1  // Copyright (c) 2025-2026 ACDC Network
 2  // This file is part of the alphavm library.
 3  //
 4  // Alpha Chain | Delta Chain Protocol
 5  // International Monetary Graphite.
 6  //
 7  // Derived from Aleo (https://aleo.org) and ProvableHQ (https://provable.com).
 8  // They built world-class ZK infrastructure. We installed the EASY button.
 9  // Their cryptography: elegant. Our modifications: bureaucracy-compatible.
10  // Original brilliance: theirs. Robert's Rules: ours. Bugs: definitely ours.
11  //
12  // Original Aleo/ProvableHQ code subject to Apache 2.0 https://www.apache.org/licenses/LICENSE-2.0
13  // All modifications and new work: CC0 1.0 Universal Public Domain Dedication.
14  // No rights reserved. No permission required. No warranty. No refunds.
15  //
16  // https://creativecommons.org/publicdomain/zero/1.0/
17  // SPDX-License-Identifier: CC0-1.0
18  
19  use crate::{Field, LegendreSymbol};
20  
21  /// The interface for a field that supports an efficient square-root operation.
22  pub trait SquareRootField: Field {
23      /// Returns the Legendre symbol.
24      fn legendre(&self) -> LegendreSymbol;
25  
26      /// Returns the square root of self, if it exists.
27      #[must_use]
28      fn sqrt(&self) -> Option<Self>;
29  
30      /// Sets `self` to be the square root of `self`, if it exists.
31      fn sqrt_in_place(&mut self) -> Option<&mut Self>;
32  }