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 sstr((re(c), im(c))) == '(0.398, -0.0209)'
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(Rational(1, 2)).evalf()
assert str(c) == '0.848826363156775'
c = catalan(I).evalf(3)
assert sstr((re(c), im(c))) == '(0.398, -0.0209)'
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(sign(x)) == "Sign[x]"
assert mcode(atanh(x), user_functions={"atanh": "ArcTanh"}) == "ArcTanh[x]"
assert (mcode(meijerg(((1, 1), (3, 4)), ((1,), ()), x)) ==
"MeijerG[{{1, 1}, {3, 4}}, {{1}, {}}, x]")
assert (mcode(hyper((1, 2, 3), (3, 4), x)) ==
"HypergeometricPFQ[{1, 2, 3}, {3, 4}, x]")
assert mcode(Min(x, y)) == "Min[x, y]"
assert mcode(Max(x, y)) == "Max[x, y]"
assert mcode(Max(x, 2)) == "Max[2, x]" # issue sympy/sympy#15344
assert mcode(binomial(x, y)) == "Binomial[x, y]"
assert mcode(log(x)) == "Log[x]"
assert mcode(tan(x)) == "Tan[x]"
assert mcode(cot(x)) == "Cot[x]"
assert mcode(asin(x)) == "ArcSin[x]"
assert mcode(acos(x)) == "ArcCos[x]"
assert mcode(atan(x)) == "ArcTan[x]"
assert mcode(acot(x)) == "ArcCot[x]"
assert mcode(sinh(x)) == "Sinh[x]"
assert mcode(cosh(x)) == "Cosh[x]"
assert mcode(tanh(x)) == "Tanh[x]"
assert mcode(coth(x)) == "Coth[x]"
assert mcode(asinh(x)) == "ArcSinh[x]"
assert mcode(acosh(x)) == "ArcCosh[x]"
assert mcode(atanh(x)) == "ArcTanh[x]"
assert mcode(acoth(x)) == "ArcCoth[x]"
assert mcode(sech(x)) == "Sech[x]"
assert mcode(csch(x)) == "Csch[x]"
assert mcode(erfc(x)) == "Erfc[x]"
assert mcode(conjugate(x)) == "Conjugate[x]"
assert mcode(re(x)) == "Re[x]"
assert mcode(im(x)) == "Im[x]"
assert mcode(polygamma(x, y)) == "PolyGamma[x, y]"
assert mcode(factorial(x)) == "Factorial[x]"
assert mcode(factorial2(x)) == "Factorial2[x]"
assert mcode(rf(x, y)) == "Pochhammer[x, y]"
assert mcode(gamma(x)) == "Gamma[x]"
assert mcode(zeta(x)) == "Zeta[x]"
assert mcode(Heaviside(x)) == "UnitStep[x]"
assert mcode(fibonacci(x)) == "Fibonacci[x]"
assert mcode(polylog(x, y)) == "PolyLog[x, y]"
class myfunc1(Function):
@classmethod
def eval(cls, x):
pass
class myfunc2(Function):
@classmethod
def eval(cls, x, y):
pass
pytest.raises(ValueError,
lambda: mcode(myfunc1(x),
user_functions={"myfunc1": ["Myfunc1"]}))
assert mcode(myfunc1(x),
user_functions={"myfunc1": "Myfunc1"}) == "Myfunc1[x]"
assert mcode(myfunc2(x, y),
user_functions={"myfunc2": [(lambda *x: False,
"Myfunc2")]}) == "myfunc2[x, y]"
def test_ccode_exceptions():
assert ccode(ceiling(x)) == "ceil(x)"
assert ccode(Abs(x)) == "fabs(x)"
assert ccode(gamma(x)) == "tgamma(x)"
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(sign(x)) == "Sign[x]"
assert mcode(atanh(x), user_functions={"atanh": "ArcTanh"}) == "ArcTanh[x]"
assert (mcode(meijerg(((1, 1), (3, 4)), ((1,), ()), x)) ==
"MeijerG[{{1, 1}, {3, 4}}, {{1}, {}}, x]")
assert (mcode(hyper((1, 2, 3), (3, 4), x)) ==
"HypergeometricPFQ[{1, 2, 3}, {3, 4}, x]")
assert mcode(Min(x, y)) == "Min[x, y]"
assert mcode(Max(x, y)) == "Max[x, y]"
assert mcode(Max(x, 2)) == "Max[2, x]" # issue sympy/sympy#15344
assert mcode(binomial(x, y)) == "Binomial[x, y]"
assert mcode(log(x)) == "Log[x]"
assert mcode(tan(x)) == "Tan[x]"
assert mcode(cot(x)) == "Cot[x]"
assert mcode(asin(x)) == "ArcSin[x]"
assert mcode(acos(x)) == "ArcCos[x]"
assert mcode(atan(x)) == "ArcTan[x]"
assert mcode(sinh(x)) == "Sinh[x]"
assert mcode(cosh(x)) == "Cosh[x]"
assert mcode(tanh(x)) == "Tanh[x]"
assert mcode(coth(x)) == "Coth[x]"
assert mcode(sech(x)) == "Sech[x]"
assert mcode(csch(x)) == "Csch[x]"
assert mcode(erfc(x)) == "Erfc[x]"
assert mcode(conjugate(x)) == "Conjugate[x]"
assert mcode(re(x)) == "Re[x]"
assert mcode(im(x)) == "Im[x]"
assert mcode(polygamma(x, y)) == "PolyGamma[x, y]"
assert mcode(factorial(x)) == "Factorial[x]"
assert mcode(factorial2(x)) == "Factorial2[x]"
assert mcode(rf(x, y)) == "Pochhammer[x, y]"
assert mcode(gamma(x)) == "Gamma[x]"
assert mcode(zeta(x)) == "Zeta[x]"
assert mcode(asinh(x)) == "ArcSinh[x]"
assert mcode(Heaviside(x)) == "UnitStep[x]"
assert mcode(fibonacci(x)) == "Fibonacci[x]"
assert mcode(polylog(x, y)) == "PolyLog[x, y]"
assert mcode(atanh(x)) == "ArcTanh[x]"
class myfunc1(Function):
@classmethod
def eval(cls, x):
pass
class myfunc2(Function):
@classmethod
def eval(cls, x, y):
pass
pytest.raises(ValueError,
lambda: mcode(myfunc1(x),
user_functions={"myfunc1": ["Myfunc1"]}))
assert mcode(myfunc1(x),
user_functions={"myfunc1": "Myfunc1"}) == "Myfunc1[x]"
assert mcode(myfunc2(x, y),
user_functions={"myfunc2": [(lambda *x: False,
"Myfunc2")]}) == "myfunc2[x, y]"
def test_ccode_exceptions():
assert ccode(ceiling(x)) == "ceil(x)"
assert ccode(Abs(x)) == "fabs(x)"
assert ccode(gamma(x)) == "tgamma(x)"