diff --git a/src/lib.rs b/src/lib.rs
index 3b5a836..17fec59 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -4,16 +4,7 @@ use crate::parser::sanitizer::sanitize_tokens;
 use crate::parser::ast_builder::{build_ast, Node};
 
 pub mod parser;
-
-struct _Rational {
-    numerator: i128,
-    denominator: i128,
-}
-
-struct _GaussianRational {
-    real: _Rational,
-    imaginary: _Rational,
-}
+pub mod maths;
 
 pub fn parse(query: &str) -> Result<Node, Box<dyn Error>> {
     let tokens = tokenize(query)?;
@@ -109,8 +100,3 @@ pub fn solve(equation: Vec<f64>) {
         _ => unreachable!(),
     }
 }
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-}
diff --git a/src/maths.rs b/src/maths.rs
new file mode 100644
index 0000000..9d34d34
--- /dev/null
+++ b/src/maths.rs
@@ -0,0 +1,101 @@
+use std::ops;
+
+//TODO slow ? check Stein's algorithm (binaryGCD)
+fn gcd(a: i128, b: i128) -> i128 {
+    if b == 0 {
+        a
+    } else {
+        gcd(b, a % b)
+    }
+}
+
+#[derive(Debug, PartialEq, Clone)]
+pub struct Rational {
+    numerator: i128,
+    denominator: i128,
+}
+
+impl Rational {
+    pub fn new(numerator: i128, denominator: i128) -> Self {
+        Self {
+            numerator,
+            denominator,
+        }
+    }
+
+    pub fn reduce(&self) -> Self {
+        let gcd = gcd(self.numerator, self.denominator);
+        Rational::new(self.numerator / gcd, self.denominator / gcd)
+    }
+}
+
+impl ops::Add<Rational> for Rational {
+    type Output = Rational;
+
+    fn add(self, rhs: Rational) -> Rational {
+        Rational::new(self.numerator * rhs.denominator + rhs.numerator * self.denominator, self.denominator * rhs.denominator).reduce()
+    }
+}
+
+impl ops::Add<i128> for Rational {
+    type Output = Rational;
+
+    fn add(self, rhs: i128) -> Rational {
+        Rational::new(self.numerator + rhs * self.denominator, self.denominator).reduce()
+    }
+}
+
+impl ops::Add<Rational> for i128 {
+    type Output = Rational;
+
+    fn add(self, rhs: Rational) -> Rational {
+        Rational::new(self * rhs.denominator + rhs.numerator, rhs.denominator).reduce()
+    }
+}
+
+impl ops::Sub<Rational> for Rational {
+    type Output = Rational;
+
+    fn sub(self, rhs: Rational) -> Rational {
+        Rational::new(self.numerator * rhs.denominator - rhs.numerator * self.denominator, self.denominator * rhs.denominator).reduce()
+    }
+}
+
+impl ops::Mul<Rational> for Rational {
+    type Output = Rational;
+
+    fn mul(self, rhs: Rational) -> Rational {
+        Rational::new(self.numerator * rhs.numerator, self.denominator * rhs.denominator).reduce()
+    }
+}
+
+impl ops::Mul<i128> for Rational {
+    type Output = Rational;
+
+    fn mul(self, rhs: i128) -> Rational {
+        Rational::new(self.numerator * rhs, self.denominator).reduce()
+    }
+}
+
+impl ops::Mul<Rational> for i128 {
+    type Output = Rational;
+
+    fn mul(self, rhs: Rational) -> Rational {
+        Rational::new(self * rhs.numerator, rhs.denominator).reduce()
+    }
+}
+
+#[derive(Debug, PartialEq, Clone)]
+pub struct GaussianRational {
+    real: Rational,
+    imaginary: Rational,
+}
+
+impl GaussianRational {
+    pub fn new(real: Rational, imaginary: Rational) -> Self {
+        Self {
+            real,
+            imaginary,
+        }
+    }
+}
diff --git a/src/parser/ast_builder.rs b/src/parser/ast_builder.rs
index 9bb8038..550b86f 100644
--- a/src/parser/ast_builder.rs
+++ b/src/parser/ast_builder.rs
@@ -1,17 +1,5 @@
 use super::Token;
-
-#[derive(Debug, PartialEq, Clone)]
-pub struct Rational {
-    numerator: i128,
-    denominator: i128,
-}
-
-#[derive(Debug, PartialEq, Clone)]
-pub struct GaussianRational {
-    real: Rational,
-    imaginary: Rational,
-}
-
+use crate::maths::{GaussianRational, Rational};
 
