Add tasks for all the new languages

Task/AKS-test-for-primes/EchoLisp/aks-test-for-primes-1.echolisp

@@ -0,0 +1,19 @@
+(lib 'math.lib)
+;; 1 - x^p  :  P = (1 0 0 0 ... 0 -1)
+(define (mono p) (append (list 1) (make-list (1- p) 0) (list -1)))
+
+;; compute (x-1)^p ,  p >= 1
+(define (aks-poly p)
+	(poly-pow (list -1 1) p))
+	
+;;
+(define (show-them n)
+	(for ((p (in-range 1 n)))
+		(writeln 'p p (poly->string 'x (aks-poly p)))))
+	
+;; aks-test
+;; P = (x-1)^p + 1 - x^p
+(define (aks-test p)
+	(let ((P (poly-add (mono p) (aks-poly p)))
+	    (test (lambda(a) (zero? (modulo a p))))) ;; p divides a[i] ?
+	    (apply and (map test P)))) ;; returns #t if true for all a[i]

Task/AKS-test-for-primes/EchoLisp/aks-test-for-primes-2.echolisp

@@ -0,0 +1,21 @@
+(show-them 13) →
+p     1     x -1
+p     2     x^2 -2x +1
+p     3     x^3 -3x^2 +3x -1
+p     4     x^4 -4x^3 +6x^2 -4x +1
+p     5     x^5 -5x^4 +10x^3 -10x^2 +5x -1
+p     6     x^6 -6x^5 +15x^4 -20x^3 +15x^2 -6x +1
+p     7     x^7 -7x^6 +21x^5 -35x^4 +35x^3 -21x^2 +7x -1
+p     8     x^8 -8x^7 +28x^6 -56x^5 +70x^4 -56x^3 +28x^2 -8x +1
+p     9     x^9 -9x^8 +36x^7 -84x^6 +126x^5 -126x^4 +84x^3 -36x^2 +9x -1
+p     10     x^10 -10x^9 +45x^8 -120x^7 +210x^6 -252x^5 +210x^4 -120x^3 +45x^2 -10x +1
+p     11     x^11 -11x^10 +55x^9 -165x^8 +330x^7 -462x^6 +462x^5 -330x^4 +165x^3 -55x^2 +11x -1
+p     12     x^12 -12x^11 +66x^10 -220x^9 +495x^8 -792x^7 +924x^6 -792x^5 +495x^4 -220x^3 +66x^2 -12x +1
+
+(lib 'bigint)
+Lib: bigint.lib loaded.
+
+(for ((p (in-range 2 100)))
+    (when (aks-test p) (write p)))  →
+
+2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

Task/AKS-test-for-primes/FreeBASIC/aks-test-for-primes.freebasic

@@ -0,0 +1,75 @@
+'METHOD -- Use the Pascal triangle to retrieve the coefficients
+'UPPER LIMIT OF FREEBASIC ULONGINT GETS PRIMES UP TO 70
+Sub string_split(s_in As String,char As String,result() As String)
+    Dim As String s=s_in,var1,var2
+    Dim As Integer n,pst
+    #macro split(stri,char,var1,var2)
+    pst=Instr(stri,char)
+    var1="":var2=""
+    If pst<>0 Then
+        var1=Mid(stri,1,pst-1)
+        var2=Mid(stri,pst+1)
+    Else
+        var1=stri
+    End If
+    Redim Preserve result(1 To 1+n-((Len(var1)>0)+(Len(var2)>0)))
+    result(n+1)=var1
+    #endmacro
+    Do
+        split(s,char,var1,var2):n=n+1:s=var2
+    Loop Until var2=""
+    Redim Preserve result(1 To Ubound(result)-1)
+End Sub
+
+'Get Pascal triangle components
+Function pasc(n As Integer,flag As Integer=0) As String
+    n+=1
+    Dim As Ulongint V(n):V(1)=1ul
+    Dim As String s,sign
+    For r  As Integer= 2 To n
+        s=""
+        For i As Integer = r To 1 Step -1
+            V(i) +=  V(i-1)
+            If i Mod 2=1 Then sign="" Else sign="-"
+            s+=sign+Str(V(i))+","
+        Next i
+    Next r
+    If flag Then 'formatted output
+        Dim As String i,i2,i3,g
+        Redim As String a(0)
+        string_split(s,",",a())
+        For n1 As Integer=1 To Ubound(a)
+            If Left(a(n1),1)="-" Then sign="" Else sign="+"
+            If n1=Ubound(a) Then i2="" Else i2=a(n1)
+            If n1=2 Then i3="x" Else i3="x^"+Str(n1-1)
+            If n1=1 Then i="":sign=" " Else i=i3
+            g+=sign+i2+i+" "
+        Next n1
+        g="(x-1)^"+Str(n-1)+" = "+g
+        Return g
+    End If
+    Return s
+End Function
+
+Function isprime(num As Integer) As Integer
+    Redim As String a(0)
+    string_split(pasc(num),",",a())
+    For n As Integer=Lbound(a)+1 To Ubound(a)-1
+        If (Valulng(Ltrim(a(n),"-"))) Mod num<>0 Then Return 0
+    Next n
+    Return -1
+End Function
+'====================================
+'Formatted output
+For n As Integer=1 To 9
+    Print pasc(n,1)
+Next n
+
+Print
+'Limit of Freebasic Ulongint sets about 70 max
+Print "Primes up to 70:"
+For n As Integer=2 To 70
+    If isprime(n) Then Print n;
+Next n
+
+Sleep

