def _eval_expand_trig(self, **hints):
arg = self.args[0]
if arg.is_Add:
from sympy import symmetric_poly
n = len(arg.args)
TX = [
tanh(x, evaluate=False)._eval_expand_trig() for x in arg.args
]
p = [0, 0] # [den, num]
for i in range(n + 1):
p[i % 2] += symmetric_poly(i, TX)
return p[1] / p[0]
elif arg.is_Mul:
from sympy.functions.combinatorial.numbers import nC
coeff, terms = arg.as_coeff_Mul()
if coeff.is_Integer and coeff > 1:
n = []
d = []
T = tanh(terms)
for k in range(1, coeff + 1, 2):
n.append(nC(range(coeff), k) * T**k)
for k in range(0, coeff + 1, 2):
d.append(nC(range(coeff), k) * T**k)
return Add(*n) / Add(*d)
return tanh(arg)
def _eval_expand_trig(self, **hints):
arg = self.args[0]
x = None
if arg.is_Add:
from sympy import symmetric_poly
n = len(arg.args)
TX = []
for x in arg.args:
tx = tan(x, evaluate=False)._eval_expand_trig()
TX.append(tx)
Yg = numbered_symbols('Y')
Y = [ Yg.next() for i in xrange(n) ]
p = [0,0]
for i in xrange(n+1):
p[1-i%2] += symmetric_poly(i,Y)*(-1)**((i%4)//2)
return (p[0]/p[1]).subs(zip(Y,TX))
else:
coeff, terms = arg.as_coeff_Mul(rational=True)
if coeff.is_Integer and coeff > 1:
I = S.ImaginaryUnit
z = C.Symbol('dummy',real=True)
P = ((1+I*z)**coeff).expand()
return (C.im(P)/C.re(P)).subs([(z,tan(terms))])
return tan(arg)
def _eval_expand_trig(self, **hints):
arg = self.args[0]
x = None
if arg.is_Add:
from sympy import symmetric_poly
n = len(arg.args)
TX = []
for x in arg.args:
tx = tan(x, evaluate=False)._eval_expand_trig()
TX.append(tx)
Yg = numbered_symbols('Y')
Y = [Yg.next() for i in xrange(n)]
p = [0, 0]
for i in xrange(n + 1):
p[1 - i % 2] += symmetric_poly(i, Y) * (-1)**((i % 4) // 2)
return (p[0] / p[1]).subs(zip(Y, TX))
else:
coeff, terms = arg.as_coeff_Mul(rational=True)
if coeff.is_Integer and coeff > 1:
I = S.ImaginaryUnit
z = C.Symbol('dummy', real=True)
P = ((1 + I * z)**coeff).expand()
return (C.im(P) / C.re(P)).subs([(z, tan(terms))])
return tan(arg)
def _eval_expand_trig(self, **hints):
arg = self.args[0]
x = None
if arg.is_Add:
from sympy import symmetric_poly
n = len(arg.args)
CX = []
for x in arg.args:
cx = cot(x, evaluate=False)._eval_expand_trig()
CX.append(cx)
Yg = numbered_symbols("Y")
Y = [Yg.next() for i in xrange(n)]
p = [0, 0]
for i in xrange(n, -1, -1):
p[(n - i) % 2] += symmetric_poly(i, Y) * (-1) ** (((n - i) % 4) // 2)
return (p[0] / p[1]).subs(zip(Y, CX))
else:
coeff, terms = arg.as_coeff_Mul(rational=True)
if coeff.is_Integer and coeff > 1:
I = S.ImaginaryUnit
z = C.Symbol("dummy", real=True)
P = ((z + I) ** coeff).expand()
return (C.re(P) / C.im(P)).subs([(z, cot(terms))])
return cot(arg)