 #[derive(Debug, PartialEq, Clone)]
 pub enum Node {
@@ -23,76 +11,37 @@ pub enum Node {
     }
 }
 
-/*
-   pub struct Node {
-   _lhs: Option<Box<Node>>,
-   _rhs: Option<Box<Node>>,
-   }
-   */
-
-fn zero() -> GaussianRational {
-    GaussianRational {
-        real: Rational {
-            numerator: 0,
-            denominator: 1,
-        },
-        imaginary: Rational {
-            numerator: 0,
-            denominator: 1,
-        }
-    }
+fn rational_zero() -> Rational {
+    Rational::new(0, 1)
 }
 
-fn minus_one() -> GaussianRational {
-    GaussianRational {
-        real: Rational {
-            numerator: -1,
-            denominator: 1,
-        },
-        imaginary: Rational {
-            numerator: 0,
-            denominator: 1,
-        }
-    }
+fn rational_one() -> Rational {
+    Rational::new(1, 1)
+}
+
+fn rational_minus_one() -> Rational {
+    Rational::new(-1, 1)
+}
+
+
+fn zero() -> GaussianRational {
+    GaussianRational::new(rational_zero(), rational_zero())
 }
 
 fn one() -> GaussianRational {
-    GaussianRational {
-        real: Rational {
-            numerator: 1,
-            denominator: 1,
-        },
-        imaginary: Rational {
-            numerator: 0,
-            denominator: 1,
-        }
-    }
+    GaussianRational::new(rational_one(), rational_zero())
+}
+
+fn minus_one() -> GaussianRational {
+    GaussianRational::new(rational_minus_one(), rational_zero())
 }
 
 fn i() -> GaussianRational {
-    GaussianRational {
-        real: Rational {
-            numerator: 0,
-            denominator: 1,
-        },
-        imaginary: Rational {
-            numerator: 1,
-            denominator: 1,
-        }
-    }
+    GaussianRational::new(rational_zero(), rational_one())
 }
 
 fn minus_i() -> GaussianRational {
-    GaussianRational {
-        real: Rational {
-            numerator: 0,
-            denominator: 1,
-        },
-        imaginary: Rational {
-            numerator: -1,
-            denominator: 1,
-        }
-    }
+    GaussianRational::new(rational_zero(), rational_minus_one())
 }
 
 fn x() -> Vec<GaussianRational> {
@@ -128,34 +77,25 @@ fn get_parentheses_map(tokens: &Vec<Token>) -> Vec<usize> {
 }
 
 fn parse_number(string: &String, sign: i128) -> GaussianRational {
-    let mut number = Rational {
-        numerator: 0,
-        denominator: 1,
-    };
+    let mut number = rational_zero();
     let mut is_floating = false;
 
     for c in string.chars() {
         match c {
             '.' => is_floating = true,
             '0'..='9' => {
-                number.numerator = 10 * number.numerator + String::from(c).parse::<i128>().unwrap();
+                number = 10 * number + String::from(c).parse::<i128>().unwrap();
                 if is_floating == true {
-                    number.denominator *= 10;
+                    number = number * Rational::new(1, 10);
                 }
             }
             _ => unreachable!(),
         }
     }
 
-    number.numerator *= sign;
+    number = number * sign;
 
-    GaussianRational {
-        real: number,
-        imaginary: Rational {
-            numerator: 0,
-            denominator: 1,
-        }
-    }
+    GaussianRational::new(number, rational_zero())
 }
 
 fn check_parentheses(tokens: &Vec<Token>) -> bool {
@@ -432,8 +372,7 @@ mod tests {
 
     #[test]
     fn two_plus_two() {
-        let mut two = one();
-        two.real.numerator = 2;
+        let two = GaussianRational::new(Rational::new(2, 1), rational_zero());
 
         let tokens = vec![two_token(), plus(), two_token()];
         let results = Node::Internal {