I am stuck with division of polynomials in python. Here is code that I modified. The while loop couldnt work. This code only output the original L as r. If I remove the while loop, only the remainder from first time division was outputted. I tried a bunch of ways to make it work, but all failed. Any suggestions will be greatly appreciated. Thanks!
def GetDegree(poly):
while poly and poly[-1] == 0:
poly.pop() # normalize
return len(poly)-1
def division(p1,p2):
d1 = GetDegree(p1)
d2 = GetDegree(p2)
if d2 < 0 or d1<0:
raise ZeroDivisionError
if d1 > d2:
S,L = p2,p1#obtain S with lower degree, L with higher degree
else:
S,L = p1,p2
d1 = GetDegree(L)
d2 = GetDegree(S)
while d1>0:
q = [0]*d1
d = [0]*(d1 - d2) + S#shift short towards right by d1-d2
mult = q[d1 - d2] = L[-1] / float(d[-1])#get the result by dividing the first term of the dividend by the highest term of the divisor
d = [coef*mult for coef in d]#multiply the above result by short
L = [fabs( coefL - coefd ) for coefL, coefd in zip(L, d)]#return a new long by subtracting long with d
d1 = GetDegree(L)#return new d1
r = L#return new long and keeping looping for there is no variable left and return as remainder
return r
I want to input any random polynomials for the computation. However, when I modified it, the results still not right. Here is the test that I ran: num:[2,1,1,1] den:[1,1,2]. Print result was: quote:[0.25,0.5], rem:[1.75,0.25]. Here is the code that I modified for the case of input, based on the answer from PM 2Ring:
def normalize(poly):
while poly and poly[-1] == 0:
poly.pop()
if poly == []:
poly.append(0)
def poly_divmod(num, den):
#Create normalized copies of the args
num = num[:]
normalize(num)
den = den[:]
normalize(den)
if len(num) >= len(den):
#Shift den towards right so it's the same degree as num
shiftlen = len(num) - len(den)
den = [0] * shiftlen + den
else:
return [0], num
quot = []
divisor = float(den[-1])
for i in range(shiftlen + 1):
#Get the next coefficient of the quotient.
mult = num[-1] / divisor
quot = [mult] + quot
#Subtract mult * den from num, but don't bother if mult == 0
#Note that when i==0, mult!=0; so quot is automatically normalized.
if mult != 0:
d = [mult * u for u in den]
num = [u - v for u, v in zip(num, d)]
num.pop()
den.pop(0)
normalize(num)
return quot, num
def test(num, den):
print ("%s / %s ->" % (num, den))
q, r = poly_divmod(num, den)
print ("quot: %s, rem: %s\n" % (q, r))
return q, r
def main():
degree = int(input('Enter the degree of your polynomial 1:'))
num = []
for i in range (0,degree+1):
coefficient = int(input('Enter the coefficient for x^ %i ? ' %i))
num.append(coefficient)
degree = int(input('Enter the degree of your polynomial 2:'))
den = []
for i in range (0,degree+1):
coefficient = int(input('Enter the coefficient for x^ %i ? ' %i))
den.append(coefficient)
test(num, den)
if __name__ == '__main__':
main()
I've modified your code slightly, so now it returns the quotient and remainder.
FWIW, it would be fairly easy to create a polynomial class, and then you could do polynomial arithmetic using standard operators and functions...
#! /usr/bin/env python
''' Polynomial long division
From http://stackoverflow.com/questions/26173058/division-of-polynomials-in-python
A polynomial is represented by a list of its coefficients, eg
5*x**3 + 4*x**2 + 1 -> [1, 0, 4, 5]
Modified by PM 2Ring 2014.10.03
'''
def normalize(poly):
while poly and poly[-1] == 0:
poly.pop()
if poly == []:
poly.append(0)
def poly_divmod(num, den):
#Create normalized copies of the args
num = num[:]
normalize(num)
den = den[:]
normalize(den)
if len(num) >= len(den):
#Shift den towards right so it's the same degree as num
shiftlen = len(num) - len(den)
den = [0] * shiftlen + den
else:
return [0], num
quot = []
divisor = float(den[-1])
for i in xrange(shiftlen + 1):
#Get the next coefficient of the quotient.
mult = num[-1] / divisor
quot = [mult] + quot
#Subtract mult * den from num, but don't bother if mult == 0
#Note that when i==0, mult!=0; so quot is automatically normalized.
if mult != 0:
d = [mult * u for u in den]
num = [u - v for u, v in zip(num, d)]
num.pop()
den.pop(0)
normalize(num)
return quot, num
def test(num, den):
print "%s / %s ->" % (num, den)
q, r = poly_divmod(num, den)
print "quot: %s, rem: %s\n" % (q, r)
return q, r
def main():
num = [1, 5, 10, 10, 5, 1]
den = [1, 2, 1]
test(num, den)
num = [5, 16, 10, 22, 7, 11, 1, 3]
den = [1, 2, 1, 3]
quot = [5, 1, 3, 0, 1]
rem = [0, 5]
q, r = test(num, den)
assert quot == q
assert rem == r
if __name__ == '__main__':
main()