def acsch(self, value):
"""
Verilen değeri kullanarak, sumpy.acsch döndürür
:param value: değer
:return: sympy.acsch
"""
return sp.acsch(value_checker(value))
def test_trig_functions(self, printer, x):
# Trig functions
assert printer.doprint(sp.acos(x)) == 'acos(x)'
assert printer.doprint(sp.acosh(x)) == 'acosh(x)'
assert printer.doprint(sp.asin(x)) == 'asin(x)'
assert printer.doprint(sp.asinh(x)) == 'asinh(x)'
assert printer.doprint(sp.atan(x)) == 'atan(x)'
assert printer.doprint(sp.atanh(x)) == 'atanh(x)'
assert printer.doprint(sp.ceiling(x)) == 'ceil(x)'
assert printer.doprint(sp.cos(x)) == 'cos(x)'
assert printer.doprint(sp.cosh(x)) == 'cosh(x)'
assert printer.doprint(sp.exp(x)) == 'exp(x)'
assert printer.doprint(sp.factorial(x)) == 'factorial(x)'
assert printer.doprint(sp.floor(x)) == 'floor(x)'
assert printer.doprint(sp.log(x)) == 'log(x)'
assert printer.doprint(sp.sin(x)) == 'sin(x)'
assert printer.doprint(sp.sinh(x)) == 'sinh(x)'
assert printer.doprint(sp.tan(x)) == 'tan(x)'
assert printer.doprint(sp.tanh(x)) == 'tanh(x)'
# extra trig functions
assert printer.doprint(sp.sec(x)) == '1 / cos(x)'
assert printer.doprint(sp.csc(x)) == '1 / sin(x)'
assert printer.doprint(sp.cot(x)) == '1 / tan(x)'
assert printer.doprint(sp.asec(x)) == 'acos(1 / x)'
assert printer.doprint(sp.acsc(x)) == 'asin(1 / x)'
assert printer.doprint(sp.acot(x)) == 'atan(1 / x)'
assert printer.doprint(sp.sech(x)) == '1 / cosh(x)'
assert printer.doprint(sp.csch(x)) == '1 / sinh(x)'
assert printer.doprint(sp.coth(x)) == '1 / tanh(x)'
assert printer.doprint(sp.asech(x)) == 'acosh(1 / x)'
assert printer.doprint(sp.acsch(x)) == 'asinh(1 / x)'
assert printer.doprint(sp.acoth(x)) == 'atanh(1 / x)'
def test_inverses():
x = Symbol('x')
assert sinh(x).inverse() == asinh
raises(AttributeError, lambda: cosh(x).inverse())
assert tanh(x).inverse() == atanh
assert coth(x).inverse() == acoth
assert asinh(x).inverse() == sinh
assert acosh(x).inverse() == cosh
assert atanh(x).inverse() == tanh
assert acoth(x).inverse() == coth
assert asech(x).inverse() == sech
assert acsch(x).inverse() == csch
def test_inverses():
x = Symbol('x')
assert sinh(x).inverse() == asinh
raises(AttributeError, lambda: cosh(x).inverse())
assert tanh(x).inverse() == atanh
assert coth(x).inverse() == acoth
assert asinh(x).inverse() == sinh
assert acosh(x).inverse() == cosh
assert atanh(x).inverse() == tanh
assert acoth(x).inverse() == coth
assert asech(x).inverse() == sech
assert acsch(x).inverse() == csch
def test_derivs():
x = Symbol('x')
assert coth(x).diff(x) == -sinh(x)**(-2)
assert sinh(x).diff(x) == cosh(x)
assert cosh(x).diff(x) == sinh(x)
assert tanh(x).diff(x) == -tanh(x)**2 + 1
assert csch(x).diff(x) == -coth(x) * csch(x)
assert sech(x).diff(x) == -tanh(x) * sech(x)
assert acoth(x).diff(x) == 1 / (-x**2 + 1)
assert asinh(x).diff(x) == 1 / sqrt(x**2 + 1)
assert acosh(x).diff(x) == 1 / sqrt(x**2 - 1)
assert atanh(x).diff(x) == 1 / (-x**2 + 1)
assert asech(x).diff(x) == -1 / (x * sqrt(1 - x**2))
assert acsch(x).diff(x) == -1 / (x**2 * sqrt(1 + x**(-2)))
def test_derivs():
x = Symbol('x')
assert coth(x).diff(x) == -sinh(x)**(-2)
