def isqrt(c):
if not isinstance(c,pol): return 1/math.sqrt(c)
a0,p=c.separate(); p/=a0
lst=[1/math.sqrt(a0)]
for n in range(1,c.order+1):
lst.append(-lst[-1]/a0/2/n*(2*n-1))
return phorner(lst,p)
def sinh(c):
"""Compute Sinh using a Taylor expansion
"""
if not isinstance(c,pol): return math.sinh(c)
a0,p=c.separate();
lst=[math.sinh(a0),math.cosh(a0)]
for n in range(2,c.order+1):
lst.append( lst[-2]/n/(n-1))
return phorner(lst,p)
def cos(c):
"""
cos(a+x)= cos(a) sin(x) - sin(a) cos(x)
"""
if not isinstance(c,pol): return math.cos(c)
a0,p=c.separate();
lst=[math.cos(a0),-math.sin(a0)]
for n in range(2,c.order+1):
lst.append( -lst[-2]/n/(n-1))
return phorner(lst,p)
def log(c):
"""Logarithm of a polynomial
log(a+x)=log(a)-log(1+x/a)
>>> from pol import *
>>> print log(exp(pol('1+x')))
1.0 + x
"""
if not isinstance(c,pol): return math.log(c)
a0,p=c.separate(); p/=a0
lst=[log(a0),1.]
for n in range(2,c.order+1):
lst.append( -lst[-1]/n*(n-1) )
return phorner(lst,p)
def exp(c):
"""Exponential of a polynomial
exp(a+x) = exp(a)exp(x)
>>> from pol import *
>>> print log(exp(pol('1+x')))
1.0 + x
"""
if not isinstance(c,pol): return math.exp(c)
a0,p=c.separate();
lst=[exp(a0)]
for n in range(1,c.order+1):
lst.append(lst[-1]/n)
return phorner(lst,p)
def sqrt(c):
"""Square root of a polynomial
>>> from pol import *
>>> print sqrt(pol('1+x'))**2
1.0 + x
>>> print sqrt(pol('1j+x'))**2
1j -1j*x
"""
if not isinstance(c,pol): return math.sqrt(c)
a0,p=c.separate(); p/=a0
lst=[math.sqrt(a0)]
for n in range(1,c.order+1):
lst.append(-lst[-1]/2/n*(2*n-3))
return phorner(lst,p)