move tests on circuits (dag)

examples/flat.rs

@@ -1,9 +1,7 @@
-use circuit_cas::poly::flat;
 use circuit_cas::var;
 
 fn main() {
-    let poly = (2
+    let poly = (2 * ((var!("x", 1, 5) ^ 5) * (var!("x", 1, 2) ^ 5) * (var!("x", 2, 5) ^ 1)))
-        * ((var!("x", 1, 5) ^ 5) * (var!("x", 1, 2) ^ 5) * (var!("x", 2, 5) ^ 1)))
         + (3 * ((var!("x", 1, 9) ^ 5) * (var!("x", 1, 2) ^ 5) * (var!("x", 2, 5) ^ 1)));
 
     let x = var!("x");
@@ -11,13 +9,13 @@ fn main() {
     let z = var!("z");
     let other = -3 * ((&x ^ 2) * (&y ^ 4));
 
-    let mono = (&x^2)*(&y^4);
+    let mono = (&x ^ 2) * (&y ^ 4);
 
-    let inside = (&x^2)*(&y^2)*(&z^1);
+    let inside = (&x ^ 2) * (&y ^ 2) * (&z ^ 1);
 
-    if mono.contains(&inside){
+    if mono.contains(&inside) {
         println!("{inside}\u{2286}{mono}");
-    }else{
+    } else {
         println!("{inside}\u{2284}{mono}");
     }
 

src/circuit/dag.rs

@@ -1,4 +1,4 @@
-use slotmap::{new_key_type, SlotMap};
+use slotmap::{SlotMap, new_key_type};
 use std::cell::RefCell;
 use std::collections::HashMap;
 use std::ops::{Add, Mul};
@@ -15,6 +15,17 @@ pub enum Node<V: Var> {
     Prod(NodeId, NodeId),
 }
 
+impl<V: Var> Node<V> {
+    pub fn children(&self) -> impl Iterator<Item = NodeId> {
+        match self {
+            Node::Leaf(_) => [None, None],
+            Node::Sum(l, r) | Node::Prod(l, r) => [Some(*l), Some(*r)],
+        }
+        .into_iter()
+        .flatten()
+    }
+}
+
 pub struct Circuit<V: Var> {
     nodes: SlotMap<NodeId, Node<V>>,
     intern: HashMap<Node<V>, NodeId>,
@@ -41,6 +52,32 @@ impl<V: Var> Circuit<V> {
         self.nodes.get(id)
     }
 
+    pub fn add(&mut self, left: NodeId, right: NodeId) -> NodeId {
+        let (l, r) = if left <= right {
+            (left, right)
+        } else {
+            (right, left)
+        };
+        self.node(Node::Sum(l, r))
+    }
+
+    pub fn mul(&mut self, left: NodeId, right: NodeId) -> NodeId {
+        let (l, r) = if left <= right {
+            (left, right)
+        } else {
+            (right, left)
+        };
+        self.node(Node::Prod(l, r))
+    }
+
+    pub fn len(&self) -> usize {
+        self.nodes.len()
+    }
+
+    pub fn children(&self, id: NodeId) -> impl Iterator<Item = NodeId> + '_ {
+        self.nodes.get(id).into_iter().flat_map(Node::children)
+    }
+
     pub fn remove(&mut self, id: NodeId) {
         if let Some(node) = self.nodes.remove(id) {
             self.intern.remove(&node);
@@ -52,15 +89,26 @@ pub struct CircuitNode<V: Var> {
     pub id: NodeId,
     circuit: Rc<RefCell<Circuit<V>>>,
 }
-
 pub trait CircuitExt<V: Var> {
     fn leaf(&self, v: V) -> CircuitNode<V>;
+    fn get_node(&self, id: NodeId) -> Option<CircuitNode<V>>;
 }
 
 impl<V: Var> CircuitExt<V> for Rc<RefCell<Circuit<V>>> {
     fn leaf(&self, v: V) -> CircuitNode<V> {
         let id = self.borrow_mut().node(Node::Leaf(v));
-        CircuitNode { id, circuit: self.clone() }
+        CircuitNode {
+            id,
+            circuit: self.clone(),
+        }
+    }
+
+    fn get_node(&self, id: NodeId) -> Option<CircuitNode<V>> {
+        self.borrow().get(id)?;
+        Some(CircuitNode {
+            id,
+            circuit: self.clone(),
+        })
     }
 }
 
