diff --git a/report.md b/report.md
index 9872337..0d2c8e7 100644
--- a/report.md
+++ b/report.md
@@ -32,7 +32,7 @@ BEGIN
 		getCellValue <- ERROR
 	endif
 
-	if (findMatrixElem( matrix , ColPos , RowPos ) == NULL)
+	if (findMatrixElem( matrix , ColPos , RowPos ) = NULL)
 		getCellValue <- false
 	endif
 
@@ -45,7 +45,7 @@ BEGIN
 	elem:*cellElement <- NULL
 
 	Row <- getElementPos(rows(matrix),RowPos)
-	if (Row == NULL)
+	if (Row = NULL)
 		findMatrixElem <- NULL
 	endif
 
@@ -60,10 +60,11 @@ END
 ```
 
 *setCellValue* is a simple function based on *createMatrixElem* and *deleteMatrixElement* :
+
 ```C
 setCellValue(matrix:Matrix, ColPos:integer, RowPos:integer,value:bool):bool
 BEGIN
-	if (value == true)
+	if (value = true)
 		setCellValue <- createMatrixElem(matrix,ColPos,RowPos)
 	else
 		if ( deleteMatrixElem(matrix,ColPos,RowPos) >= 0 )
@@ -84,7 +85,7 @@ createMatrixElem( matrix:Matrix, ColPos:integer, RowPos:integer):bool
 	tmp: *cellElement<- NULL
 
 	if (colCount(matrix) <= ColPos OR rowCount(matrix) <= RowPos )
-		createMatrixElem <- ERROR
+		createMatrixElem <- ERROR /* out of bounds */
 	endif
 
 	elem <- CreateCellElem()
@@ -93,8 +94,8 @@ createMatrixElem( matrix:Matrix, ColPos:integer, RowPos:integer):bool
 	Row <- getElementPos(rows(matrix),RowPos)
 	if (Row != NULL AND data(Row) != NULL)
 
-		if (colIndex(data(Row)) == ColPos)
-			error ++
+		if (colIndex(data(Row)) = ColPos)
+			error ++ /* the element already exists */
 		else 
 			if (colIndex(data(Row)) > ColPos)
 				nextCol(elem) <- data(Row)
@@ -102,20 +103,21 @@ createMatrixElem( matrix:Matrix, ColPos:integer, RowPos:integer):bool
 			endif
 		else 
 			tmp <- data(Row)
-			
+			/* searching the previous element */
 			while ( nextCol(tmp) != NULL AND nextCol(colIndex(tmp)) < ColPos) do
 				tmp <- nextCol(tmp)
 			endwhile
 
-			if ( nextCol(tmp) == NULL OR colIndex(nextCol(tmp)) > ColPos)
+			if ( nextCol(tmp) = NULL OR colIndex(nextCol(tmp)) > ColPos)
 				nextCol(elem) <- nextCol(tmp)
 				nextCol(tmp) <- elem
 			else 
-				error ++
+				error ++ /* the element already exists */
 			endif
 		endif
 
 	else 
+		/* if the list is empty */
 		push(rows(matrix),elem)
 		pos(tail(rows(matrix))) <- RowPos
 	endif
@@ -123,8 +125,8 @@ createMatrixElem( matrix:Matrix, ColPos:integer, RowPos:integer):bool
 	Col <- getElementPos(cols(matrix),ColPos)
 	if (Col != NULL AND data(Col) != NULL)
 
-		if (rowIndex(data(Col)) == RowPos)
-			error ++
+		if (rowIndex(data(Col)) = RowPos)
+			error ++ /* the element already exists */
 		else 
 			if (rowIndex(data(Col)) > RowPos)
 				nextRow(elem) <- data(Col)
@@ -132,25 +134,28 @@ createMatrixElem( matrix:Matrix, ColPos:integer, RowPos:integer):bool
 			endif
 		else 
 			tmp <- data(Col)
+			/* searching the previous element */
 			while (nextRow(tmp) != NULL AND rowIndex(nextRow(tmp)) < RowPos) do
 				tmp <- nextRow(tmp)
 			endwhile
 
