ + 'Ex(y)' + assert mathml(expint(IndexedBase(x)[1], IndexedBase(x)[2]), printer = 'presentation') == \ + 'Ex1(x2)' + +def test_print_jacobi(): + assert mathml(jacobi(n, a, b, x), printer = 'presentation') == \ + 'Pn(a,b)(x)' + +def test_print_gegenbauer(): + assert mathml(gegenbauer(n, a, x), printer = 'presentation') == \ + 'Cn(a)(x)' + +def test_print_chebyshevt(): + assert mathml(chebyshevt(n, x), printer = 'presentation') == \ + 'Tn(x)' + +def test_print_chebyshevu(): + assert mathml(chebyshevu(n, x), printer = 'presentation') == \ + 'Un(x)' + +def test_print_legendre(): + assert mathml(legendre(n, x), printer = 'presentation') == \ + 'Pn(x)' + +def test_print_assoc_legendre(): + assert mathml(assoc_legendre(n, a, x), printer = 'presentation') == \ + 'Pn(a)(x)' + +def test_print_laguerre(): + assert mathml(laguerre(n, x), printer = 'presentation') == \ + 'Ln(x)' + +def test_print_assoc_laguerre(): + assert mathml(assoc_laguerre(n, a, x), printer = 'presentation') == \ + 'Ln(a)(x)' + +def test_print_hermite(): + assert mathml(hermite(n, x), printer = 'presentation') == \ + 'Hn(x)' + +def test_mathml_SingularityFunction(): + assert mathml(SingularityFunction(x, 4, 5), printer='presentation') == \ + '⟨x-4⟩5' + assert mathml(SingularityFunction(x, -3, 4), printer='presentation') == \ + '⟨x+3⟩4' + assert mathml(SingularityFunction(x, 0, 4), printer='presentation') == \ + '⟨x⟩4' + assert mathml(SingularityFunction(x, a, n), printer='presentation') == \ + '⟨-a+x⟩n' + assert mathml(SingularityFunction(x, 4, -2), printer='presentation') == \ + '⟨x-4⟩-2' + assert mathml(SingularityFunction(x, 4, -1), printer='presentation') == \ + '⟨x-4⟩-1' + + +def test_mathml_matrix_functions(): + from sympy.matrices import Adjoint, Inverse, Transpose + X = MatrixSymbol('X', 2, 2) + Y = MatrixSymbol('Y', 2, 2) + assert mathml(Adjoint(X), printer='presentation') == \ + 'X†' + assert mathml(Adjoint(X + Y), printer='presentation') == \ + '(X+Y)†' + assert mathml(Adjoint(X) + Adjoint(Y), printer='presentation') == \ + 'X†+' \ + 'Y†' + assert mathml(Adjoint(X*Y), printer='presentation') == \ + '(X⁢' \ + 'Y)†' + assert mathml(Adjoint(Y)*Adjoint(X), printer='presentation') == \ + 'Y†⁢' \ + 'X†' + assert mathml(Adjoint(X**2), printer='presentation') == \ + '(X2)†' + assert mathml(Adjoint(X)**2, printer='presentation') == \ + '(X†)2' + assert mathml(Adjoint(Inverse(X)), printer='presentation') == \ + '(X-1)†' + assert mathml(Inverse(Adjoint(X)), printer='presentation') == \ + '(X†)-1' + assert mathml(Adjoint(Transpose(X)), printer='presentation') == \ + '(XT)†' + assert mathml(Transpose(Adjoint(X)), printer='presentation') == \ + '(X†)T' + assert mathml(Transpose(Adjoint(X) + Y), printer='presentation') == \ + '(X†' \ + '+Y)T' + assert mathml(Transpose(X), printer='presentation') == \ + 'XT' + assert mathml(Transpose(X + Y), printer='presentation') == \ + '(X+Y)T' + + +def test_mathml_special_matrices(): + from sympy.matrices import Identity, ZeroMatrix, OneMatrix + assert mathml(Identity(4), printer='presentation') == '𝕀' + assert mathml(ZeroMatrix(2, 2), printer='presentation') == '𝟘' + assert mathml(OneMatrix(2, 2), printer='presentation') == '𝟙' + +def test_mathml_piecewise(): + from sympy.functions.elementary.piecewise import Piecewise + # Content MathML + assert mathml(Piecewise((x, x <= 1), (x**2, True))) == \ + 'xx1x2' + + raises(ValueError, lambda: mathml(Piecewise((x, x <= 1)))) + + +def test_issue_17857(): + assert mathml(Range(-oo, oo), printer='presentation') == \ + '{…,-1,0,1,…}' + assert mathml(Range(oo, -oo, -1), printer='presentation') == \ + '{…,1,0,-1,…}' + + +def test_float_roundtrip(): + x = sympify(0.8975979010256552) + y = float(mp.doprint(x).strip('')) + assert x == y + + +def test_content_mathml_disable_split_super_sub(): + mp = MathMLContentPrinter() + assert mp.doprint(Symbol('u_b')) == 'ub' + mp = MathMLContentPrinter({'disable_split_super_sub': False}) + assert mp.doprint(Symbol('u_b')) == 'ub' + mp = MathMLContentPrinter({'disable_split_super_sub': True}) + assert mp.doprint(Symbol('u_b')) == 'u_b' + +def test_presentation_mathml_disable_split_super_sub(): + mpp = MathMLPresentationPrinter() + assert mpp.doprint(Symbol('u_b')) == 'ub' + mpp = MathMLPresentationPrinter({'disable_split_super_sub': False}) + assert mpp.doprint(Symbol('u_b')) == 'ub' + mpp = MathMLPresentationPrinter({'disable_split_super_sub': True}) + assert mpp.doprint(Symbol('u_b')) == 'u_b'