diff --git a/src/poly/flat.rs b/src/poly/flat.rs
index 16f7ac0..5c5df2a 100644
--- a/src/poly/flat.rs
+++ b/src/poly/flat.rs
@@ -1,13 +1,13 @@
 use itertools::Itertools;
 use std::fmt::{self, Display};
 
-use std::ops::{Add, Sub, BitXor, Mul};
+use std::ops::{Add, BitXor, Mul, Sub};
 
-use crate::fmt::num_to_superscript;
 use super::var::{StaticVar, Var};
+use crate::fmt::num_to_superscript;
 use std::collections::HashMap;
 
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 pub struct Poly<V: Var> {
     mono: HashMap<Mono<V>, i32>,
 }
@@ -58,25 +58,25 @@ pub struct Mono<V: Var> {
     pub term: Vec<(V, u32)>,
 }
 
-impl<V:Var> Mono<V>{
-    pub fn contains(&self, other:&Mono<V>)->bool{
-        let mut self_it=self.term.iter().peekable();
-        let mut other_it=other.term.iter().peekable();
+impl<V: Var> Mono<V> {
+    pub fn contains(&self, other: &Mono<V>) -> bool {
+        let mut self_it = self.term.iter().peekable();
+        let mut other_it = other.term.iter().peekable();
 
-        while let Some((o_term,o_exp))=other_it.peek(){
-            if let Some((s_term,s_exp))=self_it.peek(){
-                if s_term<o_term{
+        while let Some((o_term, o_exp)) = other_it.peek() {
+            if let Some((s_term, s_exp)) = self_it.peek() {
+                if s_term < o_term {
                     self_it.next();
                     continue;
-                }else if s_term>o_term{
+                } else if s_term > o_term {
                     return false;
-                }else if o_exp<=s_exp{
+                } else if o_exp <= s_exp {
                     self_it.next();
                     other_it.next();
-                }else{
+                } else {
                     return false;
                 }
-            }else{
+            } else {
                 return false;
             }
         }
@@ -103,11 +103,9 @@ impl<V: Var, U: Into<V>> FromIterator<(U, u32)> for Mono<V> {
         term.sort();
 
         // Check duplicate variables
-        assert!(
-            (term[..])
-                .windows(2)
-                .all(|window| window[0].0 != window[1].0)
-        );
+        assert!((term[..])
+            .windows(2)
+            .all(|window| window[0].0 != window[1].0));
 
         Mono { term }
     }
@@ -122,7 +120,7 @@ impl<V: Var> Display for Mono<V> {
                 .iter()
                 .map(|(t, p)| match p {
                     1 => format!("{t}"),
-                    _ => format!("{t}{}",num_to_superscript(p.to_string())),
+                    _ => format!("{t}{}", num_to_superscript(p.to_string())),
                 })
                 .join("")
         )
@@ -223,3 +221,106 @@ impl<V: Var> Sub for Poly<V> {
     }
 }
 
