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# module 'poly' -- Polynomials
# A polynomial is represented by a list of coefficients, e.g.,
# [1, 10, 5] represents 1*x**0 + 10*x**1 + 5*x**2 (or 1 + 10x + 5x**2).
# There is no way to suppress internal zeros; trailing zeros are
# taken out by normalize().
def normalize(p): # Strip unnecessary zero coefficients
n = len(p)
while n:
if p[n-1]: return p[:n]
n = n-1
return []
def plus(a, b):
if len(a) < len(b): a, b = b, a # make sure a is the longest
res = a[:] # make a copy
for i in range(len(b)):
res[i] = res[i] + b[i]
return normalize(res)
def minus(a, b):
neg_b = map(lambda x: -x, b[:])
return plus(a, neg_b)
def one(power, coeff): # Representation of coeff * x**power
res = []
for i in range(power): res.append(0)
return res + [coeff]
def times(a, b):
res = []
for i in range(len(a)):
for j in range(len(b)):
res = plus(res, one(i+j, a[i]*b[j]))
return res
def power(a, n): # Raise polynomial a to the positive integral power n
if n == 0: return [1]
if n == 1: return a
if n/2*2 == n:
b = power(a, n/2)
return times(b, b)
return times(power(a, n-1), a)
def der(a): # First derivative
res = a[1:]
for i in range(len(res)):
res[i] = res[i] * (i+1)
return res
# Computing a primitive function would require rational arithmetic...
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