improve api and simplify SumProdCircuit creation

examples/dag.rs

@@ -1,21 +1,22 @@
+use std::cell::RefCell;
+use std::rc::Rc;
 use circuit_cas::circuit::probabilistic::ProbCircuit;
 use circuit_cas::circuit::dag::CircuitExt;
-use circuit_cas::var;
 
 fn main() {
-    let circuit = ProbCircuit::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"));
+    let x = circuit.var("x");
+    let y = circuit.var("y");
+    let z = circuit.var("z");
 
-    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);

examples/quotient.rs

@@ -1,5 +1,8 @@
-use circuit_cas::circuit::quotient::Quotient;
-use circuit_cas::poly::var::StaticVar;
+use std::cell::RefCell;
+use std::rc::Rc;
+use circuit_cas::circuit::dag::CircuitExt;
+use circuit_cas::circuit::quotient::QuotientCircuit;
+use circuit_cas::circuit::traits::Circuit;
 use circuit_cas::var;
 
 fn main() {
@@ -12,7 +15,15 @@ fn main() {
         1 * ((&x ^ 1) * (&nx ^ 1)) - 1 * (&x ^ 1),
     ];
 
-    let quotient: Quotient<StaticVar> = idem.into_iter().collect();
+    let quotient: Rc<RefCell<QuotientCircuit>> = idem.into_iter().collect();
 
-    println!("{quotient:?}");
+    // Build x * x̄ + x in the DAG
+    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);
 }