72 lines
2.3 KiB
Python
72 lines
2.3 KiB
Python
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from itertools import product
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from operator import mul
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from math import sqrt
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def primitive_triplets(nbr):
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if nbr % 4 != 0:
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raise ValueError('Argument must be divisible by 4')
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prime_factors,powers = factor(nbr/2)
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args = [(1,prime_factors[i1]**powers[i1]) for i1 in range(len(powers))]
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a = [reduce(mul, p) for p in product(*args)]
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a.sort()
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factors = [(m,n) for m,n in zip(reversed(a),a) if m>n]
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ts = set()
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for m,n in factors:
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l = [nbr, m*m-n*n,m*m+n*n]
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l.sort()
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ts.update([tuple(l)])
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return ts
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def is_triplet(t):
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t = list(t)
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t.sort()
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a,b,c = t
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return c*c == a*a + b*b
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def triplets_in_range(m, n):
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t = set()
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for a in xrange(m,n+1):
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for b in xrange(a+1,n+1):
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c = int(sqrt(a*a + b*b)+0.5)
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if c*c == a*a + b*b and c >= m and c <= n:
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t.update([(a,b,c)])
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return t
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primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
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67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137,
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139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211,
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223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
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293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379,
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383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461,
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463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563,
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569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643,
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647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739,
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743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829,
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839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937,
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941, 947, 953, 967, 971, 977, 983, 991, 997]
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def factor(n):
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global primes
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if n == 1:
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return (1,),(0,)
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factors = []
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powers = []
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idx = 0
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while n > 1:
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prime = primes[idx]
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idx += 1
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if n % prime != 0:
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continue
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factors.append(prime)
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p = 0
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while n % prime == 0:
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p += 1
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n /= prime
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powers.append(p)
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return factors,powers
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if __name__ == '__main__':
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print primitive_triplets(4)
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print primitive_triplets(84)
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print primitive_triplets(288)
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print triplets_in_range(50,100)
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