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// Copyright © 2023 Marvin Beckmann
//
// 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/>.
//! This module contains implementations to transform a [`PolyOverZ`]
//! into a [`MatZ`] and reverse by using the coefficient embedding.
use crate::{
integer::{MatZ, PolyOverZ},
traits::{
FromCoefficientEmbedding, GetCoefficient, IntoCoefficientEmbedding, MatrixDimensions,
MatrixGetEntry, MatrixSetEntry, SetCoefficient,
},
};
impl IntoCoefficientEmbedding<MatZ> for &PolyOverZ {
/// Computes the coefficient embedding of the polynomial
/// in a [`MatZ`] as a column vector, where the i-th entry
/// of the vector corresponds to the i-th coefficient.
/// It inverts the operation of [`PolyOverZ::from_coefficient_embedding`].
///
/// Parameters:
/// - `size`: determines the number of rows of the embedding. It has to be larger
/// than the degree of the polynomial.
///
/// Returns a coefficient embedding as a column vector if `size` is large enough.
///
/// # Examples
/// ```
/// use std::str::FromStr;
/// use qfall_math::{
/// integer::{MatZ, PolyOverZ},
/// traits::IntoCoefficientEmbedding,
/// };
///
/// let poly = PolyOverZ::from_str("3 17 3 -5").unwrap();
/// let vector = poly.into_coefficient_embedding(4);
/// let cmp_vector = MatZ::from_str("[[17],[3],[-5],[0]]").unwrap();
/// assert_eq!(cmp_vector, vector);
/// ```
///
/// # Panics ...
/// - if `size` is not larger than the degree of the polynomial, i.e.
/// not all coefficients can be embedded.
fn into_coefficient_embedding(self, size: impl Into<i64>) -> MatZ {
let size = size.into();
let length = self.get_degree() + 1;
assert!(
size >= length,
"The polynomial can not be embedded in the vector, \
as the length of the polynomial ({length}) is larger than \
the provided size ({size})."
);
let mut out = MatZ::new(size, 1);
for j in 0..size {
let coeff = unsafe { self.get_coeff_unchecked(j) };
unsafe { out.set_entry_unchecked(j, 0, coeff) };
}
out
}
}
impl FromCoefficientEmbedding<&MatZ> for PolyOverZ {
/// Computes a polynomial from a vector.
/// The first i-th entry of the column vector is taken
/// as the coefficient of the polynomial.
/// It inverts the operation of
/// [`PolyOverZ::into_coefficient_embedding`](#method.into_coefficient_embedding).
///
/// Parameters:
/// - `embedding`: the column vector that encodes the embedding
///
/// Returns a polynomial that corresponds to the embedding.
///
/// # Examples
/// ```
/// use std::str::FromStr;
/// use qfall_math::{
/// integer::{MatZ, PolyOverZ},
/// traits::FromCoefficientEmbedding,
/// };
///
/// let vector = MatZ::from_str("[[17],[3],[-5]]").unwrap();
/// let poly = PolyOverZ::from_coefficient_embedding(&vector);
/// let cmp_poly = PolyOverZ::from_str("3 17 3 -5").unwrap();
/// assert_eq!(cmp_poly, poly);
/// ```
///
/// # Panics ...
/// - if the provided embedding is not a column vector.
fn from_coefficient_embedding(embedding: &MatZ) -> Self {
assert!(
embedding.is_column_vector(),
"This is no valid embedding, since the matrix is no column vector."
);
let mut out = PolyOverZ::default();
for i in 0..embedding.get_num_rows() {
unsafe { out.set_coeff_unchecked(i, embedding.get_entry_unchecked(i, 0)) }
}
out
}
}
#[cfg(test)]
mod test_into_coefficient_embedding {
use crate::{
integer::{MatZ, PolyOverZ},
traits::IntoCoefficientEmbedding,
};
use std::str::FromStr;
/// Ensure that the embedding works with large entries.
#[test]
fn large_entries() {
let poly = PolyOverZ::from_str(&format!("3 17 {} {}", i64::MAX, i64::MIN)).unwrap();
let vector = poly.into_coefficient_embedding(3);
let cmp_vector = MatZ::from_str(&format!("[[17],[{}],[{}]]", i64::MAX, i64::MIN)).unwrap();
assert_eq!(cmp_vector, vector);
}
/// Ensure that the function panics if the the provided size is too small.
#[test]
#[should_panic]
fn size_too_small() {
let poly = PolyOverZ::from_str("3 17 12 -1").unwrap();
let _ = poly.into_coefficient_embedding(2);
}
}
#[cfg(test)]
mod test_from_coefficient_embedding {
use crate::{
integer::{MatZ, PolyOverZ},
traits::FromCoefficientEmbedding,
};
use std::str::FromStr;
/// Ensure that the embedding works with large entries.
#[test]
fn large_entries() {
let vector = MatZ::from_str(&format!("[[17],[{}],[{}]]", i64::MAX, i64::MIN)).unwrap();
let poly = PolyOverZ::from_coefficient_embedding(&vector);
let cmp_poly = PolyOverZ::from_str(&format!("3 17 {} {}", i64::MAX, i64::MIN)).unwrap();
assert_eq!(cmp_poly, poly);
}
/// Ensure that the function panics if the provided matrix is not a column vector.
#[test]
#[should_panic]
fn not_column_vector() {
let vector = MatZ::from_str("[[17, 1],[-17, -1],[5, 9]]").unwrap();
let _ = PolyOverZ::from_coefficient_embedding(&vector);
}
}