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_mono_contains() {
+        let a: Mono<StaticVar> = [("x", 2), ("y", 1)].into();
+
+        // Lower exponent of same variable is contained
+        assert!(a.contains(&Mono::from([("x", 1)])));
+
+        // Higher exponent of same variable is not contained
+        assert!(!a.contains(&Mono::from([("x", 3)])));
+
+        // Identical monomial is contained
+        assert!(a.contains(&Mono::from([("x", 2), ("y", 1)])));
+
+        // Variable absent from self is not contained
+        assert!(!a.contains(&Mono::from([("x", 2), ("z", 1)])));
+
+        // Subset of variables with lower exponents is contained
+        assert!(a.contains(&Mono::from([("x", 1), ("y", 1)])));
+
+        // Single variable with exact exponent is contained
+        assert!(a.contains(&Mono::from([("x", 2)])));
+
+        // Insufficient exponent in self means not contained
+        assert!(!Mono::<StaticVar>::from([("x", 1)]).contains(&Mono::from([("x", 2)])));
+
+        // Missing variable in self means not contained
+        assert!(!Mono::<StaticVar>::from([("x", 1), ("y", 1)]).contains(&Mono::from([("x", 2)])));
+        assert!(!Mono::<StaticVar>::from([("x", 1)]).contains(&Mono::from([("x", 1), ("y", 1)])));
+    }
+
+    #[test]
+    fn test_mono_mul() {
+        // Same variable: exponents add
+        let a: Mono<StaticVar> = [("x", 2)].into();
+        let b: Mono<StaticVar> = [("x", 3)].into();
+        assert_eq!(a * b, Mono::from([("x", 5)]));
+
+        // Disjoint variables: both appear in result
+        let a: Mono<StaticVar> = [("x", 2)].into();
+        let b: Mono<StaticVar> = [("y", 3)].into();
+        assert_eq!(a * b, Mono::from([("x", 2), ("y", 3)]));
+
+        // Mixed: shared and disjoint variables
+        let a: Mono<StaticVar> = [("x", 1), ("y", 2)].into();
+        let b: Mono<StaticVar> = [("y", 1), ("z", 3)].into();
+        assert_eq!(a * b, Mono::from([("x", 1), ("y", 3), ("z", 3)]));
+
+        // Commutativity
+        let a: Mono<StaticVar> = [("x", 2), ("z", 1)].into();
+        let b: Mono<StaticVar> = [("y", 3)].into();
+        assert_eq!(a.clone() * b.clone(), b * a);
+
+        // Multiply by constant monomial (empty term vec = 1)
+        let a: Mono<StaticVar> = [("x", 4)].into();
+        let one: Mono<StaticVar> = Mono { term: vec![] };
+        assert_eq!(a.clone() * one, a);
+    }
+
+    #[test]
+    fn test_poly_add() {
+        // Distinct monomials are collected as separate terms
+        let a: Poly<StaticVar> = [(1, [("x", 2)]), (2, [("y", 1)])].into();
+        let b: Poly<StaticVar> = [(3, [("z", 1)])].into();
+        let expected: Poly<StaticVar> = [(1, [("x", 2)]), (2, [("y", 1)]), (3, [("z", 1)])].into();
+        assert_eq!(a + b, expected);
+
+        // Coefficients of matching monomials are summed
+        let a: Poly<StaticVar> = [(2, [("x", 1)])].into();
+        let b: Poly<StaticVar> = [(3, [("x", 1)])].into();
+        let expected: Poly<StaticVar> = [(5, [("x", 1)])].into();
+        assert_eq!(a + b, expected);
+
+        // Terms that cancel sum to zero are dropped
+        let a: Poly<StaticVar> = [(1, [("x", 1)])].into();
+        let b: Poly<StaticVar> = [(-1, [("x", 1)])].into();
+        let expected: Poly<StaticVar> = Poly::default();
+        assert_eq!(a + b, expected);
+    }
+
+    #[test]
+    fn test_poly_sub() {
+        // Distinct monomials are collected as separate terms with negated rhs coefficients
+        let a: Poly<StaticVar> = [(3, [("x", 2)])].into();
+        let b: Poly<StaticVar> = [(1, [("y", 1)])].into();
+        let expected: Poly<StaticVar> = [(3, [("x", 2)]), (-1, [("y", 1)])].into();
+        assert_eq!(a - b, expected);
+
+        // Coefficients of matching monomials are subtracted
+        let a: Poly<StaticVar> = [(5, [("x", 1)])].into();
+        let b: Poly<StaticVar> = [(3, [("x", 1)])].into();
+        let expected: Poly<StaticVar> = [(2, [("x", 1)])].into();
+        assert_eq!(a - b, expected);
+
+        // Subtracting equal polynomials yields zero
+        let a: Poly<StaticVar> = [(4, [("x", 2)]), (1, [("y", 1)])].into();
+        let b: Poly<StaticVar> = [(4, [("x", 2)]), (1, [("y", 1)])].into();
+        assert_eq!(a - b, Poly::default());
+    }
+}