improve var creation for SumProdCircuit

README.md

@@ -0,0 +1,134 @@
+# circuit-cas
+
+A computer algebra system in Rust for algebraic circuit verification over polynomial rings with integer coefficients.
+
+## Overview
+
+`circuit-cas` provides two main layers:
+
+- **`poly`** — multivariate polynomials over ℤ, Gröbner bases, and ideals
+- **`circuit`** — arithmetic circuits (DAGs of add/mul nodes) quotiented by an ideal
+
+The intended use case is verifying arithmetic circuits modulo an ideal: two circuits computing the same polynomial in the quotient ring are equivalent.
+
+## Modules
+
+### `poly`
+
+#### Variables — `poly::var`
+
+Variables are any type implementing the `Var` trait. The built-in `StaticVar` carries a static string name and optional integer indices, with a `var!` macro for construction:
+
+```rust
+use circuit_cas::var;
+
+let x   = var!("x");          // x
+let x0  = var!("x", 0);       // x₀
+let x01 = var!("x", 0, 1);    // x₀,₁
+```
+
+#### Polynomials — `poly::flat`
+
+`Poly<V>` is a multivariate polynomial over ℤ backed by a `HashMap<Mono<V>, i32>`. Arithmetic operators (`+`, `-`, `*`) and scalar multiplication are provided. Monomial ordering uses pure lexicographic order (lex) with variable names sorted alphabetically.
+
+```rust
+// x² - 2xy  (using array-of-pairs syntax)
+let f: Poly<StaticVar> = [
+    (1i32,  Mono::from([("x", 2u32)])),
+    (-2i32, Mono::from([("x", 1u32), ("y", 1u32)])),
+].into_iter().collect();
+```
+
+Key operations:
+
+| Method | Description |
+|--------|-------------|
+| `Poly::is_zero` | whether the polynomial is the zero polynomial |
+| `Poly::leading_term_lex` | leading `(monomial, coefficient)` under lex |
+| `Poly::s_poly(&other)` | S-polynomial of two polynomials |
+| `Poly::div_rem(divisor)` | pseudo-division: returns `(d, q, r)` with `lc(g)^d·f = q·g + r` |
+
+#### Ideals — `poly::ideal`
+
+`Ideal<V, S>` uses the typestate pattern to track at the type level whether its generators form a Gröbner basis:
+
+```rust
+use circuit_cas::poly::ideal::{Ideal, Generators, GroebnerBasis};
+
+// Arbitrary generators
+let ideal: Ideal<StaticVar, Generators> = Ideal::new(vec![f1, f2]);
+
+// Compute the reduced Gröbner basis — consumes the original ideal
+let gb: Ideal<StaticVar, GroebnerBasis> = ideal.groebner_basis();
+
+// Ideal membership test (only available on GroebnerBasis state)
+assert!(gb.contains(&some_poly));
+```
+
+`Ideal` implements `Display` as `<g1, g2, ...>` and `FromIterator<Poly<V>>` for construction from an iterator.
+
+#### Buchberger's algorithm — `poly::buchberger`
+
+```rust
+use circuit_cas::poly::buchberger::{groebner_basis, is_groebner_basis};
+
+let basis = groebner_basis(vec![f1, f2]);
+assert!(is_groebner_basis(&basis));
+```
+
+`groebner_basis` returns the **reduced** Gröbner basis: after running Buchberger's algorithm it minimizes (removes redundant generators) and interreduces (fully reduces each generator modulo the others).
+
+### `circuit`
+
+#### DAG — `circuit::dag`
+
+`Circuit<V>` is a DAG of `Node<V>` values, with structural sharing via interning. Nodes are `Leaf(V)`, `Scale(id, i32)`, `Sum(id, id)`, or `Prod(id, id)`.
+
+#### Quotient ring — `circuit::quotient`
+
+`Quotient<V>` pairs an arithmetic circuit with a `Ideal<V, GroebnerBasis>`, representing a circuit in the quotient ring `ℤ[vars] / I`.
+
+```rust
+use circuit_cas::circuit::quotient::Quotient;
+
+// Build from a list of generators — Gröbner basis is computed automatically
+let quotient: Quotient<StaticVar> = vec![f1, f2, f3].into_iter().collect();
+
+// Or from a pre-computed Gröbner basis
+let quotient = Quotient::from(gb);
+
+println!("{quotient}"); // C/<g1, g2>
+```
+
+## Example
+
+```rust
+use circuit_cas::{var, circuit::quotient::Quotient, poly::var::StaticVar};
+
+fn main() {
+    let x  = var!("x");
+    let xb = var!("x\u{0304}");  // x̄
+
+    // Idempotency relations: x² = x, x̄² = x̄, x·x̄ = x
+    let idem = vec![
+        1 * (&x  ^ 2) - 1 * (&x  ^ 1),
+        1 * (&xb ^ 2) - 1 * (&xb ^ 1),
+        1 * ((&x ^ 1) * (&xb ^ 1)) - 1 * (&x ^ 1),
+    ];
+
+    let quotient: Quotient<StaticVar> = idem.into_iter().collect();
+    println!("{quotient}");
+}
+```
+
+Run with:
+
+```
+cargo run --example quotient
+```
+
+## Development
+
+```
+cargo test     # run all tests
+```