@@ -68,8 +116,11 @@ impl<V: Var> Add for CircuitNode<V> {
     type Output = Self;
 
     fn add(self, rhs: Self) -> Self {
-        let id = self.circuit.borrow_mut().node(Node::Sum(self.id, rhs.id));
+        let id = self.circuit.borrow_mut().add(self.id, rhs.id);
-        CircuitNode { id, circuit: self.circuit }
+        CircuitNode {
+            id,
+            circuit: self.circuit,
+        }
     }
 }
 
@@ -77,7 +128,10 @@ impl<V: Var> Mul for CircuitNode<V> {
     type Output = Self;
 
     fn mul(self, rhs: Self) -> Self {
-        let id = self.circuit.borrow_mut().node(Node::Prod(self.id, rhs.id));
+        let id = self.circuit.borrow_mut().mul(self.id, rhs.id);
-        CircuitNode { id, circuit: self.circuit }
+        CircuitNode {
+            id,
+            circuit: self.circuit,
+        }
     }
 }

src/circuit/mod.rs

@@ -1 +1,6 @@
 pub mod dag;
+pub mod quotient;
+
+#[cfg(test)]
+mod tests;
+

src/circuit/quotient.rs

@@ -0,0 +1 @@
+

src/circuit/tests.rs

@@ -0,0 +1,53 @@
+
+use std::cell::RefCell;
+use std::rc::Rc;
+
+use super::dag::{Circuit, CircuitExt};
+use crate::poly::var::StaticVar;
+
+#[test]
+fn test_deduplication() {
+    let circuit = Rc::new(RefCell::new(Circuit::new()));
+
+    // Same leaf constructed twice returns the same NodeId
+    let x1 = circuit.leaf(StaticVar::from("x"));
+    let x2 = circuit.leaf(StaticVar::from("x"));
+    assert_eq!(x1.id, x2.id);
+    assert_eq!(circuit.borrow().len(), 1);
+
+    // Same sum constructed twice returns the same NodeId
+    let _y = circuit.leaf(StaticVar::from("y"));
+    let sum1 = circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y"));
+    let sum2 = circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y"));
+    assert_eq!(sum1.id, sum2.id);
+    assert_eq!(circuit.borrow().len(), 3); // x, y, x+y
+
+    // Shared subexpression: (x + y) * (x + y) reuses the x+y node
+    let xy = circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y"));
+    let xy2 = circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y"));
+    let _sq = xy * xy2;
+    assert_eq!(circuit.borrow().len(), 4); // x, y, x+y, (x+y)*(x+y)
+
+    // Commutativity: x+y and y+x are the same node
+    let xy = circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y"));
+    let yx = circuit.leaf(StaticVar::from("y")) + circuit.leaf(StaticVar::from("x"));
+    assert_eq!(xy.id, yx.id);
+
+    // Associativity: (x+y)+z and x+(y+z) are distinct nodes
+    let _z = circuit.leaf(StaticVar::from("z"));
+    let xy_z = (circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y")))
+        + circuit.leaf(StaticVar::from("z"));
+    let x_yz = circuit.leaf(StaticVar::from("x"))
+        + (circuit.leaf(StaticVar::from("y")) + circuit.leaf(StaticVar::from("z")));
+    assert_ne!(xy_z.id, x_yz.id);
+
+    // Deep shared structure: (x+y)*z appears twice in ((x+y)*z) + ((x+y)*z)
+    let xyz1 = (circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y")))
+        * circuit.leaf(StaticVar::from("z"));
+    let xyz2 = (circuit.leaf(StaticVar::from("x")) + circuit.leaf(StaticVar::from("y")))
+        * circuit.leaf(StaticVar::from("z"));
+    assert_eq!(xyz1.id, xyz2.id);
+    let _sum = xyz1 + xyz2;
+    // x, y, z, x+y(==y+x), (x+y)*z, (x+y)+z, y+z, x+(y+z), (x+y)*z+(x+y)*z, sq
+    assert_eq!(circuit.borrow().len(), 10);
+}

src/fmt.rs

@@ -1,34 +1,35 @@
-
+pub fn num_to_subscript(s: String) -> String {
-pub fn num_to_subscript(s:String)->String{
+    s.chars()
-    s.chars().map(|c| match c{
+        .map(|c| match c {
-        '0'=>'\u{2080}',
+            '0' => '\u{2080}',
-        '1'=>'\u{2081}',
+            '1' => '\u{2081}',
-        '2'=>'\u{2082}',
+            '2' => '\u{2082}',
-        '3'=>'\u{2083}',
+            '3' => '\u{2083}',
-        '4'=>'\u{2084}',
+            '4' => '\u{2084}',
-        '5'=>'\u{2085}',
+            '5' => '\u{2085}',
-        '6'=>'\u{2086}',
+            '6' => '\u{2086}',
-        '7'=>'\u{2087}',
+            '7' => '\u{2087}',
-        '8'=>'\u{2088}',
+            '8' => '\u{2088}',
-        '9'=>'\u{2089}',
+            '9' => '\u{2089}',
-        _=>c
+            _ => c,
-    }).collect()
+        })
+        .collect()
 }
 
