Add tasks for all the new languages

Task/Reduced-row-echelon-form/Phix/reduced-row-echelon-form.phix

@@ -0,0 +1,32 @@
+function ToReducedRowEchelonForm(sequence M)
+integer lead = 1,
+        rowCount = length(M),
+        columnCount = length(M[1]),
+        i
+    for r=1 to rowCount do
+        if lead>=columnCount then exit end if
+        i = r
+        while M[i][lead]=0 do
+            i += 1
+            if i=rowCount then
+                i = r
+                lead += 1
+                if lead=columnCount then exit end if
+            end if
+        end while
+        -- nb M[i] is assigned before M[r], which matters when i=r:
+        {M[r],M[i]} = {sq_div(M[i],M[i][lead]),M[r]}
+        for j=1 to rowCount do
+            if j!=r then
+                M[j] = sq_sub(M[j],sq_mul(M[j][lead],M[r]))
+            end if
+        end for
+        lead += 1
+    end for
+    return M
+end function
+
+? ToReducedRowEchelonForm(
+    { { 1, 2, -1, -4 },
+      { 2, 3, -1, -11 },
+      { -2, 0, -3, 22 } })

Task/Reduced-row-echelon-form/Sidef/reduced-row-echelon-form.sidef

@@ -0,0 +1,59 @@
+func rref (Array m) {
+    m.is_empty && return;
+    var (lead, rows, cols) = (0, m.len, m[0].len);
+
+    rows.range.each { |r|
+        lead >= cols && return m;
+        var i = r;
+
+        while (!m[i][lead]) {
+            ++i == rows || next;
+            i = r;
+            ++lead == cols && return m;
+        }
+
+        m[i, r] = m[r, i];
+        var lv = m[r][lead];
+        m[r] = (m[r] »/» lv);
+
+        rows.range.each { |n|
+            n == r && next;
+            m[n] = (m[n] »-« (m[r] «*« m[n][lead]))
+        }
+        ++lead;
+    }
+    return m
+}
+
+func say_it (message, array) {
+    say "\n#{message}";
+    array.each { |row|
+        say row.map { |n| " %5s" % n.as_rat }.join
+    }
+}
+
+var M = [
+    [ # base test case
+      [  1,  2,  -1,  -4 ],
+      [  2,  3,  -1, -11 ],
+      [ -2,  0,  -3,  22 ],
+    ],
+    [ # mix of number styles
+      [  3,   0,  -3,    1 ],
+      [ .5, 3/2,  -3,   -2 ],
+      [ .2, 4/5,  -1.6, .3 ],
+    ],
+    [ # degenerate case
+      [ 1,  2,  3,  4,  3,  1],
+      [ 2,  4,  6,  2,  6,  2],
+      [ 3,  6, 18,  9,  9, -6],
+      [ 4,  8, 12, 10, 12,  4],
+      [ 5, 10, 24, 11, 15, -4],
+    ],
+];
+
+M.each { |matrix|
+    say_it('Original Matrix', matrix);
+    say_it('Reduced Row Echelon Form Matrix', rref(matrix));
+    say '';
+}

Task/Reduced-row-echelon-form/Swift/reduced-row-echelon-form.swift

@@ -0,0 +1,40 @@
+var lead = 0
+var rowCount = eCount
+var columnCount = mCount
+for (var r = 0; r < rowCount; ++r) {
+	if (columnCount <= lead) {
+     		break
+    	}
+	var i = r
+	while (matrix[i][lead] == 0) {
+    		++i
+   		if (i == rowCount) {
+  			i = r
+  			++lead
+ 			if (columnCount == lead) {
+				--lead
+				break
+  			}
+    		}
+	}
+	for (var j = 0; j < columnCount; ++j) {
+   		var temp = matrix[r][j]
+    		matrix[r][j] = matrix[i][j]
+   		matrix[i][j] = temp
+	}
+	var div = matrix[r][lead]
+	if (div != 0) {
+    		for (var j = 0; j < columnCount; ++j) {
+  			matrix[r][j] /= div
+    		}
+	}
+	for (var j = 0; j < rowCount; ++j) {
+    		if (j != r) {
+  			var sub = matrix[j][lead]
+  			for (var k = 0; k < columnCount; ++k) {
+				matrix[j][k] -= (sub * matrix[r][k])
+  			}
+    		}
+	}
+	++lead
+}