examples/dag.rs

@@ -1,26 +1,25 @@
 use std::cell::RefCell;
 use std::rc::Rc;
-
-use circuit_cas::circuit::dag::{Circuit, CircuitExt};
-use circuit_cas::var;
+use circuit_cas::circuit::probabilistic::ProbCircuit;
+use circuit_cas::circuit::dag::CircuitExt;
 
 fn main() {
-    let circuit = Rc::new(RefCell::new(Circuit::new()));
+    let circuit: Rc<RefCell<ProbCircuit>> = ProbCircuit::new();
 
-    // Build (x + y) * (x + z)
-    let x = circuit.leaf(var!("x"));
-    let y = circuit.leaf(var!("y"));
-    let z = circuit.leaf(var!("z"));
+    // vars accept anything that implements Into<StaticVar>: &'static str, (&str, u32), (&str, u32, u32)
+    let x   = circuit.var("x");
+    let y   = circuit.var(("y", 1));       // indexed variable y_1
+    let z   = circuit.var(("z", 0, 1));    // doubly-indexed variable z_{0,1}
 
-    let x_plus_y = circuit.leaf(var!("x")) + y;
-    let x_plus_z = circuit.leaf(var!("x")) + z;
+    let x_plus_y = circuit.var("x") + y;
+    let x_plus_z = circuit.var("x") + z;
     let expr = x_plus_y * x_plus_z;
 
     // Deduplication: both x leaves share the same NodeId
-    let x2 = circuit.leaf(var!("x"));
+    let x2 = circuit.var("x");
     assert_eq!(x.id, x2.id);
 
-    println!("(x + y) * (x + z) root node id: {:?}", expr.id);
+    println!("(x + y_1) * (x + z_{{0,1}}) root node id: {:?}", expr.id);
     println!("x node id: {:?}", x.id);
     println!("x deduplicated node id: {:?}", x2.id);
 }

examples/quotient.rs

@@ -1,21 +1,31 @@
 use std::cell::RefCell;
 use std::rc::Rc;
-
-use circuit_cas::circuit::quotient::Quotient;
-use circuit_cas::poly::var::StaticVar;
+use circuit_cas::circuit::dag::CircuitExt;
+use circuit_cas::circuit::quotient::QuotientCircuit;
+use circuit_cas::circuit::traits::Circuit;
+use circuit_cas::poly::ideal::{Generators, Ideal};
 use circuit_cas::var;
 
 fn main() {
     let x = var!("x");
     let nx = var!("x\u{0304}");
 