assert sinh(x).diff(x) == cosh(x)
assert cosh(x).diff(x) == sinh(x)
assert tanh(x).diff(x) == -tanh(x)**2 + 1
assert csch(x).diff(x) == -coth(x)*csch(x)
assert sech(x).diff(x) == -tanh(x)*sech(x)
assert acoth(x).diff(x) == 1/(-x**2 + 1)
assert asinh(x).diff(x) == 1/sqrt(x**2 + 1)
assert acosh(x).diff(x) == 1/sqrt(x**2 - 1)
assert atanh(x).diff(x) == 1/(-x**2 + 1)
assert asech(x).diff(x) == -1/(x*sqrt(1 - x**2))
assert acsch(x).diff(x) == -1/(x**2*sqrt(1 + x**(-2)))
def test_acsch_fdiff():
x = Symbol('x')
raises(ArgumentIndexError, lambda: acsch(x).fdiff(2))
def test_acsch_rewrite():
x = Symbol('x')
assert acsch(x).rewrite(log) == log(1 / x + sqrt(1 / x**2 + 1))
def test_acsch_infinities():
assert acsch(oo) == 0
assert acsch(-oo) == 0
assert acsch(zoo) == 0
def test_acsch():
x = Symbol('x')
assert unchanged(acsch, x)
assert acsch(-x) == -acsch(x)
# values at fixed points
assert acsch(1) == log(1 + sqrt(2))
assert acsch(-1) == -log(1 + sqrt(2))
assert acsch(0) == zoo
assert acsch(2) == log((1 + sqrt(5)) / 2)
assert acsch(-2) == -log((1 + sqrt(5)) / 2)
assert acsch(I) == -I * pi / 2
assert acsch(-I) == I * pi / 2
assert acsch(-I * (sqrt(6) + sqrt(2))) == I * pi / 12
assert acsch(I * (sqrt(2) + sqrt(6))) == -I * pi / 12
assert acsch(-I * (1 + sqrt(5))) == I * pi / 10
assert acsch(I * (1 + sqrt(5))) == -I * pi / 10
assert acsch(-I * 2 / sqrt(2 - sqrt(2))) == I * pi / 8
assert acsch(I * 2 / sqrt(2 - sqrt(2))) == -I * pi / 8
assert acsch(-I * 2) == I * pi / 6
assert acsch(I * 2) == -I * pi / 6
assert acsch(-I * sqrt(2 + 2 / sqrt(5))) == I * pi / 5
assert acsch(I * sqrt(2 + 2 / sqrt(5))) == -I * pi / 5
assert acsch(-I * sqrt(2)) == I * pi / 4
assert acsch(I * sqrt(2)) == -I * pi / 4
assert acsch(-I * (sqrt(5) - 1)) == 3 * I * pi / 10
assert acsch(I * (sqrt(5) - 1)) == -3 * I * pi / 10
assert acsch(-I * 2 / sqrt(3)) == I * pi / 3
assert acsch(I * 2 / sqrt(3)) == -I * pi / 3
assert acsch(-I * 2 / sqrt(2 + sqrt(2))) == 3 * I * pi / 8
assert acsch(I * 2 / sqrt(2 + sqrt(2))) == -3 * I * pi / 8
assert acsch(-I * sqrt(2 - 2 / sqrt(5))) == 2 * I * pi / 5
assert acsch(I * sqrt(2 - 2 / sqrt(5))) == -2 * I * pi / 5
assert acsch(-I * (sqrt(6) - sqrt(2))) == 5 * I * pi / 12
assert acsch(I * (sqrt(6) - sqrt(2))) == -5 * I * pi / 12
assert acsch(nan) == nan
# properties
# acsch(x) == asinh(1/x)
assert acsch(-I * sqrt(2)) == asinh(I / sqrt(2))
assert acsch(-I * 2 / sqrt(3)) == asinh(I * sqrt(3) / 2)
# acsch(x) == -I*asin(I/x)
assert acsch(-I * sqrt(2)) == -I * asin(-1 / sqrt(2))
assert acsch(-I * 2 / sqrt(3)) == -I * asin(-sqrt(3) / 2)
# csch(acsch(x)) / x == 1
assert expand_mul(
csch(acsch(-I * (sqrt(6) + sqrt(2)))) / (-I *
(sqrt(6) + sqrt(2)))) == 1
assert expand_mul(csch(acsch(I * (1 + sqrt(5)))) / ((I *
(1 + sqrt(5))))) == 1
assert (csch(acsch(I * sqrt(2 - 2 / sqrt(5)))) /
(I * sqrt(2 - 2 / sqrt(5)))).simplify() == 1
assert (csch(acsch(-I * sqrt(2 - 2 / sqrt(5)))) /
(-I * sqrt(2 - 2 / sqrt(5)))).simplify() == 1
# numerical evaluation
assert str(acsch(5 * I + 1).n(6)) == '0.0391819 - 0.193363*I'
assert str(acsch(-5 * I + 1).n(6)) == '0.0391819 + 0.193363*I'
def test_acsch_rewrite():
x = Symbol('x')
