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factor with a bound

asked 2013-06-24 20:29:04 -0500

anonymous user

Anonymous

Hi,

I need to find relatively small prime factors of some big numbers. How do I make factor command working with a bound? For instance let's say I am just interested in prime divisors less than 20 and I want to factor 11891. The answer I want would be 11*1081.

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answered 2013-06-24 20:48:32 -0500

You can implement a small function

def factorize_small_primes(N,bound):
    res = []                  # list of pairs (prime,multiplicity)
    for p in Primes():
        if p >= bound:
            break
        k = N.valuation(p)    # the nb k such that p^k || N
        res.append((p,k))
        N /= p^k
    return Factorization(res + [(N,1)])

And use it as follows

sage: N = 2^3 * 13^5 * 523^2 * 541^3
sage: f = factorize_small_primes(N,20)
sage: f
2^3 * 13^5 * 43310697015709

You can also check that the answer is somewaht consistent

sage: f.expand() == N
True
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Asked: 2013-06-24 20:29:04 -0500

Seen: 43 times

Last updated: Jun 24 '13