-    let idem = vec![
+    let idem: Ideal<_, Generators> = vec![
         1 * (&x ^ 2) - 1 * (&x ^ 1),
         1 * (&nx ^ 2) - 1 * (&nx ^ 1),
         1 * ((&x ^ 1) * (&nx ^ 1)) - 1 * (&x ^ 1),
-    ];
+    ].into();
 
-    let mut quotient: Quotient<StaticVar> = idem.into_iter().collect();
+    let quotient: Rc<RefCell<QuotientCircuit>> = idem.into();
 
-    println!("{quotient}");
+    // Build x * x̄ + x in the DAG
+    // var accepts anything that implements Into<StaticVar>: &'static str, (&str, u32), (&str, u32, u32)
+    let xn   = quotient.var("x");
+    let nxn  = quotient.var("x\u{0304}");
+    let prod = xn * nxn;
+    let xn2  = quotient.var("x");
+    let expr = prod + xn2;
+
+    println!("dag size: {}", quotient.borrow().len());
+    println!("expr node id: {:?}", expr.id);
 }

src/circuit/dag.rs

@@ -1,57 +1,29 @@
 use slotmap::{SlotMap, new_key_type};
 use std::cell::RefCell;
 use std::collections::HashMap;
-use std::ops::{Add, Mul};
 use std::rc::Rc;
 
-use crate::poly::var::Var;
+use super::traits::{Circuit, Node};
 
 new_key_type! { pub struct NodeId; }
 
-#[derive(Clone, Debug, PartialEq, Eq, Hash)]
-pub enum Node<V: Var> {
-    Leaf(V),
-    Scale(NodeId, i32),
-    Sum(NodeId, NodeId),
-    Prod(NodeId, NodeId),
-}
-
-impl<V: Var> Node<V> {
-    pub fn children(&self) -> impl Iterator<Item = NodeId> {
-        match self {
-            Node::Leaf(_) => [None, None],
-            Node::Scale(n, _) => [Some(*n), None],
-            Node::Sum(l, r) | Node::Prod(l, r) => [Some(*l), Some(*r)],
-        }
-        .into_iter()
-        .flatten()
-    }
-}
-
 #[derive(Clone, Debug)]
-pub struct Circuit<V: Var> {
-    nodes: SlotMap<NodeId, Node<V>>,
-    intern: HashMap<Node<V>, NodeId>,
+pub struct Dag<N: Node> {
+    nodes: SlotMap<NodeId, N>,
+    intern: HashMap<N, NodeId>,
 }
 
-impl<V: Var> Default for Circuit<V> {
+impl<N: Node> Default for Dag<N> {
     fn default() -> Self {
-        Circuit {
+        Dag {
             nodes: Default::default(),
             intern: Default::default(),
         }
     }
 }
 
-impl<V: Var> Circuit<V> {
-    pub fn new() -> Self {
-        Circuit {
-            nodes: SlotMap::with_key(),
-            intern: HashMap::new(),
-        }
-    }
-
-    pub fn node(&mut self, n: Node<V>) -> NodeId {
+impl<N: Node> Dag<N> {
+    pub(super) fn node(&mut self, n: N) -> NodeId {
         if let Some(&id) = self.intern.get(&n) {
             return id;
         }
@@ -60,90 +32,33 @@ impl<V: Var> Circuit<V> {
         id
     }
 
-    pub fn get(&self, id: NodeId) -> Option<&Node<V>> {
+    pub(super) fn get(&self, id: NodeId) -> Option<&N> {
         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 {
+    pub(super) fn len(&self) -> usize {
         self.nodes.len()
     }
 
-    pub fn children(&self, id: NodeId) -> impl Iterator<Item = NodeId> + '_ {
+    pub(super) 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) {
+    pub(super) fn remove(&mut self, id: NodeId) {
         if let Some(node) = self.nodes.remove(id) {
             self.intern.remove(&node);
         }
     }
 }
 