-pub fn num_to_superscript(s:String)->String{
+pub fn num_to_superscript(s: String) -> String {
-    s.chars().map(|c| match c{
+    s.chars()
-        '0'=>'\u{2070}',
+        .map(|c| match c {
-        '1'=>'\u{20B9}',
+            '0' => '\u{2070}',
-        '2'=>'\u{00B2}',
+            '1' => '\u{20B9}',
-        '3'=>'\u{00B3}',
+            '2' => '\u{00B2}',
-        '4'=>'\u{2074}',
+            '3' => '\u{00B3}',
-        '5'=>'\u{2075}',
+            '4' => '\u{2074}',
-        '6'=>'\u{2076}',
+            '5' => '\u{2075}',
-        '7'=>'\u{2077}',
+            '6' => '\u{2076}',
-        '8'=>'\u{2078}',
+            '7' => '\u{2077}',
-        '9'=>'\u{2079}',
+            '8' => '\u{2078}',
-        _=>c
+            '9' => '\u{2079}',
-    }).collect()
+            _ => c,
+        })
+        .collect()
 }
-
-

src/lib.rs

@@ -1,3 +1,3 @@
-pub mod poly;
 pub mod circuit;
 pub mod fmt;
+pub mod poly;

src/poly/flat.rs

@@ -1,15 +1,10 @@
-use itertools::Itertools;
-use std::fmt::{self, Display};
-
-use std::ops::{Add, BitXor, Mul, Sub};
-
-use super::var::{StaticVar, Var};
-use crate::fmt::num_to_superscript;
 use std::collections::HashMap;
 
+use super::var::Var;
+
 #[derive(Clone, Debug, PartialEq)]
 pub struct Poly<V: Var> {
-    mono: HashMap<Mono<V>, i32>,
+    pub(crate) mono: HashMap<Mono<V>, i32>,
 }
 
 impl<V: Var> Default for Poly<V> {
@@ -20,22 +15,6 @@ impl<V: Var> Default for Poly<V> {
     }
 }
 
-impl<V: Var> Display for Poly<V> {
-    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
-        match self.mono.is_empty() {
-            true => write!(fmt, "∅"),
-            false => write!(
-                fmt,
-                "{}",
-                self.mono
-                    .iter()
-                    .map(|(m, c)| format!("{}{}", c, m))
-                    .join(" + ")
-            ),
-        }
-    }
-}
-
 impl<V: Var, T: IntoIterator> From<T> for Poly<V>
 where
     Poly<V>: FromIterator<<T as IntoIterator>::Item>,
@@ -53,7 +32,7 @@ impl<V: Var, U: Into<Mono<V>>> FromIterator<(i32, U)> for Poly<V> {
     }
 }
 
-#[derive(Clone, Debug, Default, PartialEq, Eq, Hash)]
+#[derive(Clone, Debug, Default, PartialEq, Eq, Hash, PartialOrd, Ord)]
 pub struct Mono<V: Var> {
     pub term: Vec<(V, u32)>,
 }
@@ -103,224 +82,12 @@ impl<V: Var, U: Into<V>> FromIterator<(U, u32)> for Mono<V> {
         term.sort();
 
         // Check duplicate variables
-        assert!((term[..])
+        assert!(
+            (term[..])
                 .windows(2)
-            .all(|window| window[0].0 != window[1].0));
+                .all(|window| window[0].0 != window[1].0)
+        );
 
