Пример #1
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def test_issue_8601():
    n = Symbol('n', integer=True, negative=True)

    assert catalan(n - 1) == S.Zero
    assert catalan(-S.Half) == S.ComplexInfinity
    assert catalan(-S.One) == -S.Half
    c1 = catalan(-5.6).evalf()
    assert str(c1) == '6.93334070531408e-5'
    c2 = catalan(-35.4).evalf()
    assert str(c2) == '-4.14189164517449e-24'
Пример #2
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def test_issue_8601():
    n = Symbol('n', integer=True, negative=True)

    assert catalan(n - 1) == S.Zero
    assert catalan(-S.Half) == S.ComplexInfinity
    assert catalan(-S.One) == -S.Half
    c1 = catalan(-5.6).evalf()
    assert str(c1) == '6.93334070531408e-5'
    c2 = catalan(-35.4).evalf()
    assert str(c2) == '-4.14189164517449e-24'
Пример #3
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def test_issue_8601():
    n = Symbol("n", integer=True, negative=True)

    assert catalan(n - 1) is S.Zero
    assert catalan(Rational(-1, 2)) is S.ComplexInfinity
    assert catalan(-S.One) == Rational(-1, 2)
    c1 = catalan(-5.6).evalf()
    assert str(c1) == "6.93334070531408e-5"
    c2 = catalan(-35.4).evalf()
    assert str(c2) == "-4.14189164517449e-24"
Пример #4
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def test_Function():
    assert mcode(f(x, y, z)) == "f[x, y, z]"
    assert mcode(sin(x)**cos(x)) == "Sin[x]^Cos[x]"
    assert mcode(conjugate(x)) == "Conjugate[x]"
    assert mcode(Max(x, y, z) * Min(y, z)) == "Max[x, y, z]*Min[y, z]"
    assert mcode(fresnelc(x)) == "FresnelC[x]"
    assert mcode(fresnels(x)) == "FresnelS[x]"
    assert mcode(gamma(x)) == "Gamma[x]"
    assert mcode(uppergamma(x, y)) == "Gamma[x, y]"
    assert mcode(polygamma(x, y)) == "PolyGamma[x, y]"
    assert mcode(loggamma(x)) == "LogGamma[x]"
    assert mcode(erf(x)) == "Erf[x]"
    assert mcode(erfc(x)) == "Erfc[x]"
    assert mcode(erfi(x)) == "Erfi[x]"
    assert mcode(erf2(x, y)) == "Erf[x, y]"
    assert mcode(expint(x, y)) == "ExpIntegralE[x, y]"
    assert mcode(erfcinv(x)) == "InverseErfc[x]"
    assert mcode(erfinv(x)) == "InverseErf[x]"
    assert mcode(erf2inv(x, y)) == "InverseErf[x, y]"
    assert mcode(Ei(x)) == "ExpIntegralEi[x]"
    assert mcode(Ci(x)) == "CosIntegral[x]"
    assert mcode(li(x)) == "LogIntegral[x]"
    assert mcode(Si(x)) == "SinIntegral[x]"
    assert mcode(Shi(x)) == "SinhIntegral[x]"
    assert mcode(Chi(x)) == "CoshIntegral[x]"
    assert mcode(beta(x, y)) == "Beta[x, y]"
    assert mcode(factorial(x)) == "Factorial[x]"
    assert mcode(factorial2(x)) == "Factorial2[x]"
    assert mcode(subfactorial(x)) == "Subfactorial[x]"
    assert mcode(FallingFactorial(x, y)) == "FactorialPower[x, y]"
    assert mcode(RisingFactorial(x, y)) == "Pochhammer[x, y]"
    assert mcode(catalan(x)) == "CatalanNumber[x]"
    assert mcode(harmonic(x)) == "HarmonicNumber[x]"
    assert mcode(harmonic(x, y)) == "HarmonicNumber[x, y]"
Пример #5
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def test_issue_8496():
    n = Symbol("n")
    k = Symbol("k")

    raises(TypeError, lambda: catalan(n, k))
Пример #6
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def test_catalan():
    n = Symbol('n', integer=True)
    m = Symbol('m', integer=True, positive=True)
    k = Symbol('k', integer=True, nonnegative=True)
    p = Symbol('p', nonnegative=True)

    catalans = [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786]
    for i, c in enumerate(catalans):
        assert catalan(i) == c
        assert catalan(n).rewrite(factorial).subs(n, i) == c
        assert catalan(n).rewrite(Product).subs(n, i).doit() == c