Task/AKS-test-for-primes/Idris/aks-test-for-primes.idris

@@ -0,0 +1,70 @@
+import Data.Vect
+
+-- Computes Binomial Coefficients
+binCoef : Nat -> Nat -> Nat
+binCoef _ Z = (S Z)
+binCoef (S n) (S k) =
+    if n == k then (S Z) else ((S n) * (binCoef n k)) `div` (S k)
+
+-- Binomial Expansion Of (x - 1)^p
+expansion : (n : Nat) -> Vect (S n) Integer
+expansion n = expansion' n 1
+  where
+    expansion' : (n : Nat) -> Integer -> Vect (S n) Integer
+    expansion' (S m) s = s * (toIntegerNat $ binCoef n (n `minus` (S m))) ::
+                            expansion' m (s * -1)
+    expansion' Z s = [s]
+
+
+showExpansion : Vect n Integer -> String
+showExpansion [] = " "
+showExpansion (x::xs) {n = S k} = (if x < 0 then "-" else "") ++
+        term x k ++ showExpansion' xs
+  where
+        term : Integer -> Nat -> String
+        term x n = if n == 0 then (show (abs x)) else
+                      (if (abs x) == 1 then "" else
+                          (show (abs x))) ++ "x" ++
+                            (if n == 1 then "" else "^" ++ show n)
+
+        sign : Integer -> String
+        sign x = if x >= 0 then " + " else " - "
+
+        showExpansion' : Vect m Integer -> String
+        showExpansion' [] = ""
+        showExpansion' (y::ys) {m = S k} = sign y ++ term y k ++
+                                                showExpansion' ys
+
+
+natToFin' : (m : Nat) -> Fin (S m)
+natToFin' n with (natToFin n (S n))
+    natToFin' n | Just y = y
+
+
+isPrime : Nat -> Bool
+isPrime Z = False
+isPrime (S Z ) = False
+isPrime n = foldl (\divs, term => divs && (term `mod` (toIntegerNat n)) == 0)
+              True (fullExpansion $ expansion n)
+
+    -- (x - 1)^p - ((x^p) - 1)
+    where fullExpansion : Vect (S m) Integer -> Vect (S m) Integer
+          fullExpansion (x::xs) {m} = updateAt (natToFin' m) (+1) $ (x-1)::xs
+
+
+printExpansions : Nat -> IO ()
+printExpansions n = do
+      putStrLn "-- p: (x-1)^p for small p"
+      sequence_ $ map printExpansion [0..n]
+  where printExpansion : Nat -> IO ()
+        printExpansion n = do
+            print n
+            putStr ": "
+            putStrLn $ showExpansion $ expansion n
+
+
+main : IO()
+main = do
+  printExpansions 10
+  putStrLn "\n-- Primes Up To 100:"
+  putStrLn $ show $ filter isPrime [0..100]

Task/AKS-test-for-primes/Oforth/aks-test-for-primes.oforth

@@ -0,0 +1,13 @@
+: nextCoef(prev)
+| i |
+   ListBuffer new dup add(0)
+   prev size 1- loop: i [ dup add(prev at(i) prev at(i 1+) - ) ]
+   dup add(0) ;
+
+: coefs(n)    [ 0, 1, 0 ] #nextCoef times(n) extract(2, n 2 + ) ;
+: isPrime(n)  coefs(n) extract(2, n) conform(#[n mod 0 == ]) ;
+
+: aks
+| i |
+   0 10 for: i [ System.Out "(x-1)^" << i << " = " << coefs(i) << cr ]
+   50 seq filter(#isPrime) apply(#[ print " " print ]) printcr ;