assert acsch(x).rewrite(log) == log(1/x + sqrt(1/x**2 + 1))
def test_acsch_infinities():
assert acsch(oo) == 0
assert acsch(-oo) == 0
assert acsch(zoo) == 0
def test_acsch():
x = Symbol('x')
assert acsch(-x) == acsch(-x)
assert acsch(x) == -acsch(-x)
# values at fixed points
assert acsch(1) == log(1 + sqrt(2))
assert acsch(-1) == - log(1 + sqrt(2))
assert acsch(0) == zoo
assert acsch(2) == log((1+sqrt(5))/2)
assert acsch(-2) == - log((1+sqrt(5))/2)
assert acsch(I) == - I*pi/2
assert acsch(-I) == I*pi/2
assert acsch(-I*(sqrt(6) + sqrt(2))) == I*pi / 12
assert acsch(I*(sqrt(2) + sqrt(6))) == -I*pi / 12
assert acsch(-I*(1 + sqrt(5))) == I*pi / 10
assert acsch(I*(1 + sqrt(5))) == -I*pi / 10
assert acsch(-I*2 / sqrt(2 - sqrt(2))) == I*pi / 8
assert acsch(I*2 / sqrt(2 - sqrt(2))) == -I*pi / 8
assert acsch(-I*2) == I*pi / 6
assert acsch(I*2) == -I*pi / 6
assert acsch(-I*sqrt(2 + 2/sqrt(5))) == I*pi / 5
assert acsch(I*sqrt(2 + 2/sqrt(5))) == -I*pi / 5
assert acsch(-I*sqrt(2)) == I*pi / 4
assert acsch(I*sqrt(2)) == -I*pi / 4
assert acsch(-I*(sqrt(5)-1)) == 3*I*pi / 10
assert acsch(I*(sqrt(5)-1)) == -3*I*pi / 10
assert acsch(-I*2 / sqrt(3)) == I*pi / 3
assert acsch(I*2 / sqrt(3)) == -I*pi / 3
assert acsch(-I*2 / sqrt(2 + sqrt(2))) == 3*I*pi / 8
assert acsch(I*2 / sqrt(2 + sqrt(2))) == -3*I*pi / 8
assert acsch(-I*sqrt(2 - 2/sqrt(5))) == 2*I*pi / 5
assert acsch(I*sqrt(2 - 2/sqrt(5))) == -2*I*pi / 5
assert acsch(-I*(sqrt(6) - sqrt(2))) == 5*I*pi / 12
assert acsch(I*(sqrt(6) - sqrt(2))) == -5*I*pi / 12
# properties
# acsch(x) == asinh(1/x)
assert acsch(-I*sqrt(2)) == asinh(I/sqrt(2))
assert acsch(-I*2 / sqrt(3)) == asinh(I*sqrt(3) / 2)
# acsch(x) == -I*asin(I/x)
assert acsch(-I*sqrt(2)) == -I*asin(-1/sqrt(2))
assert acsch(-I*2 / sqrt(3)) == -I*asin(-sqrt(3)/2)
# csch(acsch(x)) / x == 1
assert expand_mul(csch(acsch(-I*(sqrt(6) + sqrt(2)))) / (-I*(sqrt(6) + sqrt(2)))) == 1
assert expand_mul(csch(acsch(I*(1 + sqrt(5)))) / ((I*(1 + sqrt(5))))) == 1
assert (csch(acsch(I*sqrt(2 - 2/sqrt(5)))) / (I*sqrt(2 - 2/sqrt(5)))).simplify() == 1
assert (csch(acsch(-I*sqrt(2 - 2/sqrt(5)))) / (-I*sqrt(2 - 2/sqrt(5)))).simplify() == 1
# numerical evaluation
assert str(acsch(5*I+1).n(6)) == '0.0391819 - 0.193363*I'
assert str(acsch(-5*I+1).n(6)) == '0.0391819 + 0.193363*I'
sp.tan(num) # tangente
sp.cot(num) # cotangente
sp.sec(num) # secante
sp.csc(num) # cosecante
sp.asin(num) # Arcoseno
sp.acos(num) # Arcocoseno
sp.atan(num) # Arcotangente
sp.atan2(catetoY,
catetoX) # Arcotangente de un triangulo segun los catetos (Angulo)
sp.acot(num) # Arcocotangente
sp.asec(num) # Arcosecante
sp.acsc(num) # Arcocosecante
# Funciones hiperbólicas (Angulos en radianes)
sp.sinh(num) # Seno
sp.cosh(num) # Coseno
sp.tanh(num) # tangente
sp.coth(num) # cotangente
sp.sech(num) # secante
sp.csch(num) # cosecante
sp.asinh(num) # Arcoseno
sp.acosh(num) # Arcocoseno
sp.atanh(num) # Arcotangente
sp.acoth(num) # Arcocotangente
sp.asech(num) # Arcosecante
sp.acsch(num) # Arcocosecante
# Combinatoria
sp.factorial(num) # Factorial
sp.functions.combinatorial.numbers.nP(num1, num2) # Permutación
sp.functions.combinatorial.numbers.nC(num1, num2) # Combinación
