Struct MatPolyOverZ 

pub struct MatPolyOverZ { /* private fields */ }

MatPolyOverZ is a matrix with entries of type PolyOverZ.

Attributes:

• matrix: holds FLINT’s struct of the PolyOverZ matrix

Examples

Matrix usage

use qfall_math::{
    integer::{PolyOverZ, MatPolyOverZ},
    traits::{MatrixGetEntry, MatrixSetEntry},
};
use std::str::FromStr;

// instantiate new matrix
let id_mat = MatPolyOverZ::from_str("[[1  1, 0],[0, 1  1]]").unwrap();

// clone object, set and get entry
let mut clone = id_mat.clone();
clone.set_entry(0, 0, PolyOverZ::from(2));
assert_eq!(
    clone.get_entry(1, 1).unwrap(),
    PolyOverZ::from_str("1  1").unwrap(),
);

// to_string
assert_eq!("[[1  1, 0],[0, 1  1]]", &id_mat.to_string());

Vector usage

use qfall_math::{
    integer::{PolyOverZ, MatPolyOverZ},
};
use std::str::FromStr;

let row_vec = MatPolyOverZ::from_str("[[1  1, 0, 1  1]]").unwrap();
let col_vec = MatPolyOverZ::from_str("[[1  -5],[1  -1],[0]]").unwrap();

// check if matrix instance is vector
assert!(row_vec.is_row_vector());
assert!(col_vec.is_column_vector());

Implementations

impl MatPolyOverZ

pub fn add_safe(&self, other: &Self) -> Result<MatPolyOverZ, MathError>

Implements addition for two MatPolyOverZ matrices.

Parameters:

• other: specifies the value to add to self

Returns the sum of both matrices as a MatPolyOverZ or an error if the matrix dimensions mismatch.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();
let b: MatPolyOverZ = MatPolyOverZ::from_str("[[1  -42, 0, 2  24 42],[3  1 12 4, 1  -1, 1  17]]").unwrap();

let c: MatPolyOverZ = a.add_safe(&b).unwrap();

Errors and Failures

• Returns a MathError of type MathError::MismatchingMatrixDimension if the matrix dimensions mismatch.

impl MatPolyOverZ

pub fn mul_safe(&self, other: &Self) -> Result<Self, MathError>

Implements multiplication for two MatPolyOverZ values.

Parameters:

• other: specifies the value to multiply with self

Returns the product of self and other as a MatPolyOverZ or an error if the dimensions of self and other do not match for multiplication.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[0, 2  42 24],[3  17 24 42, 1  17]]").unwrap();
let b: MatPolyOverZ = MatPolyOverZ::from_str("[[1  -42, 2  24 42],[3  1 12 4, 1  17]]").unwrap();

let c: MatPolyOverZ = a.mul_safe(&b).unwrap();

Errors and Failures

• Returns a MathError of type MathError::MismatchingMatrixDimension if the dimensions of self and other do not match for multiplication.

pub fn mul_mat_poly_ring_zq_safe( &self, other: &MatPolynomialRingZq, ) -> Result<MatPolynomialRingZq, MathError>

Implements multiplication for a MatPolyOverZ matrix with a MatPolynomialRingZq matrix.

Parameters:

• other: specifies the value to multiply with self

Returns the product of self and other as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::MatPolynomialRingZq;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();
let mat_2 = MatPolynomialRingZq::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]] / 3  1 2 3 mod 17").unwrap();

let mat_3 = &mat_1.mul_mat_poly_ring_zq_safe(&mat_2).unwrap();

Errors and Failures

• Returns a MathError of type MathError::MismatchingMatrixDimension if the dimensions of self and other do not match for multiplication.

impl MatPolyOverZ

pub fn sub_safe(&self, other: &Self) -> Result<MatPolyOverZ, MathError>

Implements subtraction for two MatPolyOverZ matrices.

