diff --git a/src/computorv1.c b/src/computorv1.c
index 46326b6..1e64621 100644
--- a/src/computorv1.c
+++ b/src/computorv1.c
@@ -32,7 +32,27 @@ int main(int ac, char **av)
     i = 0;
     while (tokens[i].type != TOKEN_END)
     {
-        ft_printf("token %i :\n  type : %i\n  value : ", i, tokens[i].type);
+        ft_printf("token %2i - type : ", i);
+
+        if (tokens[i].type == TOKEN_VARIABLE)
+            ft_printf("%20s", "TOKEN_VARIABLE");
+        if (tokens[i].type == TOKEN_NUMBER)
+            ft_printf("%20s", "TOKEN_NUMBER");
+        if (tokens[i].type == TOKEN_POWER)
+            ft_printf("%20s", "TOKEN_POWER");
+        if (tokens[i].type == TOKEN_PLUS)
+            ft_printf("%20s", "TOKEN_PLUS");
+        if (tokens[i].type == TOKEN_MINUS)
+            ft_printf("%20s", "TOKEN_MINUS");
+        if (tokens[i].type == TOKEN_MULTIPLICATION)
+            ft_printf("%20s", "TOKEN_MULTIPLICATION");
+        if (tokens[i].type == TOKEN_DIVISION)
+            ft_printf("%20s", "TOKEN_DIVISION");
+        if (tokens[i].type == TOKEN_END)
+            ft_printf("%20s", "TOKEN_END");
+
+        ft_putstr(" - value : ");
+
         if (tokens[i].type == TOKEN_NUMBER)
         {
             ft_printf("%d\n", i, tokens[i].num_value);
diff --git a/src/lexer.c b/src/lexer.c
index e7d7e97..f15a80b 100644
--- a/src/lexer.c
+++ b/src/lexer.c
@@ -11,12 +11,9 @@ static int skip_whitespace(const char *input, int input_pos)
     return input_pos;
 }
 
+// any single letter is a valid variable, like "x" or "y"
 static bool token_is_variable(const char *input, int input_pos, int *token_size)
 {
-    if (input[input_pos] == 'x' || input[input_pos] == 'X')
-    {
-        return false;
-    }
     if (ft_isalpha(input[input_pos]))
     {
         *token_size = 1;
@@ -25,13 +22,13 @@ static bool token_is_variable(const char *input, int input_pos, int *token_size)
     return false;
 }
 
+// number can be double "123.456"
 static bool token_is_number(const char *input, int input_pos, int *token_size)
 {
     int number_size;
     int max_number_size;
-    int is_number;
 
-    if (!ft_isnumber(input[input_pos]))
+    if (!ft_isdigit(input[input_pos]))
     {
         return false;
     }
@@ -40,14 +37,16 @@ static bool token_is_number(const char *input, int input_pos, int *token_size)
     max_number_size = 129; // max size for double double is 128 bits, + the coma
     while (number_size <= max_number_size)
     {
-        if (ft_isnumber(input[input_pos + number_size]))
+        if (ft_isdigit(input[input_pos + number_size]))
         {
             number_size++;
         }
-        else if (input[input_pos] == '.')
+        else if (input[input_pos + number_size] == '.')
         {
             number_size++;
         }
+        else
+            break;
     }
     if (number_size > max_number_size)
     {
@@ -57,6 +56,23 @@ static bool token_is_number(const char *input, int input_pos, int *token_size)
     return true;
 }
 
+// power can be "^" and "**"
+static bool token_is_power(const char *input, int input_pos, int *token_size)
+{
+    if (input[input_pos] == '^')
+    {
+        *token_size = 1;
+        return true;
+    }
+    else if (ft_memcmp(&input[input_pos], "**", 2) == 0)
+    {
+        *token_size = 2;
+        return true;
+    }
+    return false;
+}
+
+// detect a single "+" is valid
 static bool token_is_plus(const char *input, int input_pos, int *token_size)
 {
     if (input[input_pos] == '+')
@@ -67,47 +83,30 @@ static bool token_is_plus(const char *input, int input_pos, int *token_size)
     return false;
 }
 
-static bool token_is_plus(const char *input, int input_pos, int *token_size)
-{
-    if (input[input_pos] == '+')
-    {
-        *token_size = 1;
-        return true;
-    }
-    return false;
-}
-
-static bool token_is_plus(const char *input, int input_pos, int *token_size)
-{
-    if (input[input_pos] == '+')
-    {
-        *token_size = 1;
-        return true;
-    }
-    return false;
-}
-
-static bool token_is_plus(const char *input, int input_pos, int *token_size)
-{
-    if (input[input_pos] == '+')
-    {
-        *token_size = 1;
-        return true;
-    }
-    return false;
-}
-
-static bool token_is_plus(const char *input, int input_pos, int *token_size)
-{
-    if (input[input_pos] == '+')
-    {
-        *token_size = 1;
-        return true;
-    }
-    return false;
-}
-
-static bool token_is_plus(const char *input, int input_pos, int *token_size)
+// detect a single "-"
+static bool token_is_minus(const char *input, int input_pos, int *token_size)
+{
+    if (input[input_pos] == '-')
+    {
+        *token_size = 1;
+        return true;
+    }
+    return false;
+}
+
+// detect a single "*"
+static bool token_is_multiplication(const char *input, int input_pos, int *token_size)
+{
+    if (input[input_pos] == '*')
+    {
+        *token_size = 1;
+        return true;
+    }
+    return false;
+}
+
+// detect a single "/"
+static bool token_is_division(const char *input, int input_pos, int *token_size)
 {
     if (input[input_pos] == '+')
     {
@@ -117,6 +116,9 @@ static bool token_is_plus(const char *input, int input_pos, int *token_size)
     return false;
 }
 
+/**
+ * LEXER
+ */
 int lexerize(const char *input, token tokens[MAX_TOKENS])
 {
     int token_count;
@@ -143,7 +145,7 @@ int lexerize(const char *input, token tokens[MAX_TOKENS])
         else if (token_is_number(input, input_pos, &token_size))
         {
             tokens[token_count].type = TOKEN_NUMBER;
-            tokens[token_count].num_value = ft_atoi(input[input_pos]);
+            tokens[token_count].num_value = ft_atoi(&input[input_pos]);
         }
         else if (token_is_power(input, input_pos, &token_size))
         {