New module math.primes.factors
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Samuel Tardieu
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USING: help.markup help.syntax ;
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IN: math.primes.factors
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{ factors count-factors unique-factors } related-words
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HELP: factors
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{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
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{ $description { "Factorize an integer and return an ordered list of factors, possibly repeated." } } ;
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HELP: count-factors
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{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
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{ $description { "Return a sequence of pairs representing each factor in the number and its corresponding power." } } ;
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HELP: unique-factors
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{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
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{ $description { "Return an ordered list of unique prime factors." } } ;
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HELP: totient
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{ $values { "n" "a positive integer" } { "t" "an integer" } }
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{ $description { "Return the number of integers between 1 and " { $snippet "n-1" } " relatively prime to " { $snippet "n" } "." } } ;
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USING: math.primes.factors tools.test ;
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{ { 999983 999983 1000003 } } [ 999969000187000867 factors ] unit-test
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{ { { 999983 2 } { 1000003 1 } } } [ 999969000187000867 count-factors ] unit-test
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{ { 999983 1000003 } } [ 999969000187000867 unique-factors ] unit-test
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{ 999967000236000612 } [ 999969000187000867 totient ] unit-test
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! Copyright (C) 2007 Samuel Tardieu.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays kernel lazy-lists math math.primes namespaces sequences ;
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IN: math.primes.factors
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<PRIVATE
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: (factor) ( n d -- n' )
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2dup mod zero? [ [ / ] keep dup , (factor) ] [ drop ] if ;
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: (count) ( n d -- n' )
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[ (factor) ] { } make
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dup empty? [ drop ] [ [ first ] keep length 2array , ] if ;
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: (unique) ( n d -- n' )
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[ (factor) ] { } make
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dup empty? [ drop ] [ first , ] if ;
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: (factors) ( quot list n -- )
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dup 1 > [ swap uncons >r pick call r> swap (factors) ] [ 3drop ] if ;
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: (decompose) ( n quot -- seq )
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[ lprimes rot (factors) ] { } make ;
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PRIVATE>
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: factors ( n -- seq )
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[ (factor) ] (decompose) ; foldable
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: count-factors ( n -- seq )
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[ (count) ] (decompose) ; foldable
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: unique-factors ( n -- seq )
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[ (unique) ] (decompose) ; foldable
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: totient ( n -- t )
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dup 2 < [
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drop 0
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] [
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[ unique-factors dup 1 [ 1- * ] reduce swap product / ] keep *
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] if ; foldable
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Prime factors decomposition
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