-pub struct CircuitNode<V: Var> {
+pub struct RefNode<C: Circuit> {
     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>>;
+    pub(super) circuit: Rc<RefCell<C>>,
 }
 
-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(),
-        }
-    }
 
-    fn get_node(&self, id: NodeId) -> Option<CircuitNode<V>> {
-        self.borrow().get(id)?;
-        Some(CircuitNode {
-            id,
-            circuit: self.clone(),
-        })
-    }
-}
-
-impl<V: Var> Add for CircuitNode<V> {
-    type Output = Self;
-
-    fn add(self, rhs: Self) -> Self {
-        let id = self.circuit.borrow_mut().add(self.id, rhs.id);
-        CircuitNode {
-            id,
-            circuit: self.circuit,
-        }
-    }
-}
-
-impl<V: Var> Mul for CircuitNode<V> {
-    type Output = Self;
-
-    fn mul(self, rhs: Self) -> Self {
-        let id = self.circuit.borrow_mut().mul(self.id, rhs.id);
-        CircuitNode {
-            id,
-            circuit: self.circuit,
-        }
-    }
+pub trait CircuitExt {
+    type C: Circuit;
+    type Var;
+    fn var<T: Into<Self::Var>>(&self, v: T) -> RefNode<Self::C>;
 }

src/circuit/mod.rs

@@ -1,4 +1,6 @@
+pub mod traits;
 pub mod dag;
+pub mod probabilistic;
 pub mod quotient;
 
 #[cfg(test)]

src/circuit/probabilistic.rs

@@ -0,0 +1,68 @@
+use std::cell::RefCell;
+use std::ops::{Deref, DerefMut};
+use std::rc::Rc;
+
+use crate::poly::var::{StaticVar, Var};
+use super::dag::{Dag, NodeId};
+use super::traits::{Node, SumProdCircuit};
+
+
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub enum PNode<V: Var> {
+    Var(V),
+    Sum(NodeId, NodeId),
+    Prod(NodeId, NodeId),
+}
+
+impl<V: Var> Node for PNode<V> {
+    fn children(&self) -> impl Iterator<Item = NodeId> {
+        match self {
+            Self::Var(_) => [None, None],
+            Self::Sum(l, r) | Self::Prod(l, r) => [Some(*l), Some(*r)],
+        }
+        .into_iter()
+        .flatten()
+    }
+}
+
+#[derive(Clone, Debug)]
+pub struct ProbCircuit<V: Var = StaticVar> {
+    dag: Dag<PNode<V>>,
+}
+
+impl<V: Var> Default for ProbCircuit<V> {
+    fn default() -> Self { ProbCircuit { dag: Dag::default() } }
+}
+
+impl<V: Var> ProbCircuit<V> {
+    pub fn new() -> Rc<RefCell<Self>> {
+        Rc::new(RefCell::new(Self::default()))
+    }
+}
+
+impl<V: Var> SumProdCircuit for ProbCircuit<V> {
+    type Var = V;
+
+    fn var<T: Into<V>>(&mut self, v: T) -> NodeId { self.node(PNode::Var(v.into())) }
+
+    fn add(&mut self, l: NodeId, r: NodeId) -> NodeId {
+        let (l, r) = if l <= r { (l, r) } else { (r, l) };
+        self.node(PNode::Sum(l, r))
+    }
+
+    fn mul(&mut self, l: NodeId, r: NodeId) -> NodeId {
+        let (l, r) = if l <= r { (l, r) } else { (r, l) };
+        self.node(PNode::Prod(l, r))
+    }
+}
+
+impl<V: Var> Deref for ProbCircuit<V> {
+    type Target = Dag<PNode<V>>;
+    fn deref(&self) -> &Self::Target { &self.dag }
+}
+
+impl<V: Var> DerefMut for ProbCircuit<V> {
+    fn deref_mut(&mut self) -> &mut Self::Target { &mut self.dag }
+}
+
+

src/circuit/quotient.rs

@@ -1,44 +1,73 @@
-use super::dag::{Circuit, Node, NodeId};
-use crate::poly::{flat::Poly, var::Var};
+use std::cell::RefCell;
+use std::ops::{Deref, DerefMut};
+use std::rc::Rc;
 
