Add tasks for all the new languages

Task/Matrix-arithmetic/EchoLisp/matrix-arithmetic.echolisp

@@ -0,0 +1,27 @@
+(lib 'list)
+(lib 'matrix)
+
+;; adapted from Racket
+(define (permanent M)
+    (let (( n (matrix-row-num M)))
+    (for/sum ([σ (in-permutations n)])
+        (for/product ([i n] [σi σ])
+            (array-ref M i σi)))))
+
+;; output
+(define A (list->array '(1 2 3 4) 2 2))
+(array-print A)
+  1  2
+  3  4
+(determinant A) → -2
+(permanent A) → 10
+
+(define M (list->array (iota 25) 5 5))
+(array-print M)
+   0   1   2   3   4
+   5   6   7   8   9
+  10  11  12  13  14
+  15  16  17  18  19
+  20  21  22  23  24
+(determinant M) → 0
+(permanent M) → 6778800

Task/Matrix-arithmetic/FunL/matrix-arithmetic-1.funl

@@ -0,0 +1,5 @@
+def sgn( p ) = product( (if s(0) < s(1) xor i(0) < i(1) then -1 else 1) | (s, i) <- p.combinations(2).zip( (0:p.length()).combinations(2) ) )
+
+def perm( m ) = sum( product(m(i, sigma(i)) | i <- 0:m.length()) | sigma <- (0:m.length()).permutations() )
+
+def det( m ) = sum( sgn(sigma)*product(m(i, sigma(i)) | i <- 0:m.length()) | sigma <- (0:m.length()).permutations() )

Task/Matrix-arithmetic/FunL/matrix-arithmetic-2.funl

@@ -0,0 +1,7 @@
+def perm( m )
+  | m.length() == 1 and m(0).length() == 1 = m(0, 0)
+  | otherwise = sum( m(i, 0)*perm(m(0:i, 1:m.length()) + m(i+1:m.length(), 1:m.length())) | i <- 0:m.length() )
+
+def det( m )
+  | m.length() == 1 and m(0).length() == 1 = m(0, 0)
+  | otherwise = sum( (-1)^i*m(i, 0)*det(m(0:i, 1:m.length()) + m(i+1:m.length(), 1:m.length())) | i <- 0:m.length() )

Task/Matrix-arithmetic/FunL/matrix-arithmetic-3.funl

@@ -0,0 +1,18 @@
+matrices = [
+  ( (1, 2),
+    (3, 4)),
+  ( (-2, 2, -3),
+    (-1, 1,  3),
+    ( 2, 0, -1)),
+  ( ( 1,  2,  3,  4),
+    ( 4,  5,  6,  7),
+    ( 7,  8,  9, 10),
+    (10, 11, 12, 13)),
+  ( ( 0,  1,  2,  3,  4),
+    ( 5,  6,  7,  8,  9),
+    (10, 11, 12, 13, 14),
+    (15, 16, 17, 18, 19),
+    (20, 21, 22, 23, 24)) ]
+
+for m <- matrices
+  println( m, 'perm: ' + perm(m), 'det: ' + det(m) )

Task/Matrix-arithmetic/Nim/matrix-arithmetic.nim

@@ -0,0 +1,37 @@
+import sequtils, permutationsswap
+
+type Matrix[M,N: static[int]] = array[M, array[N, float]]
+
+proc det[M,N](a: Matrix[M,N]): float =
+  let n = toSeq 0..a.high
+  for sigma, sign in n.permutations:
+    var x = sign.float
+    for i in n: x *= a[i][sigma[i]]
+    result += x
+
+proc perm[M,N](a: Matrix[M,N]): float =
+  let n = toSeq 0..a.high
+  for sigma, sign in n.permutations:
+    var x = 1.0
+    for i in n: x *= a[i][sigma[i]]
+    result += x
+
+const
+  a = [ [1.0, 2.0]
+      , [3.0, 4.0]
+      ]
+  b = [ [ 1.0,  2,  3,  4]
+      , [ 4.0,  5,  6,  7]
+      , [ 7.0,  8,  9, 10]
+      , [10.0, 11, 12, 13]
+      ]
+  c = [ [ 0.0,  1,  2,  3,  4]
+      , [ 5.0,  6,  7,  8,  9]
+      , [10.0, 11, 12, 13, 14]
+      , [15.0, 16, 17, 18, 19]
+      , [20.0, 21, 22, 23, 24]
+      ]
+
+echo "perm: ", a.perm, " det: ", a.det
+echo "perm: ", b.perm, " det: ", b.det
+echo "perm: ", c.perm, " det: ", c.det