         Mono { term }
     }
 }
-
-impl<V: Var> Display for Mono<V> {
-    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
-        write!(
-            fmt,
-            "{}",
-            self.term
-                .iter()
-                .map(|(t, p)| match p {
-                    1 => format!("{t}"),
-                    _ => format!("{t}{}", num_to_superscript(p.to_string())),
-                })
-                .join("")
-        )
-    }
-}
-
-impl BitXor<u32> for StaticVar {
-    type Output = Mono<StaticVar>;
-
-    fn bitxor(self, exp: u32) -> Self::Output {
-        [(self, exp)].into()
-    }
-}
-
-impl<'a> BitXor<u32> for &'a StaticVar {
-    type Output = Mono<StaticVar>;
-
-    fn bitxor(self, exp: u32) -> Self::Output {
-        [(self.clone(), exp)].into()
-    }
-}
-
-impl<V: Var> Mul for Mono<V> {
-    type Output = Self;
-
-    fn mul(self, other: Mono<V>) -> Self::Output {
-        let mut a_term = self.term.into_iter().peekable();
-        let mut b_term = other.term.into_iter().peekable();
-
-        let mut result: Vec<(V, u32)> = Default::default();
-
-        loop {
-            match (a_term.peek(), b_term.peek()) {
-                (Some((a_var, _)), Some((b_var, _))) => {
-                    if a_var < b_var {
-                        result.push(a_term.next().unwrap());
-                    } else if a_var > b_var {
-                        result.push(b_term.next().unwrap());
-                    } else {
-                        let (var, a_exp) = a_term.next().unwrap();
-                        let (_, b_exp) = b_term.next().unwrap();
-                        result.push((var, a_exp + b_exp));
-                    }
-                }
-                (Some(a), None) => {
-                    result.push(a.clone());
-                    a_term.next();
-                }
-                (None, Some(b)) => {
-                    result.push(b.clone());
-                    b_term.next();
-                }
-                (None, None) => {
-                    break;
-                }
-            }
-        }
-
-        Mono { term: result }
-    }
-}
-
-impl<V: Var> Mul<Mono<V>> for i32 {
-    type Output = Poly<V>;
-
-    fn mul(self, mono: Mono<V>) -> Self::Output {
-        let mut poly: HashMap<Mono<V>, i32> = Default::default();
-
-        poly.insert(mono, self);
-
-        Poly { mono: poly }
-    }
-}
-
-impl<V: Var> Add for Poly<V> {
-    type Output = Poly<V>;
-
-    fn add(mut self, other: Poly<V>) -> Self::Output {
-        for (mono, coeff) in other.mono {
-            let entry = self.mono.entry(mono).or_insert(0);
-            *entry += coeff;
-        }
-        self.mono.retain(|_, &mut coeff| coeff != 0);
-        self
-    }
-}
-
-impl<V: Var> Sub for Poly<V> {
-    type Output = Poly<V>;
-
-    fn sub(mut self, other: Poly<V>) -> Self::Output {
-        for (mono, coeff) in other.mono {
-            let entry = self.mono.entry(mono).or_insert(0);
-            *entry -= coeff;
-        }
-        self.mono.retain(|_, &mut coeff| coeff != 0);
-        self
-    }
-}
-
-#[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());
-    }
-}

src/poly/fmt.rs

@@ -0,0 +1,57 @@
+use std::fmt::{self, Display, Formatter};
+
+use itertools::Itertools;
+
+use crate::fmt::{num_to_subscript, num_to_superscript};
+use crate::poly::flat::{Mono, Poly};
+use crate::poly::var::{StaticVar, Var};
+
+impl Display for StaticVar {
+    fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), fmt::Error> {
+        let num_indices = self.indices.len();
+        match num_indices {
+            0 => write!(fmt, "{}", self.name),
+            _ => write!(
+                fmt,
+                "{}{}",
+                self.name,
+                self.indices
+                    .iter()
+                    .map(|x: &u32| num_to_subscript(x.to_string()))
+                    .join(",")
+            ),
+        }
+    }
+}
+
+impl<V: Var> Display for Poly<V> {
+    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
+        match self.mono.is_empty() {
+            true => write!(fmt, "∅"),
+            false => write!(
+                fmt,
+                "{}",
+                self.mono
+                    .iter()
+                    .map(|(m, c)| format!("{}{}", c, m))
+                    .join(" + ")
+            ),
+        }
+    }
+}
+
+impl<V: Var> Display for Mono<V> {
+    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
+        write!(
+            fmt,
+            "{}",
+            self.term
+                .iter()
+                .map(|(t, p)| match p {
+                    1 => format!("{t}"),
+                    _ => format!("{t}{}", num_to_superscript(p.to_string())),
+                })
+                .join("")
+        )
+    }
+}

src/poly/mod.rs

@@ -1,2 +1,7 @@
 pub mod flat;
+pub mod fmt;
+pub mod ops;
 pub mod var;
+
+#[cfg(test)]
+mod tests;

