diff --git a/headers/errors.h b/headers/errors.h
index b153a81..49ef8e2 100644
--- a/headers/errors.h
+++ b/headers/errors.h
@@ -9,8 +9,9 @@ typedef enum
     ERROR_UNKNOWN_TOKEN = -1,
     ERROR_NUMBER_TOO_BIG = -2,
     ERROR_PARSING = -3,
+    ERROR_TOKEN_POSITION = -4,
 } program_error;
 
-int stop_errors(int err, const char *details);
+int stop_errors(program_error err, const char *details);
 
 #endif
\ No newline at end of file
diff --git a/headers/lexer.h b/headers/lexer.h
index ea9ab62..ae53511 100644
--- a/headers/lexer.h
+++ b/headers/lexer.h
@@ -7,13 +7,14 @@
 
 typedef enum
 {
-    TOKEN_VARIABLE, // x, y, etc.
-    TOKEN_NUMBER,   // int or double -> all converted into double
-    TOKEN_POWER,    // ^ or **
-    TOKEN_SIGN,     // + or -
-    TOKEN_FACTOR,   // * or /
-    TOKEN_EQUAL,    // =
-    TOKEN_END       // null (end of input)
+    TOKEN_VARIABLE,      // x, y, etc.
+    TOKEN_NUMBER_INT,    // int
+    TOKEN_NUMBER_DOUBLE, // double
+    TOKEN_POWER,         // ^ or **
+    TOKEN_SIGN,          // + or -
+    TOKEN_FACTOR,        // * or /
+    TOKEN_EQUAL,         // =
+    TOKEN_END            // null (end of input)
 } token_type;
 
 typedef struct
@@ -22,6 +23,7 @@ typedef struct
     union
     {
         char value_char;
+        int value_int;
         double value_double;
     };
 } token;
diff --git a/src/computorv1.c b/src/computorv1.c
index 5bc7e27..e0fe3e0 100644
--- a/src/computorv1.c
+++ b/src/computorv1.c
@@ -88,8 +88,10 @@ int main(int ac, char **av)
 
         if (tokens[i].type == TOKEN_VARIABLE)
             ft_printf("%20s", "TOKEN_VARIABLE");
-        else if (tokens[i].type == TOKEN_NUMBER)
-            ft_printf("%20s", "TOKEN_NUMBER");
+        else if (tokens[i].type == TOKEN_NUMBER_INT)
+            ft_printf("%20s", "TOKEN_NUMBER_INT");
+        else if (tokens[i].type == TOKEN_NUMBER_DOUBLE)
+            ft_printf("%20s", "TOKEN_NUMBER_DOUBLE");
         else if (tokens[i].type == TOKEN_POWER)
             ft_printf("%20s", "TOKEN_POWER");
         else if (tokens[i].type == TOKEN_SIGN)
@@ -103,7 +105,11 @@ int main(int ac, char **av)
 
         ft_putstr(" - value : ");
 
-        if (tokens[i].type == TOKEN_NUMBER)
+        if (tokens[i].type == TOKEN_NUMBER_INT)
+        {
+            printf("%i\n", tokens[i].value_int);
+        }
+        else if (tokens[i].type == TOKEN_NUMBER_DOUBLE)
         {
             printf("%g\n", tokens[i].value_double);
         }
diff --git a/src/errors.c b/src/errors.c
index 5fcc214..d8a7b84 100644
--- a/src/errors.c
+++ b/src/errors.c
@@ -1,6 +1,6 @@
 #include "errors.h"
 
-int stop_errors(int err, const char *details)
+int stop_errors(program_error err, const char *details)
 {
     switch (err)
     {
@@ -13,6 +13,9 @@ int stop_errors(int err, const char *details)
     case ERROR_PARSING:
         ft_putstr_fd("error: too much terms to parse, details : ", STDERR_FILENO);
         break;
+    case ERROR_TOKEN_POSITION:
+        ft_putstr_fd("error: token position is not good in grammar, details : ", STDERR_FILENO);
+        break;
     default:
         ft_putstr_fd("unknown error, details : ", STDERR_FILENO);
         break;
diff --git a/src/lexer.c b/src/lexer.c
index b87e21f..66982b5 100644
--- a/src/lexer.c
+++ b/src/lexer.c
@@ -11,8 +11,48 @@ static bool token_is_variable(const char *input, int input_pos, int *token_size)
     return false;
 }
 