Task/Matrix-arithmetic/SPAD/matrix-arithmetic.spad

@@ -0,0 +1,16 @@
+(1) -> M:=matrix [[2, 9, 4], [7, 5, 3], [6, 1, 8]]
+
+        +2  9  4+
+        |       |
+   (1)  |7  5  3|
+        |       |
+        +6  1  8+
+                                                        Type: Matrix(Integer)
+(2) -> determinant M
+
+   (2)  - 360
+                                                                Type: Integer
+(3) -> permanent M
+
+   (3)  900
+                                                        Type: PositiveInteger

Task/Matrix-arithmetic/jq/matrix-arithmetic-1.jq

@@ -0,0 +1,18 @@
+# Eliminate row i and row j
+def except(i;j):
+  reduce del(.[i])[] as $row ([]; . + [$row | del(.[j]) ] );
+
+def det:
+  def parity(i): if i % 2 == 0 then 1 else -1 end;
+  if length == 1 and (.[0] | length) == 1 then .[0][0]
+  else . as $m
+    | reduce range(0; length) as $i
+        (0; . + parity($i) * $m[0][$i] * ( $m | except(0;$i) | det) )
+  end ;
+
+def perm:
+  if length == 1 and (.[0] | length) == 1 then .[0][0]
+  else . as $m
+    | reduce range(0; length) as $i
+        (0; . + $m[0][$i] * ( $m | except(0;$i) | perm) )
+  end ;

Task/Matrix-arithmetic/jq/matrix-arithmetic-2.jq

@@ -0,0 +1,22 @@
+def matrices:
+  [ [1, 2],
+    [3, 4]],
+
+  [ [-2, 2, -3],
+    [-1, 1,  3],
+    [ 2, 0, -1]],
+
+  [ [ 1,  2,  3,  4],
+    [ 4,  5,  6,  7],
+    [ 7,  8,  9, 10],
+    [10, 11, 12, 13]],
+
+  [ [ 0,  1,  2,  3,  4],
+    [ 5,  6,  7,  8,  9],
+    [10, 11, 12, 13, 14],
+    [15, 16, 17, 18, 19],
+    [20, 21, 22, 23, 24]]
+;
+
+"Determinants: ", (matrices | det),
+"Permanents:   ",  (matrices | perm)

Task/Matrix-arithmetic/jq/matrix-arithmetic-3.jq

@@ -0,0 +1,11 @@
+$ jq -n -r -f Matrix_arithmetic.jq
+Determinants:
+-2
+18
+0
+0
+Permanents:
+10
+10
+29556
+6778800

Task/Matrix-arithmetic/jq/matrix-arithmetic-4.jq

@@ -0,0 +1,8 @@
+# Requires lup/0
+def det:
+  def product_diagonal:
+    . as $m | reduce range(0;length) as $i (1; . * $m[$i][$i]);
+  def tidy: if . == -0 then 0 else . end;
+  lup
+  | (.[0]|product_diagonal) as $l
+  | if $l == 0 then 0 else $l * (.[1]|product_diagonal) | tidy end ;

Task/Matrix-arithmetic/jq/matrix-arithmetic-5.jq

@@ -0,0 +1 @@
+matrices | det