Python sympy.dirichlet_eta函数代码示例

def test_dirichlet_eta():

    assert dirichlet_eta(0) == Rational(1,2)
    assert dirichlet_eta(-1) == Rational(1,4)
    assert dirichlet_eta(1) == log(2)
    assert dirichlet_eta(2) == pi**2/12
    assert dirichlet_eta(4) == pi**4*Rational(7,720)

def test_rewriting():
    assert dirichlet_eta(x).rewrite(zeta) == (1 - 2 ** (1 - x)) * zeta(x)
    assert zeta(x).rewrite(dirichlet_eta) == dirichlet_eta(x) / (1 - 2 ** (1 - x))
    assert tn(dirichlet_eta(x), dirichlet_eta(x).rewrite(zeta), x)
    assert tn(zeta(x), zeta(x).rewrite(dirichlet_eta), x)

    assert zeta(x, a).rewrite(lerchphi) == lerchphi(1, x, a)
    assert polylog(s, z).rewrite(lerchphi) == lerchphi(z, s, 1) * z

    assert lerchphi(1, x, a).rewrite(zeta) == zeta(x, a)
    assert z * lerchphi(z, s, 1).rewrite(polylog) == polylog(s, z)

def test_polylog_expansion():
    from sympy import factor, log
    assert polylog(s, 0) == 0
    assert polylog(s, 1) == zeta(s)
    assert polylog(s, -1) == dirichlet_eta(s)

    assert myexpand(polylog(1, z), -log(1 + exp_polar(-I*pi)*z))
    assert myexpand(polylog(0, z), z/(1 - z))
    assert myexpand(polylog(-1, z), z**2/(1 - z)**2 + z/(1 - z))
    assert myexpand(polylog(-5, z), None)

def test_polylog_expansion():
    from sympy import log
    assert polylog(s, 0) == 0
    assert polylog(s, 1) == zeta(s)
    assert polylog(s, -1) == -dirichlet_eta(s)
    assert polylog(s, exp_polar(4*I*pi/3)) == polylog(s, exp(4*I*pi/3))
    assert polylog(s, exp_polar(I*pi)/3) == polylog(s, exp(I*pi)/3)

    assert myexpand(polylog(1, z), -log(1 - z))
    assert myexpand(polylog(0, z), z/(1 - z))
    assert myexpand(polylog(-1, z), z/(1 - z)**2)
    assert ((1-z)**3 * expand_func(polylog(-2, z))).simplify() == z*(1 + z)
    assert myexpand(polylog(-5, z), None)

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

    f = Function("f")
    assert latex(f(x)) == "\\operatorname{f}{\\left (x \\right )}"

    beta = Function("beta")

    assert latex(beta(x)) == r"\beta{\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(factorial(k)) == r"k!"
    assert latex(factorial(-k)) == r"\left(- k\right)!"

    assert latex(subfactorial(k)) == r"!k"
    assert latex(subfactorial(-k)) == r"!\left(- k\right)"

    assert latex(factorial2(k)) == r"k!!"
    assert latex(factorial2(-k)) == r"\left(- k\right)!!"

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

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

    assert latex(floor(x)) == r"\lfloor{x}\rfloor"
    assert latex(ceiling(x)) == r"\lceil{x}\rceil"
    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"\lvert{x}\rvert"
    assert latex(re(x)) == r"\Re{x}"
    assert latex(re(x + y)) == r"\Re{x} + \Re{y}"
    assert latex(im(x)) == r"\Im{x}"
    assert latex(conjugate(x)) == r"\overline{x}"
    assert latex(gamma(x)) == r"\Gamma\left(x\right)"
    assert latex(Order(x)) == r"\mathcal{O}\left(x\right)"
    assert latex(lowergamma(x, y)) == r"\gamma\left(x, y\right)"
    assert latex(uppergamma(x, y)) == r"\Gamma\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"\Re{x}"
    assert latex(im(x)) == r"\Im{x}"
    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)) == 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(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) ** 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(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}"

    # 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 )}"

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

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

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

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

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

    beta = Function('beta')

    # not to be confused with the beta function
    assert latex(beta(x)) == r"\beta{\left (x \right )}"
    assert latex(beta) == r"\beta"

    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(factorial(k)) == r"k!"
    assert latex(factorial(-k)) == r"\left(- k\right)!"

    assert latex(subfactorial(k)) == r"!k"
    assert latex(subfactorial(-k)) == r"!\left(- k\right)"

    assert latex(factorial2(k)) == r"k!!"
    assert latex(factorial2(-k)) == r"\left(- k\right)!!"

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

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

    assert latex(floor(x)) == r"\lfloor{x}\rfloor"
    assert latex(ceiling(x)) == r"\lceil{x}\rceil"
    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\lvert{x}\right\rvert"
    assert latex(re(x)) == r"\Re{x}"
    assert latex(re(x + y)) == r"\Re{x} + \Re{y}"
    assert latex(im(x)) == r"\Im{x}"
    assert latex(conjugate(x)) == r"\overline{x}"
    assert latex(gamma(x)) == r"\Gamma\left(x\right)"
    assert latex(Order(x)) == r"\mathcal{O}\left(x\right)"
    assert latex(lowergamma(x, y)) == r'\gamma\left(x, y\right)'
    assert latex(uppergamma(x, y)) == r'\Gamma\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'\Re{x}'
    assert latex(im(x)) == r'\Im{x}'
    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)) == 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(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)"
#.........这里部分代码省略.........

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

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

    beta = Function('beta')

    assert latex(beta(x)) == r"\beta{\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(factorial(k)) == r"k!"
    assert latex(factorial(-k)) == r"\left(- k\right)!"

    assert latex(factorial2(k)) == r"k!!"
    assert latex(factorial2(-k)) == r"\left(- k\right)!!"

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

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

    assert latex(floor(x)) == r"\lfloor{x}\rfloor"
    assert latex(ceiling(x)) == r"\lceil{x}\rceil"
    assert latex(Abs(x)) == r"\lvert{x}\rvert"
    assert latex(re(x)) == r"\Re{x}"
    assert latex(re(x+y)) == r"\Re {\left (x + y \right )}"
    assert latex(im(x)) == r"\Im{x}"
    assert latex(conjugate(x)) == r"\overline{x}"
    assert latex(gamma(x)) == r"\Gamma\left(x\right)"
    assert latex(Order(x)) == r"\mathcal{O}\left(x\right)"
    assert latex(lowergamma(x, y)) == r'\gamma\left(x, y\right)'
    assert latex(uppergamma(x, y)) == r'\Gamma\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'\Re{x}'
    assert latex(im(x)) == r'\Im{x}'
    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)) == 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(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)**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 )}'