Add operator tests on `Assigned` for cases including `1/0`

The tests for addition and subtraction expose a bug in the addition
implementation, which does not correctly handle the `1/0 -> 0` map that
`inv0` is defined to perform.

src/plonk/assigned.rs

@@ -163,3 +163,69 @@ impl<F: Field> Assigned<F> {
         }
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use pasta_curves::Fp;
+
+    use super::Assigned;
+
+    #[test]
+    fn add_trivial_to_inv0_rational() {
+        // a = 2
+        // b = inv0(1/0)
+        let a = Assigned::Trivial(Fp::from(2));
+        let b = Assigned::Rational(Fp::one(), Fp::zero());
+
+        // 2 + inv0(1/0) = 2 + 0 = 1/2
+        // This fails if addition is implemented using normal rules for rationals.
+        assert_eq!((a + b).evaluate(), a.evaluate());
+    }
+
+    #[test]
+    fn add_rational_to_inv0_rational() {
+        // a = inv0(1/2)
+        // b = inv0(1/0)
+        let a = Assigned::Rational(Fp::one(), Fp::from(2));
+        let b = Assigned::Rational(Fp::one(), Fp::zero());
+
+        // inv0(1/2) + inv0(1/0) = 1/2 + 0 = 1/2
+        // This fails if addition is implemented using normal rules for rationals.
+        assert_eq!((a + b).evaluate(), a.evaluate());
+    }
+
+    #[test]
+    fn sub_trivial_from_inv0_rational() {
+        // a = 2
+        // b = inv0(1/0)
+        let a = Assigned::Trivial(Fp::from(2));
+        let b = Assigned::Rational(Fp::one(), Fp::zero());
+
+        // inv0(1/0) - 2 = 0 - 2 = -2
+        // This fails if subtraction is implemented using normal rules for rationals.
+        assert_eq!((b - a).evaluate(), (-a).evaluate());
+    }
+
+    #[test]
+    fn sub_rational_from_inv0_rational() {
+        // a = inv0(1/2)
+        // b = inv0(1/0)
+        let a = Assigned::Rational(Fp::one(), Fp::from(2));
+        let b = Assigned::Rational(Fp::one(), Fp::zero());
+
+        // inv0(1/0) - inv0(1/2) = 0 - 1/2 = -1/2
+        // This fails if subtraction is implemented using normal rules for rationals.
+        assert_eq!((b - a).evaluate(), (-a).evaluate());
+    }
+
+    #[test]
+    fn mul_rational_by_inv0_rational() {
+        // a = inv0(1/2)
+        // b = inv0(1/0)
+        let a = Assigned::Rational(Fp::one(), Fp::from(2));
+        let b = Assigned::Rational(Fp::one(), Fp::zero());
+
+        // inv0(1/2) * inv0(1/0) = 1/2 * 0 = 0
+        assert_eq!((a * b).evaluate(), Fp::zero());
+    }
+}