#On the name of ALLAH and may the blessing and peace of Allah
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Author : Fouad Teniou
#Date : 06/07/10
#version :2.6
"""
maclaurin_binomial is a function to compute(1+x)^m using maclaurin
binomial series and the interval of convergence is -1 < x < 1
(1+x)^m = 1 + mx + m(m-1)x^2/2! + m(m-1)(m-2)x^3/3!...........
note: if m is a nonegative integer the binomial is a polynomial of
degree m and it is valid on -inf < x < +inf,thus, the error function
will not be valid.
"""
from math import *
def error(number):
""" Raises interval of convergence error."""
if number >= 1 or number <= -1 :
raise TypeError,\
"\n<The interval of convergence should be -1 < value < 1 \n"
def maclaurin_binomial(value,m,k):
"""
Compute maclaurin's binomial series approximation for (1+x)^m.
"""
global first_value
first_value = 0.0
error(value)
#attempt to Approximate (1+x)^m for given values
try:
for item in xrange(1,k):
next_value =m*(value**item)/factorial(item)
for i in range(2,item+1):
next_second_value =(m-i+1)
next_value *= next_second_value
first_value += next_value
return first_value + 1
#Raise TypeError if input is not within
#the interval of convergence
except TypeError,exception:
print exception
#Raise OverflowError if an over flow occur
except OverflowError:
print '\n<Please enter a lower k value to avoid the Over flow\n '
if __name__ == "__main__":
maclaurin_binomial_1 = maclaurin_binomial(0.777,-0.5,171)
print maclaurin_binomial_1
maclaurin_binomial_2 = maclaurin_binomial(0.37,0.5,171)
print maclaurin_binomial_2
maclaurin_binomial_3 = maclaurin_binomial(0.3,0.717,171)
print maclaurin_binomial_3
########################################################################
#c:python
#
#0.750164116353
#1.17046999107
#1.20697252357
#######################################################################
#Version : Python 3.2
#import math
#def maclaurin_binomial(value,m,k):
# """
# Compute maclaurin's binomial series approximation for (1+x)^m.
# """
# global first_value
# first_value = 0.0
#
# #attempt to Approximate (1+x)^m for given values
# try:
#
# for item in range(1,k):
# next_value =m*(value**item)/math.factorial(item)
#
# for i in range(2,item+1):
# next_second_value =(m-i+1)
# next_value *= next_second_value
# first_value += next_value
# return first_value + 1
#
# #Raise TypeError if input is not within
# #the interval of convergence
# except TypeError as exception:
# print (exception)
#
# #Raise OverflowError if an over flow occur
# except OverflowError:
# print ('\n<Please enter a lower k value to avoid the Over flow\n ')
#
#
#if __name__ == "__main__":
# maclaurin_binomial_1 = maclaurin_binomial(0.777,-0.5,171)
# print (maclaurin_binomial_1 )
# maclaurin_binomial_2 = maclaurin_binomial(0.37,0.5,171)
# print (maclaurin_binomial_2)
# maclaurin_binomial_3 = maclaurin_binomial(0.3,0.717,171)
# print (maclaurin_binomial_3)
######################################################################################
#decimal Version Python 3.2
#from math import *
#from decimal import Decimal as D,Context, localcontext
#def error(number):
# """ Raises interval of convergence error."""
# if number >= 1 or number <= -1 :
# raise TypeError("\n<The interval of convergence should be -1 < value < 1 \n")
#def maclaurin_binomial(value,m,k):
# """
# Compute maclaurin's binomial series approximation for (1+x)^m.
# """
# global first_value
# first_value = 0
#
# #attempt to Approximate (1+x)^m for given values
# try:
#
# for item in range(1,k):
# next_value = (m*(value**item))/factorial(item)
# for i in range(2,item+1):
# next_second_value =(m-i+1)
# next_value *= next_second_value
# first_value += next_value
#
# return (first_value) + (1)
#
# #Raise TypeError if input is not within
# #the interval of convergence
# except TypeError as exception:
# print(exception)
#
# #Raise OverflowError if an over flow occur
# except OverflowError:
# print('\n<Please enter a lower k value to avoid the Over flow\n ')
#
#
#if __name__ == "__main__":
#
# with localcontext(Context(prec= 1777)):
# for arg in range(2,-8,-2):
# print(maclaurin_binomial(D("0.777"),arg,171))
Diff to Previous Revision
--- revision 4 2011-02-02 13:04:25
+++ revision 5 2011-02-03 12:31:50
@@ -112,3 +112,52 @@
# print (maclaurin_binomial_2)
# maclaurin_binomial_3 = maclaurin_binomial(0.3,0.717,171)
# print (maclaurin_binomial_3)
+######################################################################################
+
+#decimal Version Python 3.2
+
+#from math import *
+#from decimal import Decimal as D,Context, localcontext
+#def error(number):
+# """ Raises interval of convergence error."""
+
+# if number >= 1 or number <= -1 :
+# raise TypeError("\n<The interval of convergence should be -1 < value < 1 \n")
+
+
+
+#def maclaurin_binomial(value,m,k):
+# """
+# Compute maclaurin's binomial series approximation for (1+x)^m.
+# """
+# global first_value
+# first_value = 0
+#
+# #attempt to Approximate (1+x)^m for given values
+# try:
+#
+# for item in range(1,k):
+# next_value = (m*(value**item))/factorial(item)
+
+# for i in range(2,item+1):
+# next_second_value =(m-i+1)
+# next_value *= next_second_value
+# first_value += next_value
+#
+# return (first_value) + (1)
+#
+# #Raise TypeError if input is not within
+# #the interval of convergence
+# except TypeError as exception:
+# print(exception)
+#
+# #Raise OverflowError if an over flow occur
+# except OverflowError:
+# print('\n<Please enter a lower k value to avoid the Over flow\n ')
+#
+#
+#if __name__ == "__main__":
+#
+# with localcontext(Context(prec= 1777)):
+# for arg in range(2,-8,-2):
+# print(maclaurin_binomial(D("0.777"),arg,171))