    assert catalan(x) == catalan(x)
    assert catalan(2 *
                   x).rewrite(binomial) == binomial(4 * x, 2 * x) / (2 * x + 1)
    assert catalan(Rational(1, 2)).rewrite(gamma) == 8 / (3 * pi)
    assert catalan(Rational(1, 2)).rewrite(factorial).rewrite(gamma) ==\
        8 / (3 * pi)
    assert catalan(3 * x).rewrite(gamma) == 4**(
        3 * x) * gamma(3 * x + Rational(1, 2)) / (sqrt(pi) * gamma(3 * x + 2))
    assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2, ), 1)

    assert catalan(n).rewrite(factorial) == factorial(
        2 * n) / (factorial(n + 1) * factorial(n))
    assert isinstance(catalan(n).rewrite(Product), catalan)
    assert isinstance(catalan(m).rewrite(Product), Product)

    assert diff(catalan(x), x) == (polygamma(0, x + Rational(1, 2)) -
                                   polygamma(0, x + 2) + log(4)) * catalan(x)

    assert catalan(x).evalf() == catalan(x)
    c = catalan(S.Half).evalf()
    assert str(c) == '0.848826363156775'
    c = catalan(I).evalf(3)
    assert str((re(c), im(c))) == '(0.398, -0.0209)'

    # Assumptions
    assert catalan(p).is_positive is True
    assert catalan(k).is_integer is True
    assert catalan(m + 3).is_composite is True
Пример #7
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def test_catalan():
    assert catalan(1) == 1
    assert catalan(2) == 2
    assert catalan(3) == 5
    assert catalan(4) == 14

    assert catalan(x) == catalan(x)
    assert catalan(2*x).rewrite(binomial) == binomial(4*x, 2*x)/(2*x + 1)
    assert catalan(Rational(1, 2)).rewrite(gamma) == 8/(3*pi)
    assert catalan(3*x).rewrite(gamma) == 4**(
        3*x)*gamma(3*x + Rational(1, 2))/(sqrt(pi)*gamma(3*x + 2))
    assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2,), 1)

    assert diff(catalan(x), x) == (polygamma(
        0, x + Rational(1, 2)) - polygamma(0, x + 2) + log(4))*catalan(x)

    c = catalan(0.5).evalf()
    assert str(c) == '0.848826363156775'
Пример #8
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def test_issue_8496():
    n = Symbol("n")
    k = Symbol("k")

    raises(TypeError, lambda: catalan(n, k))
    raises(TypeError, lambda: euler(n, k))
Пример #9
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def test_catalan():
    n = Symbol('n', integer=True)
    m = Symbol('n', integer=True, positive=True)

    catalans = [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786]
    for i, c in enumerate(catalans):
        assert catalan(i) == c
        assert catalan(n).rewrite(factorial).subs(n, i) == c
        assert catalan(n).rewrite(Product).subs(n, i).doit() == c

    assert catalan(x) == catalan(x)
    assert catalan(2*x).rewrite(binomial) == binomial(4*x, 2*x)/(2*x + 1)
    assert catalan(Rational(1, 2)).rewrite(gamma) == 8/(3*pi)
    assert catalan(Rational(1, 2)).rewrite(factorial).rewrite(gamma) ==\
        8 / (3 * pi)
    assert catalan(3*x).rewrite(gamma) == 4**(
        3*x)*gamma(3*x + Rational(1, 2))/(sqrt(pi)*gamma(3*x + 2))
    assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2,), 1)

    assert catalan(n).rewrite(factorial) == factorial(2*n) / (factorial(n + 1)
                                                              * factorial(n))
    assert isinstance(catalan(n).rewrite(Product), catalan)
    assert isinstance(catalan(m).rewrite(Product), Product)

    assert diff(catalan(x), x) == (polygamma(
        0, x + Rational(1, 2)) - polygamma(0, x + 2) + log(4))*catalan(x)

    assert catalan(x).evalf() == catalan(x)
    c = catalan(S.Half).evalf()
    assert str(c) == '0.848826363156775'
    c = catalan(I).evalf(3)
    assert str((re(c), im(c))) == '(0.398, -0.0209)'
Пример #10
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def test_catalan():
    assert catalan(1) == 1
    assert catalan(2) == 2
    assert catalan(3) == 5
    assert catalan(4) == 14

    assert catalan(x) == catalan(x)
    assert catalan(2 *
                   x).rewrite(binomial) == binomial(4 * x, 2 * x) / (2 * x + 1)
    assert catalan(Rational(1, 2)).rewrite(gamma) == 8 / (3 * pi)
    assert catalan(3 * x).rewrite(gamma) == 4**(
        3 * x) * gamma(3 * x + Rational(1, 2)) / (sqrt(pi) * gamma(3 * x + 2))
    assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2, ), 1)

    assert diff(catalan(x), x) == (polygamma(0, x + Rational(1, 2)) -
                                   polygamma(0, x + 2) + log(4)) * catalan(x)

    c = catalan(0.5).evalf()
    assert str(c) == '0.848826363156775'