1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
# 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):
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 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...
|
