From a8f5a23786c4cf6cbff80f0ffbc22c53f14d5b41 Mon Sep 17 00:00:00 2001
From: supinie <86788874+supinie@users.noreply.github.com>
Date: Wed, 5 Aug 2026 18:14:14 +0100
Subject: [PATCH 1/2] Add Neg trait for Z

---
 src/integer/z/arithmetic.rs     |  1 +
 src/integer/z/arithmetic/neg.rs | 80 +++++++++++++++++++++++++++++++++
 2 files changed, 81 insertions(+)
 create mode 100644 src/integer/z/arithmetic/neg.rs

diff --git a/src/integer/z/arithmetic.rs b/src/integer/z/arithmetic.rs
index 4800b616..99a17edf 100644
--- a/src/integer/z/arithmetic.rs
+++ b/src/integer/z/arithmetic.rs
@@ -15,6 +15,7 @@ mod exp;
 mod logarithm;
 mod modulo;
 mod mul;
+mod neg;
 mod pow;
 mod root;
 mod sub;
diff --git a/src/integer/z/arithmetic/neg.rs b/src/integer/z/arithmetic/neg.rs
new file mode 100644
index 00000000..8bda59fa
--- /dev/null
+++ b/src/integer/z/arithmetic/neg.rs
@@ -0,0 +1,80 @@
+// Copyright 2026 Joshua Limbrey
+//
+// This file is part of qFALL-math
+//
+// qFALL-math is free software: you can redistribute it and/or modify it under
+// the terms of the Mozilla Public License Version 2.0 as published by the
+// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.
+
+//! Implementation of the [`Neg`] trait for [`Z`] values.
+
+use super::super::Z;
+use flint3_sys::fmpz_neg;
+use std::ops::Neg;
+
+impl Neg for Z {
+    type Output = Z;
+
+    /// Implements the [`Neg`] trait for [`Z`] values.
+    /// [`Neg`] is implemented for both borrowed and owned [`Z`].
+    ///
+    /// When called on owned [`Z`] it will reuse the memory of `self`.
+    ///
+    /// Returns the additive inverse of `self` as a [`Z`].
+    ///
+    /// # Examples
+    /// ```
+    /// use qfall_math::integer::Z;
+    ///
+    /// let a: Z = Z::from(42);
+    ///
+    /// let b: Z = -&a;
+    /// let c: Z = -a;
+    /// ```
+    fn neg(mut self) -> Self::Output {
+        unsafe { fmpz_neg(&mut self.value, &self.value) };
+        self
+    }
+}
+
+impl Neg for &Z {
+    type Output = Z;
+
+    /// Documentation at [`Z::neg`].
+    fn neg(self) -> Self::Output {
+        let mut out = Z::default();
+        unsafe { fmpz_neg(&mut out.value, &self.value) };
+        out
+    }
+}
+
+#[cfg(test)]
+mod test_neg {
+    use super::Z;
+
+    /// Ensure that `neg` works for small numbers.
+    #[test]
+    fn correct_small() {
+        let a: Z = Z::ONE;
+        let b: Z = Z::MINUS_ONE;
+        let c: Z = Z::ZERO;
+
+        assert_eq!(a, -(-&a));
+        assert_eq!(a, -&b);
+        assert_eq!(b, -&a);
+        assert_eq!(a, -b.clone());
+        assert_eq!(b, -a);
+        assert_eq!(c, -&c);
+        assert_eq!(c.clone(), -c);
+    }
+
+    /// Ensure that `neg` works for large numbers.
+    #[test]
+    fn correct_large() {
+        let a: Z = Z::from(u64::MAX);
+        let b: Z = Z::from(i64::MAX);
+
+        assert_eq!(a, -(-&a));
+        assert_eq!(b, -(-&b));
+    }
+}

From c6c2e2408ff3d1a0678dd2fa739e7bce20adf2a2 Mon Sep 17 00:00:00 2001
From: supinie <86788874+supinie@users.noreply.github.com>
Date: Thu, 6 Aug 2026 12:03:48 +0100
Subject: [PATCH 2/2] Add Neg trait for Q

---
 src/rational/q/arithmetic.rs     |  1 +
 src/rational/q/arithmetic/neg.rs | 84 ++++++++++++++++++++++++++++++++
 2 files changed, 85 insertions(+)
 create mode 100644 src/rational/q/arithmetic/neg.rs

diff --git a/src/rational/q/arithmetic.rs b/src/rational/q/arithmetic.rs
index 0463437b..43edf024 100644
--- a/src/rational/q/arithmetic.rs
+++ b/src/rational/q/arithmetic.rs
@@ -14,6 +14,7 @@ mod div;
 mod exp;
 mod logarithm;
 mod mul;
+mod neg;
 mod pow;
 mod root;
 mod sub;
diff --git a/src/rational/q/arithmetic/neg.rs b/src/rational/q/arithmetic/neg.rs
new file mode 100644
index 00000000..58ddf60c
--- /dev/null
+++ b/src/rational/q/arithmetic/neg.rs
@@ -0,0 +1,84 @@
+// Copyright 2026 Joshua Limbrey
+//
+// This file is part of qFALL-math
+//
+// qFALL-math is free software: you can redistribute it and/or modify it under
+// the terms of the Mozilla Public License Version 2.0 as published by the
+// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.
+
+//! Implementation of the [`Neg`] trait for [`Q`] values.
+
+use super::super::Q;
+use flint3_sys::fmpq_neg;
+use std::ops::Neg;
+
+impl Neg for Q {
+    type Output = Q;
+
+    /// Implements the [`Neg`] trait for [`Q`] values.
+    /// [`Neg`] is implements for both borrowed and owned [`Q`].
+    ///
+    /// When called on owned [`Q`] it will reuse the memory of `self`.
+    ///
+    /// Returns the additive inverse of `self` as a [`Q`].
+    ///
+    /// # Examples
+    /// ```
+    /// use qfall_math::rational::Q;
+    ///
+    /// let a: Q = Q::from((1, 42));
+    ///
+    /// let b: Q = -&a;
+    /// let c: Q = -a;
+    /// ```
+    fn neg(mut self) -> Self::Output {
+        unsafe { fmpq_neg(&mut self.value, &self.value) };
+        self
+    }
+}
+
+impl Neg for &Q {
+    type Output = Q;
+
+    /// Documentation at [`Q::neg`].
+    fn neg(self) -> Self::Output {
+        let mut out = Q::default();
+        unsafe { fmpq_neg(&mut out.value, &self.value) };
+        out
+    }
+}
+
+#[cfg(test)]
+mod test_neg {
+    use super::Q;
+
+    /// Ensure that `neg` works for small numbers.
+    #[test]
+    fn correct_small() {
+        let a: Q = Q::ONE;
+        let b: Q = Q::MINUS_ONE;
+        let c: Q = Q::ZERO;
+
+        let d: Q = Q::from((1, 42));
+
+        assert_eq!(a, -(-&a));
+        assert_eq!(a, -&b);
+        assert_eq!(b, -&a);
+        assert_eq!(a, -b.clone());
+        assert_eq!(b, -a);
+        assert_eq!(c, -&c);
+        assert_eq!(c.clone(), -c);
+        assert_eq!(d, -(-&d));
+        assert_eq!(d.clone(), -(-d));
+    }
+
+    /// Ensure that `neg` works for large numbers.
+    #[test]
+    fn correct_large() {
+        let a: Q = Q::from(u64::MAX);
+        let b: Q = Q::from(i64::MAX);
+
+        assert_eq!(a, -(-&a));
+        assert_eq!(b, -(-&b));
+    }
+}