src/poly/ops.rs

@@ -0,0 +1,115 @@
+use std::collections::HashMap;
+use std::ops::{Add, BitXor, Mul, Sub};
+
+use crate::poly::flat::{Mono, Poly};
+use crate::poly::var::{StaticVar, Var};
+
+impl BitXor<u32> for StaticVar {
+    type Output = Mono<StaticVar>;
+
+    fn bitxor(self, exp: u32) -> Self::Output {
+        [(self, exp)].into()
+    }
+}
+
+impl<'a> BitXor<u32> for &'a StaticVar {
+    type Output = Mono<StaticVar>;
+
+    fn bitxor(self, exp: u32) -> Self::Output {
+        [(self.clone(), exp)].into()
+    }
+}
+
+impl<V: Var> Mul for Mono<V> {
+    type Output = Self;
+
+    fn mul(self, other: Mono<V>) -> Self::Output {
+        let mut a_term = self.term.into_iter().peekable();
+        let mut b_term = other.term.into_iter().peekable();
+
+        let mut result: Vec<(V, u32)> = Default::default();
+
+        loop {
+            match (a_term.peek(), b_term.peek()) {
+                (Some((a_var, _)), Some((b_var, _))) => {
+                    if a_var < b_var {
+                        result.push(a_term.next().unwrap());
+                    } else if a_var > b_var {
+                        result.push(b_term.next().unwrap());
+                    } else {
+                        let (var, a_exp) = a_term.next().unwrap();
+                        let (_, b_exp) = b_term.next().unwrap();
+                        result.push((var, a_exp + b_exp));
+                    }
+                }
+                (Some(a), None) => {
+                    result.push(a.clone());
+                    a_term.next();
+                }
+                (None, Some(b)) => {
+                    result.push(b.clone());
+                    b_term.next();
+                }
+                (None, None) => {
+                    break;
+                }
+            }
+        }
+
+        Mono { term: result }
+    }
+}
+
+impl<V: Var> Mul<Mono<V>> for i32 {
+    type Output = Poly<V>;
+
+    fn mul(self, mono: Mono<V>) -> Self::Output {
+        let mut poly: HashMap<Mono<V>, i32> = Default::default();
+
+        poly.insert(mono, self);
+
+        Poly { mono: poly }
+    }
+}
+
+impl<V: Var> Mul for Poly<V> {
+    type Output = Poly<V>;
+
+    fn mul(self, other: Poly<V>) -> Self::Output {
+        let mut result = Poly::default();
+        for (m1, c1) in &self.mono {
+            for (m2, c2) in &other.mono {
+                let entry = result.mono.entry(m1.clone() * m2.clone()).or_insert(0i32);
+                *entry += c1 * c2;
+            }
+        }
+        result.mono.retain(|_, &mut c| c != 0);
+        result
+    }
+}
+
+impl<V: Var> Add for Poly<V> {
+    type Output = Poly<V>;
+
+    fn add(mut self, other: Poly<V>) -> Self::Output {
+        for (mono, coeff) in other.mono {
+            let entry = self.mono.entry(mono).or_insert(0);
+            *entry += coeff;
+        }
+        self.mono.retain(|_, &mut coeff| coeff != 0);
+        self
+    }
+}
+
+impl<V: Var> Sub for Poly<V> {
+    type Output = Poly<V>;
+
+    fn sub(mut self, other: Poly<V>) -> Self::Output {
+        for (mono, coeff) in other.mono {
+            let entry = self.mono.entry(mono).or_insert(0);
+            *entry -= coeff;
+        }
+        self.mono.retain(|_, &mut coeff| coeff != 0);
+        self
+    }
+}

src/poly/tests.rs

@@ -0,0 +1,101 @@
+use super::flat::{Mono, Poly};
+use super::var::StaticVar;
+
+#[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());
+}

src/poly/var.rs

@@ -1,27 +1,14 @@
-use itertools::Itertools;
+use std::fmt::{Debug, Display};
-use std::fmt::{self, Debug, Display, Formatter};
 use std::hash::Hash;
 
-use crate::fmt::num_to_subscript;
-
 #[derive(Clone, Debug, PartialEq, Eq, Hash, PartialOrd, Ord)]
 pub struct StaticVar {
-    name: &'static str,
+    pub(crate) name: &'static str,
-    indices: Vec<u32>,
+    pub(crate) indices: Vec<u32>,
 }
 
 pub trait Var: PartialEq + Eq + PartialOrd + Ord + Clone + Hash + Debug + Display {}
 
-impl Display for StaticVar {
-    fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), fmt::Error> {
-        let num_indices = self.indices.len();
-        match num_indices {
-            0 => write!(fmt, "{}", self.name),
-            _ => write!(fmt, "{}{}", self.name, self.indices.iter().map(|x| num_to_subscript(x.to_string())).join(",")),
-        }
-    }
-}
-
 impl Var for StaticVar {}
 
 impl From<&'static str> for StaticVar {