move tests and implement dag

examples/flat.rs

@@ -2,8 +2,7 @@ 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 +10,13 @@ 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};
@@ -53,12 +53,20 @@ impl<V: Var> Circuit<V> {
     }
 
     pub fn add(&mut self, left: NodeId, right: NodeId) -> NodeId {
-        let (l, r) = if left <= right { (left, right) } else { (right, left) };
+        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) };
+        let (l, r) = if left <= right {
+            (left, right)
+        } else {
+            (right, left)
+        };
         self.node(Node::Prod(l, r))
     }
 
@@ -89,12 +97,18 @@ pub trait CircuitExt<V: Var> {
 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() })
+        Some(CircuitNode {
+            id,
+            circuit: self.clone(),
+        })
     }
 }
 
@@ -103,7 +117,10 @@ impl<V: Var> Add for CircuitNode<V> {
 
     fn add(self, rhs: Self) -> Self {
         let id = self.circuit.borrow_mut().add(self.id, rhs.id);
-        CircuitNode { id, circuit: self.circuit }
+        CircuitNode {
+            id,
+            circuit: self.circuit,
+        }
     }
 }
 
@@ -112,7 +129,10 @@ impl<V: Var> Mul for CircuitNode<V> {
 
     fn mul(self, rhs: Self) -> Self {
         let id = self.circuit.borrow_mut().mul(self.id, rhs.id);
-        CircuitNode { id, circuit: self.circuit }
+        CircuitNode {
+            id,
+            circuit: self.circuit,
+        }
     }
 }
 
@@ -168,5 +188,3 @@ mod tests {
         assert_eq!(circuit.borrow().len(), 10);
     }
 }
-
-

src/circuit/mod.rs

@@ -1 +1,2 @@
 pub mod dag;
+pub mod quotient;

src/circuit/quotient.rs

@@ -0,0 +1 @@
+

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

@@ -53,7 +53,7 @@ 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)>,
 }
@@ -103,9 +103,11 @@ impl<V: Var, U: Into<V>> FromIterator<(U, u32)> for Mono<V> {
         term.sort();
 
         // Check duplicate variables
-        assert!((term[..])
+        assert!(
-            .windows(2)
+            (term[..])
-            .all(|window| window[0].0 != window[1].0));
+                .windows(2)
+                .all(|window| window[0].0 != window[1].0)
+        );
 
         Mono { term }
     }
@@ -195,6 +197,22 @@ impl<V: Var> Mul<Mono<V>> for i32 {
     }
 }
 
+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(0);
+                *entry += c1 * c2;
+            }
+        }
+        result.mono.retain(|_, &mut c| c != 0);
+        result
+    }
+}
+
 impl<V: Var> Add for Poly<V> {
     type Output = Poly<V>;
 
@@ -220,107 +238,3 @@ impl<V: Var> Sub for Poly<V> {
         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/mod.rs

@@ -1,2 +1,5 @@
 pub mod flat;
 pub mod var;
+
+#[cfg(test)]
+mod tests;

src/poly/tests.rs

@@ -0,0 +1,102 @@
+
+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

@@ -17,7 +17,15 @@ impl Display for StaticVar {
         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(",")),
+            _ => write!(
+                fmt,
+                "{}{}",
+                self.name,
+                self.indices
+                    .iter()
+                    .map(|x| num_to_subscript(x.to_string()))
+                    .join(",")
+            ),
         }
     }
 }