-use itertools::Itertools;
+use crate::poly::var::{StaticVar, Var};
+use crate::poly::ideal::{Generators, GroebnerBasis, Ideal};
+use super::dag::{Dag, NodeId};
+use super::traits::{Node, SumProdCircuit};
 
-use std::fmt::{self, Display};
+
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub enum QNode<V: Var> {
+    Var(V),
+    Sum(NodeId, NodeId),
+    Prod(NodeId, NodeId),
+    DivStep(NodeId, NodeId),
+}
+
+impl<V: Var> Node for QNode<V> {
+    fn children(&self) -> impl Iterator<Item = NodeId> {
+        match self {
+            Self::Var(_) => [None, None],
+            Self::Sum(l, r) | Self::Prod(l, r) | Self::DivStep(l, r) => [Some(*l), Some(*r)],
+        }
+        .into_iter()
+        .flatten()
+    }
+}
 
 #[derive(Clone, Debug)]
-pub struct Quotient<V: Var> {
-    basis: Vec<Poly<V>>,
-    circuit: Circuit<V>,
+pub struct QuotientCircuit<V: Var = StaticVar> {
+    basis: Ideal<V, GroebnerBasis>,
+    dag: Dag<QNode<V>>,
 }
 
-impl<V: Var> FromIterator<Poly<V>> for Quotient<V> {
-    fn from_iter<T: IntoIterator<Item = Poly<V>>>(iter: T) -> Self {
-        Quotient {
-            basis: iter.into_iter().collect(),
-            circuit: Default::default(),
-        }
+impl<V: Var> From<Ideal<V, Generators>> for Rc<RefCell<QuotientCircuit<V>>> {
+    fn from(ideal: Ideal<V, Generators>) -> Self {
+        ideal.groebner_basis().into()
     }
 }
 
-impl<V: Var> Display for Quotient<V> {
-    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
-        write!(
-            fmt,
-            "C/<{}>",
-            self.basis.iter().map(|p| format!("{p}")).join(",")
-        )
+impl<V: Var> From<Ideal<V, GroebnerBasis>> for Rc<RefCell<QuotientCircuit<V>>> {
+    fn from(basis: Ideal<V, GroebnerBasis>) -> Self {
+        Rc::new(RefCell::new(QuotientCircuit { basis, dag: Default::default() }))
     }
 }
 
-impl<V: Var> Quotient<V> {
-    pub fn node(&mut self, n: Node<V>) -> NodeId {
-        self.circuit.node(n)
+impl<V: Var> Deref for QuotientCircuit<V> {
+    type Target = Dag<QNode<V>>;
+    fn deref(&self) -> &Self::Target { &self.dag }
+}
+
+impl<V: Var> DerefMut for QuotientCircuit<V> {
+    fn deref_mut(&mut self) -> &mut Self::Target { &mut self.dag }
+}
+
+impl<V: Var> SumProdCircuit for QuotientCircuit<V> {
+    type Var = V;
+
+    fn var<T: Into<V>>(&mut self, v: T) -> NodeId { self.node(QNode::Var(v.into())) }
+
+    fn add(&mut self, l: NodeId, r: NodeId) -> NodeId {
+        let (l, r) = if l <= r { (l, r) } else { (r, l) };
+        self.node(QNode::Sum(l, r))
     }
 
