def _vintersect_sphcyl_ellip(rs, rc, b): """ The cases for which evaluating the volume of intersection of a sphere with a cylinder makes use of elliptic integrals. """ rs3 = rs ** 3 bprc = b + rc bmrc = b - rc A = max(rs ** 2, bprc ** 2) B = min(rs ** 2, bprc ** 2) C = bmrc ** 2 AB = A - B AC = A - C BC = B - C k2 = BC / AC s = bprc * bmrc e1 = ellipk(k2) e2 = ellipe(k2) if bmrc == 0: if rs == bprc: vi = - 4. / 3 * AC ** 0.5 * (s + 2. / 3 * AC) elif rs < bprc: vi = 4. / 3 / A ** 0.5 * (e1 * AB * (3 * B - 2 * A) + e2 * A * (2 * A - 4 * B)) / 3 else: vi = 4. / 3 / A ** 0.5 * (e1 * AB * A - e2 * A * (4 * A - 2 * B)) / 3 else: a2 = 1 - B / C e3 = elliptic_pi(a2, k2) if rs == bprc: vi = (4. / 3 * rs3 * np.arctan(2 * (b * rc) ** 0.5 / bmrc) - 4. / 3 * AC ** 0.5 * (s + 2. / 3 * AC)) elif rs < bprc: vi = (4. / 3 / AC ** 0.5 * (e3 * B ** 2 * s / C + e1 * (s * (A - 2. * B) + AB * (3 * B - C - 2 * A) / 3) + e2 * AC * (-s + (2 * A + 2 * C - 4 * B) / 3))) else: vi = 4. / 3 / AC ** 0.5 * (e3 * A ** 2 * s / C - e1 * (A * s - AB * AC / 3.) - e2 * AC * (s + (4. * A - 2 * B - 2 * C) / 3)) return vi
def _vintersect_sphcyl_ellip(rs, rc, b): """ The cases for which evaluating the volume of intersection of a sphere with a cylinder makes use of elliptic integrals. """ rs3 = rs**3 bprc = b + rc bmrc = b - rc A = max(rs**2, bprc**2) B = min(rs**2, bprc**2) C = bmrc**2 AB = A - B AC = A - C BC = B - C k2 = BC / AC s = bprc * bmrc e1 = ellipk(k2) e2 = ellipe(k2) if bmrc == 0: if rs == bprc: vi = -4. / 3 * AC**0.5 * (s + 2. / 3 * AC) elif rs < bprc: vi = 4. / 3 / A**0.5 * (e1 * AB * (3 * B - 2 * A) + e2 * A * (2 * A - 4 * B)) / 3 else: vi = 4. / 3 / A**0.5 * (e1 * AB * A - e2 * A * (4 * A - 2 * B)) / 3 else: a2 = 1 - B / C e3 = elliptic_pi(a2, k2) if rs == bprc: vi = (4. / 3 * rs3 * np.arctan(2 * (b * rc)**0.5 / bmrc) - 4. / 3 * AC**0.5 * (s + 2. / 3 * AC)) elif rs < bprc: vi = (4. / 3 / AC**0.5 * (e3 * B**2 * s / C + e1 * (s * (A - 2. * B) + AB * (3 * B - C - 2 * A) / 3) + e2 * AC * (-s + (2 * A + 2 * C - 4 * B) / 3))) else: vi = 4. / 3 / AC**0.5 * (e3 * A**2 * s / C - e1 * (A * s - AB * AC / 3.) - e2 * AC * (s + (4. * A - 2 * B - 2 * C) / 3)) return vi
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)" 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)**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 )}', latex(Chi(x)**2) 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)' # 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}'
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"\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)" 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)**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 )}" assert latex(totient(n)) == r'\phi\left( n \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)}" w = Wild('w') assert latex(gamma(w)) == r"\Gamma{\left(w \right)}" assert latex(Order(x)) == r"\mathcal{O}\left(x\right)" assert latex(Order(x, x)) == r"\mathcal{O}\left(x\right)" assert latex(Order(x, x, 0)) == r"\mathcal{O}\left(x\right)" assert latex(Order(x, x, oo)) == r"\mathcal{O}\left(x; x\rightarrow\infty\right)" assert latex( Order(x, x, y) ) == r"\mathcal{O}\left(x; \begin{pmatrix}x, & y\end{pmatrix}\rightarrow0\right)" assert latex( Order(x, x, y, 0) ) == r"\mathcal{O}\left(x; \begin{pmatrix}x, & y\end{pmatrix}\rightarrow0\right)" assert latex( Order(x, x, y, oo) ) == r"\mathcal{O}\left(x; \begin{pmatrix}x, & y\end{pmatrix}\rightarrow\infty\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)" 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)**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)' # 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}'