diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ed8ebf5
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+__pycache__
\ No newline at end of file
diff --git a/example.py b/example.py
index 0a8f06e..c276946 100644
--- a/example.py
+++ b/example.py
@@ -1,7 +1,21 @@
-from legrandchien import *
+import legrandchien as lgc
 
 if __name__ == "__main__":
-    k = Const(3)
-    kk = Const(4)
+    g = lgc.Const(-10)
+    m = lgc.Const(1)
 
-    eq = k + kk
+    x = lgc.Var("x")
+
+    T = 0.5 * m * x.diff() * x.diff()
+    V = m * g * x
+    L = T - V
+
+    dL = L.diff()
+
+    dico = {
+        "x" : 0,
+        "d_x" : 1,
+        "d_d_x" : 1,
+    }
+
+    print(dL.evaluate(dico))
\ No newline at end of file
diff --git a/legrandchien.py b/legrandchien.py
index 14f94fe..202792e 100644
--- a/legrandchien.py
+++ b/legrandchien.py
@@ -20,13 +20,20 @@ class Const:
         self.value = value
         self.type = "Const"
 
+    
+    def evaluate(self, dico):
+        return self.value
+
+    def copy(self):
+        return Const(self.value)
+
     def __add__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) + Equation(
                 Operation.CONST,
                 None,
@@ -38,7 +45,7 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) + Equation(
                 Operation.VAR,
                 None,
@@ -50,16 +57,20 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) + other
         
+    def __radd__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) + self
+
     def __sub__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) - Equation(
                 Operation.CONST,
                 None,
@@ -71,7 +82,7 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) - Equation(
                 Operation.VAR,
                 None,
@@ -83,16 +94,20 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) - other
         
+    def __rsub__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) - self
+        
     def __mul__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) * Equation(
                 Operation.CONST,
                 None,
@@ -104,7 +119,7 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) * Equation(
                 Operation.VAR,
                 None,
@@ -116,16 +131,20 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) * other
         
+    def __rmul__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) * self
+        
     def __truediv__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) / Equation(
                 Operation.CONST,
                 None,
@@ -137,7 +156,7 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) / Equation(
                 Operation.VAR,
                 None,
@@ -149,8 +168,12 @@ class Const:
                 Operation.CONST,
                 None,
                 None,
-                self.value
+                self.copy()
             ) / other
+        
+    def __truediv__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) / self
 
 # var class
 class Var:
@@ -159,13 +182,22 @@ class Var:
         self.type = "Var"
         self.degree = degree
 
+    def copy(self):
+        return Var(self.name, self.degree)
+
+    def diff(self, n=1):
+        return Var("d_"+self.name, self.degree+n)
+    
+    def evaluate(self, dico):
+        return dico[self.name]
+
     def __add__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) + Equation(
                 Operation.CONST,
                 None,
@@ -177,7 +209,7 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) + Equation(
                 Operation.VAR,
                 None,
@@ -189,16 +221,20 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) + other
         
+    def __radd__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) + self
+        
     def __sub__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) - Equation(
                 Operation.CONST,
                 None,
@@ -210,7 +246,7 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) - Equation(
                 Operation.VAR,
                 None,
@@ -222,16 +258,20 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) - other
         
+    def __rsub__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) - self
+        
     def __mul__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) * Equation(
                 Operation.CONST,
                 None,
@@ -243,7 +283,7 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) * Equation(
                 Operation.VAR,
                 None,
@@ -255,16 +295,20 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) * other
         
+    def __rmul__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) * self
+        
     def __truediv__(self, other):
         if other.type == "Const":
             return Equation(
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) / Equation(
                 Operation.CONST,
                 None,
@@ -276,7 +320,7 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) / Equation(
                 Operation.VAR,
                 None,
@@ -288,8 +332,12 @@ class Var:
                 Operation.VAR,
                 None,
                 None,
-                self.name
+                self.copy()
             ) / other
+        
+    def __rtruediv__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) / self
 
 # equation class
 class Equation:
@@ -305,13 +353,13 @@ class Equation:
             return Const(self.value.value)
         if self.op == Operation.VAR:
             return Var(self.value.name, self.value.degree)
-        return Operation(self.op, self.left.copy(), self.right.copy(), None)
+        return Equation(self.op, self.left.copy(), self.right.copy(), None)
 
     def diff(self):
         if self.op == Operation.CONST:
-            return Const(0)
+            return Equation(Operation.CONST, None, None, Const(0))
         if self.op == Operation.VAR:
-            return Var(self.value.name, self.value.degree+1)
+            return Equation(Operation.VAR, None, None, Var("d_"+self.value.name, self.value.degree+1))
         if self.op == Operation.ADD:
             return self.left.diff() + self.right.diff()
         if self.op == Operation.SUB:
@@ -322,6 +370,39 @@ class Equation:
             return (self.left.diff()*self.right.copy() - self.left.copy()*self.right.diff()) \
                 / (self.right.copy()*self.right.copy())
         
+    def partial(self, var_name):
+        if self.op == Operation.CONST:
+            return Equation(Operation.CONST, None, None, Const(0))
+        if self.op == Operation.VAR:
+            if self.value.name == var_name:
+                return Equation(Operation.CONST, None, None, Const(1))
+            else:
+                return Equation(Operation.CONST, None, None, Const(0))
+        if self.op == Operation.ADD:
+            return self.left.partial(var_name) + self.right.partial(var_name)
+        if self.op == Operation.SUB:
+            return self.left.partial(var_name) - self.right.partial(var_name)
+        if self.op == Operation.MULT:
+            return self.left.partial(var_name)*self.right.copy() + self.left.copy()*self.right.partial(var_name)
+        if self.op == Operation.DIV:
+            return (self.left.partial(var_name)*self.right.copy() - self.left.copy()*self.right.partial(var_name)) \
+                / (self.right.copy()*self.right.copy())
+        
+    def evaluate(self, dico):
+        if self.op == Operation.CONST:
+            return self.value.value
+        if self.op == Operation.VAR:
+            return dico[self.value.name]
+        if self.op == Operation.ADD:
+            return self.left.evaluate(dico) + self.right.evaluate(dico)
+        if self.op == Operation.SUB:
+            return self.left.evaluate(dico) - self.right.evaluate(dico)
+        if self.op == Operation.MULT:
+            return self.left.evaluate(dico) * self.right.evaluate(dico)
+        if self.op == Operation.DIV:
+            return self.left.evaluate(dico) / self.right.evaluate(dico)
+        
+        
     def __add__(self, other):
         if other.type == "Const":
             return self + Equation(
@@ -340,6 +421,10 @@ class Equation:
         if other.type == "Equation":
             return Equation(Operation.ADD, self, other, None)
         
+    def __radd__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) + self
+        
     def __sub__(self, other):
         if other.type == "Const":
             return self - Equation(
@@ -358,6 +443,10 @@ class Equation:
         if other.type == "Equation":
             return Equation(Operation.SUB, self, other, None)
         
+    def __rsub__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) - self
+        
     def __mul__(self, other):
         if other.type == "Const":
             return self * Equation(
@@ -376,6 +465,10 @@ class Equation:
         if other.type == "Equation":
             return Equation(Operation.MULT, self, other, None)
         
+    def __rmul__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) * self
+        
     def __truediv__(self, other):
         if other.type == "Const":
             return self / Equation(
@@ -393,3 +486,7 @@ class Equation:
             )
         if other.type == "Equation":
             return Equation(Operation.DIV, self, other, None)
+        
+    def __rtruediv__(self, other):
+        if isinstance(other, (int, float)):
+            return Const(other) / self