Add tasks for all the new languages

Task/Matrix-exponentiation-operator/ERRE/matrix-exponentiation-operator.erre

@@ -0,0 +1,53 @@
+PROGRAM MAT_PROD
+
+!$MATRIX
+
+!-----------------
+! calculate A[]^N
+!-----------------
+
+CONST ORDER=1
+
+DIM A[1,1],B[1,1],ANS[1,1]
+
+BEGIN
+
+DATA(3,2,2,1)
+DATA(10)  ! integer power only
+
+FOR I=0 TO ORDER DO
+   FOR J=0 TO ORDER DO
+      READ(A[I,J])
+   END FOR
+END FOR
+
+READ(M)  N=M-1
+
+IF N=0 THEN   ! A[]^0=matrice identit…
+   for I=0 TO ORDER DO
+      B[I,I]=1
+   END FOR
+ ELSE
+   B[]=A[]
+   FOR Z=1 TO N DO
+      ANS[]=0
+      FOR I=0 TO ORDER DO
+         FOR J=0 TO ORDER DO
+            FOR K=0 TO ORDER DO
+               ANS[I,J]=ANS[I,J]+(A[I,K]*B[K,J])
+            END FOR
+         END FOR
+      END FOR
+      B[]=ANS[]
+  END FOR
+END IF
+
+! print answer
+  FOR I=0 TO ORDER DO
+     FOR J=0 TO ORDER DO
+        PRINT(B[I,J],)
+     END FOR
+     PRINT
+  END FOR
+
+END PROGRAM

Task/Matrix-exponentiation-operator/SPAD/matrix-exponentiation-operator.spad

@@ -0,0 +1,24 @@
+(1) -> A:=matrix [[0,-%i],[%i,0]]
+
+        +0   - %i+
+   (1)  |        |
+        +%i   0  +
+                                               Type: Matrix(Complex(Integer))
+(2) -> A^4
+
+        +1  0+
+   (2)  |    |
+        +0  1+
+                                               Type: Matrix(Complex(Integer))
+(3) -> A^(-1)
+
+        +0   - %i+
+   (3)  |        |
+        +%i   0  +
+                                     Type: Matrix(Fraction(Complex(Integer)))
+(4) -> inverse A
+
+        +0   - %i+
+   (4)  |        |
+        +%i   0  +
+                          Type: Union(Matrix(Fraction(Complex(Integer))),...)

Task/Matrix-exponentiation-operator/jq/matrix-exponentiation-operator-1.jq

@@ -0,0 +1,24 @@
+# produce an array of length n that is 1 at i and 0 elsewhere
+def indicator(i;n): [range(0;n) | 0] | .[i] = 1;
+
+# Identity matrix:
+def identity(n): reduce range(0;n) as $i ([]; . + [indicator( $i; n )] );
+
+def direct_matrix_exp(n):
+  . as $in
+  | if n == 0 then identity($in|length)
+    else reduce range(1;n) as $i ($in; . as $m | multiply($m; $in))
+    end;
+
+def matrix_exp(n):
+  if n < 4 then direct_matrix_exp(n)
+  else . as $in
+  | ((n|2)|floor) as $m
+  | matrix_exp($m) as $ans
+  | multiply($ans;$ans) as $ans
+  | (n - (2 * $m) ) as $residue
+  | if $residue == 0 then $ans
+    else matrix_exp($residue) as $residue
+    | multiply($ans; $residue )
+    end
+  end;

Task/Matrix-exponentiation-operator/jq/matrix-exponentiation-operator-2.jq

@@ -0,0 +1,10 @@
+def pi: 4 * (1|atan);
+
+def rotation_matrix(theta):
+  [[(theta|cos), (theta|sin)], [-(theta|sin), (theta|cos)]];
+
+def demo_matrix_exp(n):
+  rotation_matrix( pi / 4 ) | matrix_exp(n) ;
+
+def demo_direct_matrix_exp(n):
+  rotation_matrix( pi / 4 ) | direct_matrix_exp(n) ;

Task/Matrix-exponentiation-operator/jq/matrix-exponentiation-operator-3.jq

@@ -0,0 +1,5 @@
+# For demo_matrix_exp(10000)
+$ time jq -n -c -f Matrix-exponentiation_operator.rc
+[[1,-1.1102230246251565e-12],[1.1102230246251565e-12,1]]
+user	0m0.490s
+sys	0m0.008s

Task/Matrix-exponentiation-operator/jq/matrix-exponentiation-operator-4.jq

@@ -0,0 +1,5 @@
+# For demo_direct_matrix_exp(10000)
+$ time jq -n -c -f Matrix-exponentiation_operator.rc
+[[1,-7.849831895612169e-13],[7.849831895612169e-13,1]]
+user	0m0.625s
+sys	0m0.006s