Task/AKS-test-for-primes/Phix/aks-test-for-primes.phix

@@ -0,0 +1,80 @@
+-- Does not work for primes above 53, which is actually beyond the original task anyway.
+-- Translated from the C version, just about everything is (working) out-by-1, what fun.
+
+sequence c = repeat(0,100)
+
+procedure coef(integer n)
+-- out-by-1, ie coef(1)==^0, coef(2)==^1, coef(3)==^2 etc.
+    c[n] = 1
+    for i=n-1 to 2 by -1 do
+        c[i] = c[i]+c[i-1]
+    end for
+end procedure
+
+function is_prime(integer n)
+    coef(n+1); -- (I said it was out-by-1)
+    for i=2 to n-1 do   -- (technically "to n" is more correct)
+        if remainder(c[i],n)!=0 then
+            return 0
+        end if
+    end for
+    return 1
+end function
+
+procedure show(integer n)
+-- (As per coef, this is (working) out-by-1)
+object ci
+    for i=n to 1 by -1 do
+        ci = c[i]
+        if ci=1 then
+            if remainder(n-i,2)=0 then
+                if i=1 then
+                    if n=1 then
+                        ci = "1"
+                    else
+                        ci = "+1"
+                    end if
+                else
+                    ci = ""
+                end if
+            else
+                ci = "-1"
+            end if
+        else
+            if remainder(n-i,2)=0 then
+                ci = sprintf("+%d",ci)
+            else
+                ci = sprintf("-%d",ci)
+            end if
+        end if
+        if i=1 then -- ie ^0
+            printf(1,"%s",{ci})
+        elsif i=2 then -- ie ^1
+            printf(1,"%sx",{ci})
+        else
+            printf(1,"%sx^%d",{ci,i-1})
+        end if
+    end for
+end procedure
+
+procedure AKS_test_for_primes()
+    for n=1 to 10 do -- (0 to 9 really)
+        coef(n);
+        printf(1,"(x-1)^%d = ", n-1);
+        show(n);
+        puts(1,'\n');
+    end for
+
+    puts(1,"\nprimes (<=53):");
+--  coef(2); -- (needed to reset c, if we want to avoid saying 1 is prime...)
+    c[2] = 1 -- (this manages "", which is all that call did anyway...)
+    for n = 2 to 53 do
+        if is_prime(n) then
+            printf(1," %d", n);
+        end if
+    end for
+    puts(1,'\n');
+    if getc(0) then end if
+end procedure
+
+    AKS_test_for_primes()

Task/AKS-test-for-primes/Sidef/aks-test-for-primes.sidef

@@ -0,0 +1,23 @@
+func binprime(p) {
+    p >= 2 || return false
+    for i in (1 .. p>>1) {
+        (binomial(p, i) % p) && return false
+    }
+    return true
+}
+
+func coef(n, e) {
+    (e == 0) && return "#{n}"
+    (n == 1) && (n = "")
+    (e == 1) ? "#{n}x" : "#{n}x^#{e}"
+}
+
+func binpoly(p) {
+    join(" ", coef(1, p), ^p -> map {|i|
+        join(" ", %w(+ -)[(p-i)&1], coef(binomial(p, i), i))
+    }.reverse...)
+}
+
+say "expansions of (x-1)^p:"
+for i in ^10 { say binpoly(i) }
+say "Primes to 80: [#{2..80 -> grep { binprime(_) }.join(' ')}]"

Task/AKS-test-for-primes/Swift/aks-test-for-primes.swift

@@ -0,0 +1,80 @@
+func polynomialCoeffs(n: Int) -> [Int] {
+    var result = [Int](count : n+1, repeatedValue : 0)
+
+    result[0]=1
+    for i in 1 ..< n/2+1 { //Progress up, until reaching the middle value
+        result[i] = result[i-1] * (n-i+1)/i;
+    }
+    for i in n/2+1 ..< n+1 { //Copy the inverse of the first part
+        result[i] = result[n-i];
+    }
+    // Take into account the sign
+    for i in stride(from: 1, through: n, by: 2) {
+        result[i] = -result[i]
+    }
+
+    return result
+}
+
+func isPrime(n: Int) -> Bool {
+
+    var coeffs = polynomialCoeffs(n)
+
+    coeffs[0]--
+    coeffs[n]++
+
+    for i in 1 ... n {
+        if coeffs[i]%n != 0 {
+            return false
+        }
+    }
+
+    return true
+}
+
+for i in 0...10 {
+
+    let coeffs = polynomialCoeffs(i)
+
+    print("(x-1)^\(i) = ")
+    if i == 0 {
+        print("1")
+    } else {
+        if i == 1 {
+            print("x")
+        } else {
+            print("x^\(i)")
+            if i == 2 {
+                print("\(coeffs[i-1])x")
+            } else {
+                for j in 1...(i - 2) {
+                    if j%2 == 0 {
+                        print("+\(coeffs[j])x^\(i-j)")
+                    } else {
+                        print("\(coeffs[j])x^\(i-j)")
+                    }
+                }
+                if (i-1)%2 == 0 {
+                    print("+\(coeffs[i-1])x")
+                } else {
+                    print("\(coeffs[i-1])x")
+                }
+            }
+        }
+        if i%2 == 0 {
+            print("+\(coeffs[i])")
+        } else {
+            print("\(coeffs[i])")
+        }
+    }
+    println()
+}
+
+println()
+print("Primes under 50 : ")
+
+for i in 1...50 {
+    if isPrime(i) {
+        print("\(i) ")
+    }
+}

