Another update from ingydotnet^djgoku

Task/Vector-products/ALGOL-W/vector-products.alg

@@ -0,0 +1,45 @@
+begin
+    % define the Vector record type                                          %
+    record Vector( integer X, Y, Z );
+
+    % calculates the dot product of two Vectors                              %
+    integer procedure dotProduct( reference(Vector) value A, B ) ;
+        ( X(A) * X(B) ) + ( Y(A) * Y(B) ) + ( Z(A) * Z(B) );
+
+    % calculates the cross product or two Vectors                            %
+    reference(Vector) procedure crossProduct( reference(Vector) value A, B ) ;
+        Vector( ( Y(A) * Z(B) ) - ( Z(A) * Y(B) )
+              , ( Z(A) * X(B) ) - ( X(A) * Z(B) )
+              , ( X(A) * Y(B) ) - ( Y(A) * X(B) )
+              );
+
+    % calculates the scaler triple product of two vectors                    %
+    integer procedure scalerTripleProduct( reference(Vector) value A, B, C ) ;
+        dotProduct( A, crossProduct( B, C ) );
+
+    % calculates the vector triple product of two vectors                    %
+    reference(Vector) procedure vectorTripleProduct( reference(Vector) value A, B, C ) ;
+        crossProduct( A, crossProduct( B, C ) );
+
+    % test the Vector routines                                               %
+    begin
+        procedure writeonVector( reference(Vector) value v ) ;
+            writeon( "(", X(v), ", ", Y(v), ", ", Z(v), ")" );
+
+        Reference(Vector) a, b, c;
+
+        a := Vector(  3,   4,   5 );
+        b := Vector(  4,   3,   5 );
+        c := Vector( -5, -12, -13 );
+
+        i_w := 1; s_w := 0; % set output formatting                          %
+
+        write( "            a: " ); writeonVector( a );
+        write( "            b: " ); writeonVector( b );
+        write( "            c: " ); writeonVector( c );
+        write( "        a . b: ", dotProduct( a, b ) );
+        write( "        a x b: " ); writeonVector( crossProduct( a, b ) );
+        write( "a . ( b x c ): ", scalerTripleProduct( a, b, c ) );
+        write( "a x ( b x c ): " ); writeonVector( vectorTripleProduct( a, b, c ) )
+    end
+end.

Task/Vector-products/Common-Lisp/vector-products-2.lisp

@@ -0,0 +1,22 @@
+(defun cross (a b)
+  (when (and (equal (length a) 3) (equal (length b) 3))
+      (vector
+       (- (* (elt a 1) (elt b 2)) (* (elt a 2) (elt b 1)))
+       (- (* (elt a 2) (elt b 0)) (* (elt a 0) (elt b 2)))
+       (- (* (elt a 0) (elt b 1)) (* (elt a 1) (elt b 0))))))
+
+(defun dot (a b)
+  (when (equal (length a) (length b))
+      (loop for ai across a for bi across b sum (* ai bi))))
+
+(defun scalar-triple (a b c)
+  (dot a (cross b c)))
+
+(defun vector-triple (a b c)
+  (cross a (cross b c)))
+
+(defun task (a b c)
+  (values (dot a b)
+          (cross a b)
+          (scalar-triple a b c)
+          (vector-triple a b c)))

Task/Vector-products/J/vector-products-1.j

@@ -1,3 +1 @@
-CT=: C.!.2 @ (#:i.) @ $~
-ip=: +/ .*    NB. inner product
-cross=: ] ip CT@#@[ ip [
+cross=: (1&|.@[ * 2&|.@]) - 2&|.@[ * 1&|.@]

Task/Vector-products/J/vector-products-2.j

@@ -1 +1,3 @@
-cross=: [: > [: -&.>/ .(*&.>) (<"1=i.3) , ,:&:(<"0)
+CT=: C.!.2 @ (#:i.) @ $~
+ip=: +/ .*    NB. inner product
+cross=: ] ip CT@#@[ ip [

Task/Vector-products/J/vector-products-3.j

@@ -1,12 +1 @@
-a=:  3 4 5
-b=:  4 3 5
-c=: -5 12 13
-
-A=: 0 {:: ]    NB. contents of the first box on the right
-B=: 1 {:: ]    NB. contents of the second box on the right
-C=: 2 {:: ]    NB. contents of the third box on the right
-
-dotP=: A ip B
-crossP=: A cross B
-scTriP=: A ip B cross C
-veTriP=: A cross B cross C
+cross=: [: > [: -&.>/ .(*&.>) (<"1=i.3) , ,:&:(<"0)

Task/Vector-products/J/vector-products-4.j

@@ -1,8 +1,12 @@
-   dotP a;b
-49
-   crossP a;b
-5 5 _7
-   scTriP a;b;c
-6
-   veTriP a;b;c
-_267 204 _3
+a=:  3 4 5
+b=:  4 3 5
+c=: -5 12 13
+
+A=: 0 {:: ]    NB. contents of the first box on the right
+B=: 1 {:: ]    NB. contents of the second box on the right
+C=: 2 {:: ]    NB. contents of the third box on the right
+
+dotP=: A ip B
+crossP=: A cross B
+scTriP=: A ip B cross C
+veTriP=: A cross B cross C

Task/Vector-products/J/vector-products-5.j

@@ -0,0 +1,8 @@
+   dotP a;b
+49
+   crossP a;b
+5 5 _7
+   scTriP a;b;c
+6
+   veTriP a;b;c
+_267 204 _3

Task/Vector-products/Julia/vector-products.julia

@@ -0,0 +1,26 @@
+function scltrip{T<:Number}(a::AbstractArray{T,1},
+                            b::AbstractArray{T,1},
+                            c::AbstractArray{T,1})
+    dot(a, cross(b, c))
+end
+
+function vectrip{T<:Number}(a::AbstractArray{T,1},
+                            b::AbstractArray{T,1},
+                            c::AbstractArray{T,1})
+    cross(a, cross(b, c))
+end
+
+a = [3, 4, 5]
+b = [4, 3, 5]
+c = [-5, -12, -13]
+
+println("Test Vectors:")
+println("   a = ", a)
+println("   b = ", a)
+println("   c = ", a)
+
+println("\nVector Products:")
+println("   a dot b = ", dot(a, b))
+println("   a cross b = ", cross(a, b))
+println("   a dot b cross c = ", scltrip(a, b, c))
+println("   a cross b cross c = ", vectrip(a, b, c))

Task/Vector-products/PowerShell/vector-products.psh

@@ -0,0 +1,27 @@
+function dot-product($a,$b) {
+    $a[0]*$b[0] +  $a[1]*$b[1] +  $a[2]*$b[2]
+}
+
+function cross-product($a,$b) {
+    $v1 = $a[1]*$b[2] - $a[2]*$b[1]
+    $v2 = $a[2]*$b[0] - $a[0]*$b[2]
+    $v3 = $a[0]*$b[1] - $a[1]*$b[0]
+    @($v1,$v2,$v3)
+}
+
+function scalar-triple-product($a,$b,$c) {
+    dot-product $a (cross-product $b $c)
+}
+
+function vector-triple-product($a,$b) {
+    cross-product $a (cross-product $b $c)
+}
+
+$a = @(3, 4, 5)
+$b = @(4, 3, 5)
+$c = @(-5, -12, -13)
+
+"a.b = $(dot-product $a $b)"
+"axb = $(cross-product $a $b)"
+"a.(bxc) = $(scalar-triple-product $a $b $c)"
+"ax(bxc) = $(vector-triple-product $a $b $c)"