mirror of
https://github.com/python/cpython.git
synced 2024-11-24 10:24:35 +08:00
53 lines
1.3 KiB
Python
53 lines
1.3 KiB
Python
# 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 p:
|
|
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...
|