Task/AKS-test-for-primes/jq/aks-test-for-primes-1.jq

@@ -0,0 +1,35 @@
+# add_pairs is a helper function for optpascal/0
+# Input: an OptPascal array
+# Output: the next OptPascal array (obtained by adding adjacent items,
+# but if the last two items are unequal, then their sum is repeated)
+def add_pairs:
+  if length <= 1 then .
+  elif length == 2 then (.[0] + .[1]) as $S
+  | if (.[0] == .[1]) then [$S]
+    else [$S,$S]
+    end
+  else [.[0] + .[1]] + (.[1:]|add_pairs)
+  end;
+
+# Input: an OptPascal row
+# Output: the next OptPascalRow
+def next_optpascal: [1] + add_pairs;
+
+# generate a stream of OptPascal arrays, beginning with []
+def optpascals: [] | recurse(next_optpascal);
+
+# generate a stream of Pascal arrays
+def pascals:
+  # pascalize takes as input an OptPascal array and produces
+  # the corresponding Pascal array;
+  # if the input ends in a pair, then peel it off before reversing it.
+  def pascalize:
+  . + ((if .[-2] == .[-1] then .[0:-2] else .[0:-1] end) | reverse);
+
+  optpascals | pascalize;
+
+# Input: integer n
+# Output: the n-th Pascal row
+def pascal: nth(.; pascals);
+
+def optpascal: nth(.; optpascals);

Task/AKS-test-for-primes/jq/aks-test-for-primes-2.jq

@@ -0,0 +1,4 @@
+def coefficients:
+  def alternate_signs: . as $in
+  | reduce range(0; length) as $i ([]; . + [$in[$i] * (if $i % 2 == 0 then 1 else -1 end )]);
+  (.+1) | pascal | alternate_signs;

Task/AKS-test-for-primes/jq/aks-test-for-primes-3.jq

@@ -0,0 +1 @@
+range(0;8) | "Coefficient for (x - 1)^\(.): \(coefficients)"

Task/AKS-test-for-primes/jq/aks-test-for-primes-4.jq

@@ -0,0 +1,8 @@
+Coefficients for (x - 1)^0: [1]
+Coefficients for (x - 1)^1: [1,-1]
+Coefficients for (x - 1)^2: [1,-2,1]
+Coefficients for (x - 1)^3: [1,-3,3,-1]
+Coefficients for (x - 1)^4: [1,-4,6,-4,1]
+Coefficients for (x - 1)^5: [1,-5,10,-10,5,-1]
+Coefficients for (x - 1)^6: [1,-6,15,-20,15,-6,1]
+Coefficients for (x - 1)^7: [1,-7,21,-35,35,-21,7,-1]

Task/AKS-test-for-primes/jq/aks-test-for-primes-5.jq

@@ -0,0 +1,6 @@
+def is_prime:
+  . as $N
+  | if . < 2 then false
+    else (1+.) | optpascal
+    | all(  .[2:][]; . % $N == 0 )
+    end;

Task/AKS-test-for-primes/jq/aks-test-for-primes-6.jq

@@ -0,0 +1 @@
+range(0;36) | select(is_prime)

Task/AKS-test-for-primes/jq/aks-test-for-primes-7.jq

@@ -0,0 +1,11 @@
+2
+3
+5
+7
+11
+13
+17
+19
+23
+29
+31

Task/AKS-test-for-primes/jq/aks-test-for-primes-8.jq

@@ -0,0 +1 @@
+[range(0;50) | select(is_prime)]

Task/AKS-test-for-primes/jq/aks-test-for-primes-9.jq

@@ -0,0 +1 @@
+[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]