added new functions in library/tools

Alain Prouté
1 parent 1be798c1
Showing 2 changed files with 53 additions and 0 deletions Show diff stats
anubis_dev/library/tools/int.anubis
anubis_dev/library/tools/list.anubis
@@ -63,6 +63,11 @@ public define              Int       Int x ^ Int y.            raises x to the p
 public define              Bool      odd     (Int x).       
 public define              Bool      even    (Int x).       
  
+   *** (7) Greatest common divisor, ... 
+ 
+public define              Int       gcd     (Int x, Int y).     
+public define              Int       lcm     (Int x, Int y).    least common multiple
+
  
    --- That's all for the public part ! -----------------------------------------------
  
@@ -226,6 +231,38 @@ public define Bool
   }. 
  
  
+public define Int       
+   gcd     
+   (
+     Int     x, 
+     Int     y
+   ) =
+   /* Euclid's algorithm */ 
+   if x > y then gcd(y,x) else
+   if x = 0 then abs(y) else
+   if x < 0 then gcd(-x,y) else
+   if y/x is
+    {
+      failure    then should_not_happen(0), 
+      success(p) then if p is (q,r) then gcd(r,x)
+    }. 
+
+
+
+public define Int       
+  lcm     
+  (
+    Int x, 
+    Int y
+  ) =
+  with d = gcd(x,y), 
+  if d = 0
+  then 0
+  else if (x*y)/d is 
+  {
+    failure    then should_not_happen(0), 
+    success(p) then if p is (q,_) then q 
+  }.
  
  
  
@@ -910,3 +910,19 @@ public define (List($T1), List($T2)) unzip(List(($T1, $T2)) l) = unzip(reverse(l
  
  
  
+   Compute the list of all sublists of a list (beware: for a list of length n, 
+   this gives a list of length 2^n). 
+   
+public define List(List($T))
+   sublists
+   (
+     List($T)  l
+   ) =
+   if l is 
+   {
+     [ ] then [[ ]], 
+     [h . t] then with p = sublists(t),
+       map((List($T) u) |-> [h . u],p) + p
+   }.
+
+