Task/Reduced-row-echelon-form/Visual-FoxPro/reduced-row-echelon-form.visual

@@ -0,0 +1,90 @@
+CLOSE DATABASES ALL
+LOCAL lnRows As Integer, lnCols As Integer, lcSafety As String
+LOCAL ARRAY matrix[1]
+lcSafety = SET("Safety")
+SET SAFETY OFF
+CLEAR
+CREATE CURSOR results (c1 B(6), c2 B(6), c3 B(6), c4 B(6))
+CREATE CURSOR curs1(c1 I, c2 I, c3 I, c4 I)
+INSERT INTO curs1 VALUES (1,2,-1,-4)
+INSERT INTO curs1 VALUES (2,3,-1,-11)
+INSERT INTO curs1 VALUES (-2,0,-3,22)
+lnRows = RECCOUNT()	&& 3
+lnCols = FCOUNT()	&& 4
+SELECT * FROM curs1 INTO ARRAY matrix
+IF RREF(@matrix, lnRows, lnCols)
+	SELECT results
+	APPEND FROM ARRAY matrix
+	BROWSE NORMAL IN SCREEN
+ENDIF
+SET SAFETY &lcSafety
+
+FUNCTION RREF(mat, tnRows As Integer, tnCols As Integer) As Boolean
+LOCAL lnPivot As Integer, i As Integer, r As Integer, j As Integer, ;
+p As Double. llResult As Boolean, llExit As Boolean
+llResult = .T.
+llExit = .F.
+lnPivot = 1
+FOR r = 1 TO tnRows
+	IF lnPivot > tnCols
+		EXIT
+	ENDIF
+	i = r
+	DO WHILE mat[i,lnPivot] = 0
+		i = i + 1 	
+		IF i = tnRows
+			i = r
+			lnPivot = lnPivot + 1
+			IF lnPivot > tnCols
+				llExit = .T.
+				EXIT
+			ENDIF
+		ENDIF
+	ENDDO
+	IF llExit
+		EXIT
+	ENDIF	
+	ASwapRows(@mat, i, r)
+	p = mat[r,lnPivot]
+	IF p # 0
+		FOR j = 1 TO tnCols
+			mat[r,j] = mat[r,j]/p
+		ENDFOR
+	ELSE
+		? "Divison by zero."
+		llResult = .F.
+		EXIT
+	ENDIF	
+	FOR i = 1 TO tnRows
+		IF i # r
+			p = mat[i,lnPivot]
+			FOR j = 1 TO tnCols
+				mat[i,j] = mat[i,j] - mat[r,j]*p
+			ENDFOR
+		ENDIF
+	ENDFOR
+	lnPivot = lnPivot + 1 										
+ENDFOR
+RETURN llResult
+ENDFUNC
+
+PROCEDURE ASwapRows(arr, tnRow1 As Integer, tnRow2 As Integer)
+*!* Interchange rows tnRow1 and tnRow2 of array arr.
+LOCAL n As Integer
+n = ALEN(arr,2)
+LOCAL ARRAY tmp[1,n]
+STORE 0 TO tmp
+ACPY2(@arr, @tmp, tnRow1, 1)
+ACPY2(@arr, @arr, tnRow2, tnRow1)
+ACPY2(@tmp, @arr, 1, tnRow2)
+ENDPROC
+
+PROCEDURE ACPY2(m1, m2, tnSrcRow As Integer, tnDestRow As Integer)
+*!* Copy m1[tnSrcRow,*] to m2[tnDestRow,*]
+*!* m1 and m2 must have the same number of columns.
+LOCAL n As Integer, e1 As Integer, e2 As Integer
+n = ALEN(m1,2)
+e1 = AELEMENT(m1,tnSrcRow,1)
+e2 = AELEMENT(m2,tnDestRow,1)
+ACOPY(m1, m2, e1, n, e2)
+ENDPROC