New module math.primes.factors

extra/math/primes/factors/authors.txt

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+Samuel Tardieu

extra/math/primes/factors/factors-docs.factor

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+USING: help.markup help.syntax ;
+IN: math.primes.factors
+
+{ factors count-factors unique-factors } related-words
+
+HELP: factors
+{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
+{ $description { "Factorize an integer and return an ordered list of factors, possibly repeated." } } ;
+
+HELP: count-factors
+{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
+{ $description { "Return a sequence of pairs representing each factor in the number and its corresponding power." } } ;
+
+HELP: unique-factors
+{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
+{ $description { "Return an ordered list of unique prime factors." } } ;
+
+HELP: totient
+{ $values { "n" "a positive integer" } { "t" "an integer" } }
+{ $description { "Return the number of integers between 1 and " { $snippet "n-1" } " relatively prime to " { $snippet "n" } "." } } ;

extra/math/primes/factors/factors-tests.factor

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+USING: math.primes.factors tools.test ;
+
+{ { 999983 999983 1000003 } } [ 999969000187000867 factors ] unit-test
+{ { { 999983 2 } { 1000003 1 } } } [ 999969000187000867 count-factors ] unit-test
+{ { 999983 1000003 } } [ 999969000187000867 unique-factors ] unit-test
+{ 999967000236000612 } [ 999969000187000867 totient ] unit-test

extra/math/primes/factors/factors.factor

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+! Copyright (C) 2007 Samuel Tardieu.
+! See http://factorcode.org/license.txt for BSD license.
+USING: arrays kernel lazy-lists math math.primes namespaces sequences ;
+IN: math.primes.factors
+
+<PRIVATE
+
+: (factor) ( n d -- n' )
+  2dup mod zero? [ [ / ] keep dup , (factor) ] [ drop ] if ;
+
+: (count) ( n d -- n' )
+  [ (factor) ] { } make
+  dup empty? [ drop ] [ [ first ] keep length 2array , ] if ;
+
+: (unique) ( n d -- n' )
+  [ (factor) ] { } make
+  dup empty? [ drop ] [ first , ] if ;
+
+: (factors) ( quot list n -- )
+  dup 1 > [ swap uncons >r pick call r> swap (factors) ] [ 3drop ] if ;
+
+: (decompose) ( n quot -- seq )
+  [ lprimes rot (factors) ] { } make ;
+
+PRIVATE>
+
+: factors ( n -- seq )
+  [ (factor) ] (decompose) ; foldable
+
+: count-factors ( n -- seq )
+  [ (count) ] (decompose) ; foldable
+
+: unique-factors ( n -- seq )
+  [ (unique) ] (decompose) ; foldable
+
+: totient ( n -- t )
+  dup 2 < [
+    drop 0
+  ] [
+   [ unique-factors dup 1 [ 1- * ] reduce swap product / ] keep *
+  ] if ; foldable

extra/math/primes/factors/summary.txt

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+Prime factors decomposition