-// number can be int "123" or double "123.456"
-static bool token_is_number(const char *input, int input_pos, int *token_size)
+// number can be int "123"
+static bool token_is_number_int(const char *input, int input_pos, int *token_size)
+{
+    int number_size;
+    int max_number_size;
+
+    if (!ft_isdigit(input[input_pos]))
+    {
+        return false;
+    }
+
+    number_size = 1;
+    max_number_size = 16; // max size for int
+    while (number_size <= max_number_size)
+    {
+        if (ft_isdigit(input[input_pos + number_size]))
+        {
+            number_size++;
+        }
+        else if (input[input_pos + number_size] == '.')
+        {
+            if (ft_isdigit(input[input_pos + number_size + 1]))
+            {
+                // number is double
+                return false;
+            }
+            else
+                break;
+        }
+        else
+            break;
+    }
+    if (number_size > max_number_size)
+    {
+        stop_errors(ERROR_NUMBER_TOO_BIG, &input[input_pos]);
+    }
+    *token_size = number_size;
+    return true;
+}
+
+// number can be double "123.456"
+static bool token_is_number_double(const char *input, int input_pos, int *token_size)
 {
     int number_size;
     int max_number_size;
@@ -147,9 +187,14 @@ int lexerize(const char *input, token *tokens)
             tokens[tokens_count].type = TOKEN_VARIABLE;
             tokens[tokens_count].value_char = 'x';
         }
-        else if (token_is_number(input, input_pos, &token_size))
+        else if (token_is_number_int(input, input_pos, &token_size))
         {
-            tokens[tokens_count].type = TOKEN_NUMBER;
+            tokens[tokens_count].type = TOKEN_NUMBER_INT;
+            tokens[tokens_count].value_int = ft_atoi(&input[input_pos]);
+        }
+        else if (token_is_number_double(input, input_pos, &token_size))
+        {
+            tokens[tokens_count].type = TOKEN_NUMBER_DOUBLE;
             tokens[tokens_count].value_double = ft_atof(&input[input_pos]);
         }
         else if (token_is_power(input, input_pos, &token_size))
diff --git a/src/parser.c b/src/parser.c
index d68a88e..1eee6d5 100644
--- a/src/parser.c
+++ b/src/parser.c
@@ -10,9 +10,9 @@
     TOKEN_EQUAL,         // =
     TOKEN_END            // null (end of input)
 
-    1. VARIABLE | NUMBER_INT | NUMBER_DOUBLE | POWER | SIGN | FACTOR | EQUAL | END
-    2. VARIABLE | NUMBER_INT | NUMBER_DOUBLE | POWER | SIGN | FACTOR | EQUAL | END
-    3. VARIABLE | NUMBER_INT | NUMBER_DOUBLE | POWER | SIGN | FACTOR | EQUAL | END
+    1.   VARIABLE |   NUMBER_INT |   NUMBER_DOUBLE | ! POWER |   SIGN | ! FACTOR | ! EQUAL | END
+    2.   VARIABLE |   NUMBER_INT |   NUMBER_DOUBLE |   POWER |   SIGN |   FACTOR |   EQUAL | END
+    3.   VARIABLE |   NUMBER_INT |   NUMBER_DOUBLE |   POWER |   SIGN |   FACTOR |   EQUAL | END
 
     term_position position;
     term_sign sign;
@@ -21,23 +21,52 @@
     int exponent;
  */
 
-static term_sign get_sign(token *tokens, int *token_count)
+static term_sign get_sign(token *tokens, int i, int *token_count)
 {
-    if (tokens)           // placeholder
-        *token_count = 1; // placeholder
-    return '+';           // placeholder
+    // forbidden tokens
+    if (tokens[i].type == TOKEN_POWER)
+    {
+        stop_errors(ERROR_TOKEN_POSITION, "at begining of term, we should not have a power token : " + tokens[i].value_char);
+    }
+    if (tokens[i].type == TOKEN_FACTOR)
+    {
+        stop_errors(ERROR_TOKEN_POSITION, "at begining of term, we should not have a factor token : " + tokens[i].value_char);
+    }
+    if (tokens[i].type == TOKEN_EQUAL)
+    {
+        stop_errors(ERROR_TOKEN_POSITION, "at begining of term, we should not have an equal token : " + tokens[i].value_char);
+    }
+
+    // sign
+    if (tokens[i].type == TOKEN_SIGN)
+    {
+        *token_count = 1;
+        return tokens[i].value_char;
+    }
+    else if (i == 0) // if most left term, the sign can be ommited for a '+' sign in front of a number or variable
+    {
+        *token_count = 1;
+        return '+';
+    }
+    else if (tokens[i - 1].type == TOKEN_EQUAL) // if first token after 'equal', the sign can be ommited for a '+' sign in front of a number or variable
+    {
+        *token_count = 1;
+        return '+';
+    }
+
+    return stop_errors(ERROR_TOKEN_POSITION, "at begining of term, we should have a sign token " + tokens[i].value_char);
 }
 
-static double get_coefficient(token *tokens, int *token_count)
+static double get_coefficient(token *tokens, int i, int *token_count)
 {
-    if (tokens)           // placeholder
+    if (tokens[i].type)   // placeholder
         *token_count = 1; // placeholder
     return 1.0;           // placeholder
 }
 
-static int get_exponent(token *tokens, int *token_count)
+static int get_exponent(token *tokens, int i, int *token_count)
 {
-    if (tokens)           // placeholder
+    if (tokens[i].type)   // placeholder
         *token_count = 1; // placeholder
     return 1;             // placeholder
 }
@@ -66,22 +95,22 @@ int parse(token *tokens, term *terms, int terms_count_max)
         terms[terms_count].position = term_position;
 
         // sign
-        terms[terms_count].sign = get_sign(&tokens[i], &token_count);
+        terms[terms_count].sign = get_sign(tokens, i, &token_count);
         i += token_count;
 
         // coefficient
-        terms[terms_count].coefficient = get_coefficient(&tokens[i], &token_count);
+        terms[terms_count].coefficient = get_coefficient(tokens, i, &token_count);
         i += token_count;
 
         // exponent
-        terms[terms_count].exponent = get_exponent(&tokens[i], &token_count);
+        terms[terms_count].exponent = get_exponent(tokens, i, &token_count);
         i += token_count;
 
         i++;
         terms_count++;
     }
 
-    // last token is TOKEN_END, and terms[] should have at least one more spot for a null
+    // last token is TOKEN_END, and terms[] should have at least one more spot for the END term
     if (tokens[i].type == TOKEN_END && terms_count < terms_count_max)
     {
         terms[terms_count].position = TERM_END;