-    pub fn add(&mut self, left: NodeId, right: NodeId) -> NodeId {
-        self.circuit.add(left, right)
-    }
-    pub fn mul(&mut self, left: NodeId, right: NodeId) -> NodeId {
-        self.circuit.mul(left, right)
+    fn mul(&mut self, l: NodeId, r: NodeId) -> NodeId {
+        let (l, r) = if l <= r { (l, r) } else { (r, l) };
+        self.node(QNode::Prod(l, r))
     }
 }
+
+

src/circuit/tests.rs

@@ -1,50 +1,48 @@
 use std::cell::RefCell;
 use std::rc::Rc;
-
-use super::dag::{Circuit, CircuitExt};
-use crate::poly::var::StaticVar;
-
+use super::probabilistic::ProbCircuit;
+use super::dag::CircuitExt;
 #[test]
 fn test_deduplication() {
-    let circuit = Rc::new(RefCell::new(Circuit::new()));
+    let circuit: Rc<RefCell<ProbCircuit>> = ProbCircuit::new();
 
     // Same leaf constructed twice returns the same NodeId
-    let x1 = circuit.leaf(StaticVar::from("x"));
-    let x2 = circuit.leaf(StaticVar::from("x"));
+    let x1 = circuit.var("x");
+    let x2 = circuit.var("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"));
+    let _y = circuit.var("y");
+    let sum1 = circuit.var("x") + circuit.var("y");
+    let sum2 = circuit.var("x") + circuit.var("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 xy = circuit.var("x") + circuit.var("y");
+    let xy2 = circuit.var("x") + circuit.var("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"));
+    let xy = circuit.var("x") + circuit.var("y");
+    let yx = circuit.var("y") + circuit.var("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")));
+    let _z = circuit.var("z");
+    let xy_z = (circuit.var("x") + circuit.var("y"))
+        + circuit.var("z");
+    let x_yz = circuit.var("x")
+        + (circuit.var("y") + circuit.var("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"));
+    let xyz1 = (circuit.var("x") + circuit.var("y"))
+        * circuit.var("z");
+    let xyz2 = (circuit.var("x") + circuit.var("y"))
+        * circuit.var("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

src/circuit/traits.rs

@@ -0,0 +1,63 @@
+use std::cell::RefCell;
+use std::hash::Hash;
+use std::ops::{Add, DerefMut, Mul};
+use std::rc::Rc;
+
+use super::dag::{CircuitExt, Dag, NodeId, RefNode};
+
+pub trait Node: Clone + PartialEq + Eq + Hash {
+    fn children(&self) -> impl Iterator<Item = NodeId>;
+}
+
+pub trait Circuit: Clone + DerefMut<Target = Dag<Self::Node>> {
+    type Node: Node;
+
+    fn node(&mut self, n: Self::Node) -> NodeId { (**self).node(n) }
+    fn remove(&mut self, id: NodeId) { (**self).remove(id) }
+    fn get(&self, id: NodeId) -> Option<&Self::Node> { (**self).get(id) }
+    fn len(&self) -> usize { (**self).len() }
+    fn children(&self, id: NodeId) -> impl Iterator<Item = NodeId> + '_ { (**self).children(id) }
+}
+
+impl<T, N> Circuit for T
+where
+    T: Clone + DerefMut<Target = Dag<N>>,
+    N: Node,
+{
+    type Node = N;
+}
+
+pub trait SumProdCircuit: Circuit {
+    type Var;
+    fn var<T: Into<Self::Var>>(&mut self, v: T) -> NodeId;
+    fn add(&mut self, l: NodeId, r: NodeId) -> NodeId;
+    fn mul(&mut self, l: NodeId, r: NodeId) -> NodeId;
+}
+
+impl<C: SumProdCircuit> Add for RefNode<C> {
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self {
+        let id = self.circuit.borrow_mut().add(self.id, rhs.id);
+        RefNode { id, circuit: self.circuit }
+    }
+}
+
+impl<C: SumProdCircuit> Mul for RefNode<C> {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self {
+        let id = self.circuit.borrow_mut().mul(self.id, rhs.id);
+        RefNode { id, circuit: self.circuit }
+    }
+}
+
+impl<C: SumProdCircuit> CircuitExt for Rc<RefCell<C>> {
+    type C = C;
+    type Var = C::Var;
+
+    fn var<T: Into<C::Var>>(&self, v: T) -> RefNode<C> {
+        let id = self.borrow_mut().var(v);
+        RefNode { id, circuit: self.clone() }
+    }
+}

