Add tasks for all the new languages

Task/Chinese-remainder-theorem/EchoLisp/chinese-remainder-theorem.echolisp

@@ -0,0 +1,8 @@
+(lib 'math)
+math.lib v1.10 ® EchoLisp
+Lib: math.lib loaded.
+
+(crt-solve '(2 3 2) '(3 5 7))
+   → 23
+(crt-solve '(2 3 2) '(7 1005 15))
+💥 error: mod[i] must be co-primes : assertion failed : 1005

Task/Chinese-remainder-theorem/FunL/chinese-remainder-theorem.funl

@@ -0,0 +1,7 @@
+import integers.modinv
+
+def crt( congruences ) =
+    N = product( n | (_, n) <- congruences )
+    sum( a*modinv(N/n, n)*N/n | (a, n) <- congruences ) mod N
+
+println( crt([(2, 3), (3, 5), (2, 7)]) )

Task/Chinese-remainder-theorem/Nim/chinese-remainder-theorem.nim

@@ -0,0 +1,24 @@
+proc mulInv(a0, b0): int =
+  var (a, b, x0) = (a0, b0, 0)
+  result = 1
+  if b == 1: return
+  while a > 1:
+    let q = a div b
+    a = a mod b
+    swap a, b
+    result = result - q * x0
+    swap x0, result
+  if result < 0: result += b0
+
+proc chineseRemainder[T](n, a: T): int =
+  var prod = 1
+  var sum = 0
+  for x in n: prod *= x
+
+  for i in 0 .. <n.len:
+    let p = prod div n[i]
+    sum += a[i] * mulInv(p, n[i]) * p
+
+  sum mod prod
+
+echo chineseRemainder([3,5,7], [2,3,2])

Task/Chinese-remainder-theorem/Sidef/chinese-remainder-theorem.sidef

@@ -0,0 +1,20 @@
+func mul_inv(a, b) {
+    b == 1 && return 1;
+    var (b0, x0, x1) = (0, 0, 1);
+    while (a > 1) {
+        (a, b, x0, x1) = (b, a % b, x1 - x0*int(a / b), x0);
+    };
+    x1 < 0 ? x1+b0 : x1;
+}
+
+func chinese_remainder(*n) {
+    var N = n«*»;
+    func (*a) {
+        n.range.map { |i|
+            var p = int(N / n[i]);
+            a[i] * mul_inv(p, n[i]) * p;
+        }.sum
+    }
+}
+
+say chinese_remainder(3, 5, 7)(2, 3, 2);

Task/Chinese-remainder-theorem/jq/chinese-remainder-theorem.jq

@@ -0,0 +1,31 @@
+# mul_inv(a;b) returns x where (a * x) % b == 1, or else null
+def mul_inv(a; b):
+
+  # state: [a, b, x0, x1]
+  def iterate:
+    .[0] as $a | .[1] as $b
+    | if $a > 1 then
+        if $b == 0 then null
+        else ($a / $b | floor) as $q
+           | [$b, ($a % $b), (.[3] - ($q * .[2])), .[2]] | iterate
+        end
+      else .
+      end ;
+
+  if (b == 1) then 1
+  else [a,b,0,1] | iterate
+       | if . == null then .
+         else  .[3] | if . <  0 then . + b else . end
+         end
+  end;
+
+def chinese_remainder(mods; remainders):
+  (reduce mods[] as $i (1; . * $i)) as $prod
+  | reduce range(0; mods|length) as $i
+      (0;
+       ($prod/mods[$i]) as $p
+       | mul_inv($p; mods[$i]) as $mi
+       | if $mi == null then error("nogo: p=\($p) mods[\($i)]=\(mods[$i])")
+         else . + (remainders[$i] * $mi * $p)
+         end )
+  | . % $prod ;