Initial data commit

Task/Tonelli-Shanks-algorithm/J/tonelli-shanks-algorithm-1.j

@@ -0,0 +1,29 @@
+leg=: dyad define
+  x (y&|)@^ (y-1)%2
+)
+
+tosh=:dyad define
+  assert. 1=1 p: y [ 'y must be prime'
+  assert. 1=x leg y [ 'x must be square mod y'
+  pow=. y&|@^
+  if. 1=m=. {.1 q: y-1 do.
+    r=. x pow (y+1)%4
+  else.
+    z=. 1x while. 1>: z leg y do. z=.z+1 end.
+    c=. z pow q=. (y-1)%2^m
+    r=. x pow (q+1)%2
+    t=. x pow q
+    while. t~:1 do.
+      n=. t
+      i=. 0
+      whilst. 1~:n do.
+        n=. n pow 2
+        i=. i+1
+      end.
+      r=. y|r*b=. c pow 2^m-i+1
+      m=. i
+      t=. y|t*c=. b pow 2
+    end.
+  end.
+  y|(,-)r
+)

Task/Tonelli-Shanks-algorithm/J/tonelli-shanks-algorithm-2.j

@@ -0,0 +1,17 @@
+   10 tosh 13
+7 6
+   56 tosh 101
+37 64
+   1030 tosh 10009
+1632 8377
+   1032 tosh 10009
+|assertion failure: tosh
+|   1=x leg y['x must be square mod y'
+   44402 tosh 100049
+30468 69581
+   665820697x tosh 1000000009x
+378633312 621366697
+   881398088036 tosh 1000000000039x
+791399408049 208600591990
+   41660815127637347468140745042827704103445750172002x tosh (10^50x)+577
+32102985369940620849741983987300038903725266634508 67897014630059379150258016012699961096274733366069