src/poly/flat.rs

@@ -4,8 +4,8 @@ use std::collections::HashMap;
 use super::var::Var;
 
 pub fn lex_cmp<V: Var>(a: &Mono<V>, b: &Mono<V>) -> Ordering {
-    let mut a_it = a.term.iter().peekable();
-    let mut b_it = b.term.iter().peekable();
+    let mut a_it = a.vars.iter().peekable();
+    let mut b_it = b.vars.iter().peekable();
 
     loop {
         match (a_it.peek(), b_it.peek()) {
@@ -95,20 +95,20 @@ impl<V: Var, U: Into<Mono<V>>> FromIterator<(i32, U)> for Poly<V> {
 
 #[derive(Clone, Debug, Default, PartialEq, Eq, Hash, PartialOrd, Ord)]
 pub struct Mono<V: Var> {
-    pub term: Vec<(V, u32)>,
+    pub vars: 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();
+        let mut self_it = self.vars.iter().peekable();
+        let mut other_it = other.vars.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_var, o_exp)) = other_it.peek() {
+            if let Some((s_var, s_exp)) = self_it.peek() {
+                if s_var < o_var {
                     self_it.next();
                     continue;
-                } else if s_term > o_term {
+                } else if s_var > o_var {
                     return false;
                 } else if o_exp <= s_exp {
                     self_it.next();
@@ -126,8 +126,8 @@ impl<V: Var> Mono<V> {
 
     /// Returns the lcm of self and other (element-wise max of exponents).
     pub fn lcm(&self, other: &Mono<V>) -> Mono<V> {
-        let mut self_it = self.term.iter().peekable();
-        let mut other_it = other.term.iter().peekable();
+        let mut self_it = self.vars.iter().peekable();
+        let mut other_it = other.vars.iter().peekable();
         let mut result: Vec<(V, u32)> = vec![];
 
         loop {
@@ -149,13 +149,13 @@ impl<V: Var> Mono<V> {
             }
         }
 
-        Mono { term: result }
+        Mono { vars: result }
     }
 
     /// Divides self by other. Assumes `self.contains(other)`.
     pub fn div(self, other: &Mono<V>) -> Mono<V> {
-        let mut self_it = self.term.into_iter().peekable();
-        let mut other_it = other.term.iter().peekable();
+        let mut self_it = self.vars.into_iter().peekable();
+        let mut other_it = other.vars.iter().peekable();
         let mut result: Vec<(V, u32)> = vec![];
 
         loop {
@@ -179,7 +179,7 @@ impl<V: Var> Mono<V> {
             }
         }
 
-        Mono { term: result }
+        Mono { vars: result }
     }
 }
 
@@ -194,19 +194,19 @@ where
 
 impl<V: Var, U: Into<V>> FromIterator<(U, u32)> for Mono<V> {
     fn from_iter<T: IntoIterator<Item = (U, u32)>>(iter: T) -> Self {
-        let mut term = iter
+        let mut vars = iter
             .into_iter()
             .map(|(t, pow)| (t.into(), pow))
             .collect::<Vec<(V, u32)>>();
-        term.sort();
+        vars.sort();
 
         // Check duplicate variables
         assert!(
-            (term[..])
+            (vars[..])
                 .windows(2)
                 .all(|window| window[0].0 != window[1].0)
         );
 
-        Mono { term }
+        Mono { vars }
     }
 }

src/poly/fmt.rs

@@ -64,7 +64,7 @@ impl<V: Var> Display for Mono<V> {
         write!(
             fmt,
             "{}",
-            self.term
+            self.vars
                 .iter()
                 .map(|(t, p)| match p {
                     1 => format!("{t}"),

src/poly/ideal.rs

@@ -5,11 +5,14 @@ use super::flat::Poly;
 use super::var::Var;
 
