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