-			if (nextRow(tmp) == NULL OR rowIndex(nextRow(tmp)) > RowPos)
+			if (nextRow(tmp) = NULL OR rowIndex(nextRow(tmp)) > RowPos)
 				nexRow(elem) <- nextRow(tmp)
 				newRow(tmp) <- elem
 			else 
-				error ++
+				error ++ /* the element already exists */
 			endif
 		endif
 
 	else 
+		/* if the list is empty */
 		push(cols(matrix),elem)
 		pos(tail(cols(matrix))) <- ColPos
 	endif
 
 
 	if (error != 0)
+		/* if the element already exists, free it */
 		FreeCellElement(elem)
 		createMatrixElem <- true
 	else
@@ -168,64 +173,77 @@ BEGIN
 	Col  : *ListElement <- NULL
 
 	elem <- findMatrixElem(matrix,ColPos,RowPos)
-	if (elem == NULL)
+	if (elem = NULL)
+		/* if the element does not exists */
 		deleteMatrixElem <- 0
 	endif
 
 	Row <- getElementPos(rows(matrix),RowPos)
-	if (Row == NULL)
+	if (Row = NULL)
+		/* this shouldn't happend */
 		deleteMatrixElem <- -1
 	endif
 
-	if (data(Row) == NULL)
+	if (data(Row) = NULL)
+		/* this shouldn't happend too */
 		removeElementPos(rows(matrix),RowPos)
 		deleteMatrixElem <- -1
 	endif
 
-	if (colIndex(data(Row)) == ColPos)
+	if (colIndex(data(Row)) = ColPos)
+		/* the element is the first element */
 		data(Row) <- nextCol(elem)
 	else 
 		tmp <- data(Row)
-	
+		/* finding prefious element */
 		while (nextCol(tmp) != NULL AND nextCol(tmp) != elem) do
 			tmp <- nextCol(tmp)
 		endwhile
 
 		if (nextCol(tmp) != NULL)
+			/* linking correctly the previous element */
 			nextCol(tmp) <- nextCol(elem)
 		endif
 	
 	endif
 
-	if (data(Row) == NULL)
+	if (data(Row) = NULL)
+		/* if the row is empty now we delete it to save memory */
 		removeElementPos(rows(matrix),RowPos)
 	endif
 
 
 	Col <- getElementPos(cols(matrix),ColPos)
-	if (Col == NULL)
+	if (Col = NULL)
+		/* this shouldn't happend */
 		deleteMatrixElem <- -2
 	endif
 
-	if (data(Col) == NULL)
+	if (data(Col) = NULL)
+		/* this shouldn't happend too */
 		removeElementPos(cols(matrix),ColPos)
 		deleteMatrixElem <- -1
 	endif
-	if (rowIndex(data(Col)) == RowPos)
+
+	if (rowIndex(data(Col)) = RowPos)
+		/* the element is the first element */
 		data(Col) <- nextRow(elem)
 	else
 		tmp <- data(Col)
+		/* finding prefious element */
 		while (nextRow(tmp) != NULL AND nextRow(tmp) != elem) do
 			tmp <- nextRow(tmp)
 		endwhile
 
 		if (nextRow(tmp) != NULL)
+			/* linking correctly the previous element */
 			nextRow(tmp) <- nextRow(elem)
 		endif
 
 	endif
 
-	if (data(Col) == NULL)
+	if (data(Col) = NULL)
+		/* if the col is empty now we delete it to save memory */
 		removeElementPos(cols(matrix),ColPos)
 	endif
 
@@ -277,7 +295,7 @@ Here are the algorithm of the function *applyRules* and all the one related to i
 ```C
 applyRules ( matrix:Matrix, Rules:integer, N:integer):Matrix
 BEGIN
-	RulesMatrix :integer[9]
+	RulesMatrix :integer[9] /* the size is the number of fundamental rules */
 	i:integer <- 0
 	power:integer <- 2
 	sum:integer <- 0
@@ -290,6 +308,7 @@ BEGIN
 		applyRules <- matrix
 	endif
 
+	/* decompotition of the rule in basic rules */ 
 	while(power <= 512) do
 
 		RulesMatrix[i] <- Rules%power - sum
@@ -303,6 +322,8 @@ BEGIN
 
 	endwhile
 
+	/* application of the rule */
+
 	tempMatrix1 <- matrixFromRules(matrix, i, RulesMatrix)
 
 	for j from 0 to N do
@@ -315,8 +336,6 @@ BEGIN
 	applyRules <- tempMatrix1
 
 END
-
-
 ```
 
 # Conclusion
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