Add RationalSemiring with the rational crate

Cargo.toml

@@ -22,6 +22,7 @@ segment-tree = "2.0.0"
 bumpalo = "3.11.1"
 petgraph = "0.6.2"
 rand_chacha = "0.3.1"
+rational = "1.2.2"
 # optional: only used to build [[bin]]
 clap = { version = "4.2.1", features = ["derive"], optional = true }
 serde_json = { version = "1.0.81", optional = true }

src/util/semirings/mod.rs

@@ -1,13 +1,15 @@
 mod boolean;
 mod expectation;
 mod finitefield;
+mod rational;
 mod realsemiring;
 mod semiring_traits;
 mod tropical;
 
 pub use self::boolean::*;
 pub use self::expectation::*;
 pub use self::finitefield::*;
+pub use self::rational::*;
 pub use self::realsemiring::*;
 pub use self::semiring_traits::*;
 pub use self::tropical::*;

src/util/semirings/rational.rs

@@ -0,0 +1,39 @@
+use rational::Rational;
+use std::{fmt::Display, ops};
+
+use super::semiring_traits::Semiring;
+
+#[derive(Debug, Clone, Copy, PartialEq, PartialOrd)]
+pub struct RationalSemiring(Rational);
+
+impl Semiring for RationalSemiring {
+    fn one() -> Self {
+        RationalSemiring(Rational::new(1, 1))
+    }
+
+    fn zero() -> Self {
+        RationalSemiring(Rational::new(0, 1))
+    }
+}
+
+impl Display for RationalSemiring {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(f, "{}/{}", self.0.numerator(), self.0.denominator())
+    }
+}
+
+impl ops::Add<RationalSemiring> for RationalSemiring {
+    type Output = RationalSemiring;
+
+    fn add(self, rhs: RationalSemiring) -> Self::Output {
+        RationalSemiring(self.0 + rhs.0)
+    }
+}
+
+impl ops::Mul<RationalSemiring> for RationalSemiring {
+    type Output = RationalSemiring;
+
+    fn mul(self, rhs: RationalSemiring) -> Self::Output {
+        RationalSemiring(self.0 * rhs.0)
+    }
+}