add docs on multiplication and inversion algorithms

Author: FrancoGiachetta

crates/starknet-types-core/src/qm31/mod.rs

@@ -160,14 +160,14 @@ impl QM31 {
     /// Computes the multiplication of two [QM31] elements in reduced form.
     ///
     /// In reduced form, a QM31 is composed of 4 limbs, each represented a value from the Mersenne 31 field.
-    /// 
+    ///
     /// The algorithm can be deduced from the implementation of the QM31 multiplication from the Stwo prover:
     /// [Link](https://github.com/starkware-libs/stwo/blob/d9176e6e22319370a8501f799829b920c0db2eac/crates/stwo/src/core/fields/qm31.rs#L81).
-    /// Which multiplies 2 complex extension fields of M31: 
+    /// Which multiplies 2 complex extension fields of M31:
     /// [Link](https://github.com/starkware-libs/stwo/blob/d9176e6e22319370a8501f799829b920c0db2eac/crates/stwo/src/core/fields/cm31.rs#L47).
-    /// Whose real and imaginary components result from the M31 multiplication: 
+    /// Whose real and imaginary components result from the M31 multiplication:
     /// [Link](https://github.com/starkware-libs/stwo/blob/d9176e6e22319370a8501f799829b920c0db2eac/crates/stwo/src/core/fields/m31.rs#L105).
-    /// 
+    ///
     /// The implementation of the QM31 multiplication is based on the following paper: [Link](https://github.com/ingonyama-zk/papers/blob/main/Mersenne31_polynomial_arithmetic.pdf)
     /// Section 1.3, Ecuation 1.20.
     pub fn mul(&self, rhs: &QM31) -> QM31 {
@@ -233,17 +233,17 @@ impl QM31 {
     /// Computes the inverse of a [QM31] element in reduced form.
     ///
     /// In reduced form, a QM31 is composed of 4 limbs, each represented a value from the Mersenne 31 field.
-    /// 
+    ///
     /// The algorithm can be deduced from the implementation of the inverse of a QM31 from the Stwo prover:
     /// [Link](https://github.com/starkware-libs/stwo/blob/d9176e6e22319370a8501f799829b920c0db2eac/crates/stwo/src/core/fields/qm31.rs#L120).
-    /// 
-    /// Having the following inverse operation: `(a + bu)^-1 = (a - bu) / (a^2 - (2+i)b^2)`, the algorithm computes the denominator by computing 
-    /// `(a^2 - (2+i)b^2)` first and then inverting it. The denominator's value inverse is computed as the inverse of a complex extension 
+    ///
+    /// Having the following inverse operation: `(a + bu)^-1 = (a - bu) / (a^2 - (2+i)b^2)`, the algorithm computes the denominator by computing
+    /// `(a^2 - (2+i)b^2)` first and then inverting it. The denominator's value inverse is computed as the inverse of a complex extension
     /// field of M31:
     /// [Link](https://github.com/starkware-libs/stwo/blob/d9176e6e22319370a8501f799829b920c0db2eac/crates/stwo/src/core/fields/cm31.rs#L68).
     /// Finally, the inverse of the QM31 is computed:
     /// [Link](https://github.com/starkware-libs/stwo/blob/d9176e6e22319370a8501f799829b920c0db2eac/crates/stwo/src/core/fields/qm31.rs#L127).
-    /// 
+    ///
     /// The implementation of the QM31 inversion is based on the following papper: [Link](https://github.com/ingonyama-zk/papers/blob/main/Mersenne31_polynomial_arithmetic.pdf)
     /// Section 1.3, Ecuation 1.23.
     ///