Use math.algebra to solve project Euler problem 134

extra/project-euler/134/134.factor

@@ -1,7 +1,7 @@
 ! Copyright (c) 2007 Samuel Tardieu.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: arrays kernel math math.functions math.ranges math.primes.list namespaces
-       sequences vars ;
+USING: arrays kernel math.algebra math math.functions math.primes.list
+       math.ranges sequences ;
 IN: project-euler.134
 
 ! http://projecteuler.net/index.php?section=problems&id=134
@@ -23,36 +23,15 @@ IN: project-euler.134
 ! SOLUTION
 ! --------
 
-<PRIVATE
-
 ! Compute the smallest power of 10 greater than m
 : next-power-of-10 ( m -- n )
   10 swap log 10 log / >integer [ 10 * ] times ; foldable
 
-! Helper variables and words for the extended Euclidian algorithm
-! See http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
-
-VARS: r-1 u-1 v-1 r u v ;
-
-: init ( a b -- )
-  >r >r-1 0 >u 1 >u-1 1 >v 0 >v-1 ;
-
-: advance ( r u v -- )
-  v> >v-1 >v u> >u-1 >u r> >r-1 >r ;
-
-: step ( -- )
-  r-1> r> 2dup / >integer [ * - ] keep u-1> over u> * - v-1> rot v> * -
-  advance ;
-
-! Compute the inverse of a in field Z/bZ where b is prime
-: inverse ( a b -- a-1 )
-  [ init [ r> 0 > ] [ step ] [ ] while u-1> ] with-scope ;
-
-! Compute S for a given pair (p1, p2)
+! Compute S for a given pair (p1, p2) -- that is the smallest positive
+! number such that X = p1 [npt] and X = 0 [p2] (npt being the smallest
+! power of 10 above p1)
 : s ( p1 p2 -- s )
-  over next-power-of-10 [ over inverse pick * neg swap rem ] keep * + ;
-
-PRIVATE>
+  over 0 2array rot next-power-of-10 rot 2array chinese-remainder ;
 
 : euler134 ( -- answer )
   primes-under-million 2 tail dup 1 tail 1000003 add  [ s ] 2map sum ;