 /// Marker: the ideal's generators are arbitrary polynomials.
+#[derive(Clone, Debug)]
 pub struct Generators;
 
 /// Marker: the ideal's generators form a Gröbner basis.
+#[derive(Clone, Debug)]
 pub struct GroebnerBasis;
 
+#[derive(Clone, Debug)]
 pub struct Ideal<V: Var, S> {
     generators: Vec<Poly<V>>,
     _state: PhantomData<S>,

src/poly/ops.rs

@@ -24,31 +24,31 @@ 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 a_vars = self.vars.into_iter().peekable();
+        let mut b_vars = other.vars.into_iter().peekable();
 
         let mut result: Vec<(V, u32)> = Default::default();
 
         loop {
-            match (a_term.peek(), b_term.peek()) {
+            match (a_vars.peek(), b_vars.peek()) {
                 (Some((a_var, _)), Some((b_var, _))) => {
                     if a_var < b_var {
-                        result.push(a_term.next().unwrap());
+                        result.push(a_vars.next().unwrap());
                     } else if a_var > b_var {
-                        result.push(b_term.next().unwrap());
+                        result.push(b_vars.next().unwrap());
                     } else {
-                        let (var, a_exp) = a_term.next().unwrap();
-                        let (_, b_exp) = b_term.next().unwrap();
+                        let (var, a_exp) = a_vars.next().unwrap();
+                        let (_, b_exp) = b_vars.next().unwrap();
                         result.push((var, a_exp + b_exp));
                     }
                 }
                 (Some(a), None) => {
                     result.push(a.clone());
-                    a_term.next();
+                    a_vars.next();
                 }
                 (None, Some(b)) => {
                     result.push(b.clone());
-                    b_term.next();
+                    b_vars.next();
                 }
                 (None, None) => {
                     break;
@@ -56,7 +56,7 @@ impl<V: Var> Mul for Mono<V> {
             }
         }
 
-        Mono { term: result }
+        Mono { vars: result }
     }
 }
 

src/poly/tests.rs

@@ -57,7 +57,7 @@ fn test_mono_mul() {
 
     // Multiply by constant monomial (empty term vec = 1)
     let a: Mono<StaticVar> = [("x", 4)].into();
-    let one: Mono<StaticVar> = Mono { term: vec![] };
+    let one: Mono<StaticVar> = Mono { vars: vec![] };
     assert_eq!(a.clone() * one, a);
 }
 
@@ -110,7 +110,7 @@ fn test_lex_cmp() {
     let xy: Mono<StaticVar> = [("x", 1), ("y", 1)].into();
     let y2: Mono<StaticVar> = [("y", 2)].into();
     let x: Mono<StaticVar> = [("x", 1)].into();
-    let one: Mono<StaticVar> = Mono { term: vec![] };
+    let one: Mono<StaticVar> = Mono { vars: vec![] };
 
     // x² > xy (x exponent 2 vs 1)
     assert_eq!(lex_cmp(&x2, &xy), Ordering::Greater);
@@ -144,7 +144,7 @@ fn test_mono_div() {
     // x / x = 1
     let a: Mono<StaticVar> = [("x", 1)].into();
     let b: Mono<StaticVar> = [("x", 1)].into();
-    assert_eq!(a.div(&b), Mono { term: vec![] });
+    assert_eq!(a.div(&b), Mono { vars: vec![] });
 }
 
 #[test]
@@ -210,7 +210,7 @@ fn test_s_poly() {
 
 fn make_const_poly(c: i32) -> Poly<StaticVar> {
     Poly {
-        mono: [(Mono { term: vec![] }, c)].into_iter().collect(),
+        mono: [(Mono { vars: vec![] }, c)].into_iter().collect(),
     }
 }