special_factors.sf

#!/usr/bin/ruby

# Find special factors for FactorDB, given a list of numbers.

define(
    USE_BATCH_GCD = false
    TRIAL_DIVISION = false
    TRIAL_LIMIT   = 1e7     # trial division limit
)

var seen = Set()

for file in (ARGV) {

    var nums = File(file).open_r.lines.map{.nums.last}.grep { defined(_) && (_ > 1e19) }.sort.uniq.grep{!seen.has(_)}
    var gcds = (USE_BATCH_GCD ? Math.batch_gcd(nums...).uniq : [])

    seen << nums...

    for n in (nums) {

    #~ var f = [n]\
       #~ .map { .cop_factor(100)... }\
       #~ .map { .is_prime ? _ : .trial_factor(1e7)... }\
       #~ .map { (.is_prime || .len>=200) ? _ : .cyclotomic_factor... }\
       #~ .map { .factor { .fermat_factor(1e3) }... }\
       #~ .map { .factor { .holf_factor(1e3) }... }\
       #~ .map { .factor { .pell_factor(1e3) }... }\
       #~ .map { .factor { .flt_factor(1e3) }... }\
       #~ .map { .is_prime ? _ : .miller_factor... }\
       #~ .map { .is_prime ? _ : .lucas_factor... }\
       #~ .map { .factor { .pm1_factor(1e5) }... }\
       #~ .map { .factor { .pp1_factor(1e4) }... }\
       #~ .map { .factor { .chebyshev_factor(1e4) }... }\
       #~ .map { .factor { .dop_factor(200) }... }\
       #~ .map { .factor { .cyclotomic_factor(2, 10) }... }

    #~ f = Math.gcd_factors(n, f + gcds)
    #~ f = f.first(-1)

        var f = []
        var t = n

        if (TRIAL_DIVISION) {
            f += TRIAL_LIMIT.smooth_part(n).factor
            n = idiv(n, f.prod)
        }

        f += if (USE_BATCH_GCD) {
            Math.gcd_factors(n, gcds + n.special_factors).first(-1)
        }
        else {
            n.special_factors.first(-1)
        }

        f = f.uniq

        f || next
        say "#{t} = #{f.join(' * ')}"
    }
}