Parameters:

• other: specifies the value to subtract fromself

Returns the result of the subtraction as a MatPolyOverZ or an error if the matrix dimensions mismatch.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();
let b: MatPolyOverZ = MatPolyOverZ::from_str("[[1  -42, 0, 2  24 42],[3  1 12 4, 1  -1, 1  17]]").unwrap();

let c: MatPolyOverZ = a.sub_safe(&b).unwrap();

Errors

• Returns a MathError of type MathError::MismatchingMatrixDimension if the matrix dimensions mismatch.

pub fn sub_mat_poly_ring_zq_safe( &self, other: &MatPolynomialRingZq, ) -> Result<MatPolynomialRingZq, MathError>

Implements subtraction for a MatPolyOverZ matrix with a MatPolynomialRingZq matrix.

Parameters:

• other: specifies the value to subtract from self

Returns the subtraction of self by other as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::MatPolynomialRingZq;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();
let mat_2 = MatPolynomialRingZq::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]] / 3  1 2 3 mod 17").unwrap();

let mat_3 = &mat_1.sub_mat_poly_ring_zq_safe(&mat_2).unwrap();

Errors and Failures

• Returns a MathError of type MathError::MismatchingMatrixDimension if the dimensions of self and other do not match for multiplication.

impl MatPolyOverZ

pub fn new( num_rows: impl TryInto<i64> + Display, num_cols: impl TryInto<i64> + Display, ) -> Self

Creates a new matrix with num_rows rows, num_cols columns and zeros as entries, where each entry is a PolyOverZ.

Parameters:

• num_rows: number of rows the new matrix should have
• num_cols: number of columns the new matrix should have

Returns a new MatPolyOverZ instance of the provided dimensions.

Examples

use qfall_math::integer::MatPolyOverZ;

let matrix = MatPolyOverZ::new(5, 10);

Panics …

• if the number of rows or columns is negative, 0, or does not fit into an i64.

pub fn identity( num_rows: impl TryInto<i64> + Display, num_cols: impl TryInto<i64> + Display, ) -> Self

Generate a num_rows times num_columns matrix with 1 on the diagonal and 0 anywhere else.

Parameters:

• rum_rows: the number of rows of the identity matrix
• num_columns: the number of columns of the identity matrix

Returns a matrix with 1 across the diagonal and 0 anywhere else.

Examples

use qfall_math::integer::MatPolyOverZ;

let matrix = MatPolyOverZ::identity(2, 3);

let identity = MatPolyOverZ::identity(10, 10);

Panics …

• if the provided number of rows and columns are not suited to create a matrix. For further information see MatPolyOverZ::new.

impl MatPolyOverZ

pub fn norm_l_2_infty_sqrd(&self) -> Z

Outputs the squared l_{2, ∞}-norm, i.e. it computes the squared Euclidean norm of each column of the matrix and returns the largest one.

Examples

use qfall_math::integer::{MatPolyOverZ, Z};
use std::str::FromStr;

let mat = MatPolyOverZ::from_str("[[1  2, 1  3],[1  2, 0]]").unwrap();

let eucl_norm = mat.norm_l_2_infty_sqrd();

// 3^2 + 0^2 = 9
assert_eq!(Z::from(9), eucl_norm);

pub fn norm_l_2_infty(&self) -> Q

Outputs the l_{2, ∞}-norm, i.e. it computes the Euclidean norm of each column of the matrix and returns the largest one.

Examples

use qfall_math::{integer::MatPolyOverZ, rational::Q};
use std::str::FromStr;

let mat = MatPolyOverZ::from_str("[[1  2, 1  3],[1  2, 0]]").unwrap();

let eucl_norm = mat.norm_l_2_infty();

// sqrt(3^2 + 0^2) = 3
assert_eq!(Q::from(3), eucl_norm);

pub fn norm_l_infty_infty(&self) -> Z

Outputs the l_{∞, ∞}-norm, i.e. it computes the ∞-norm of each column of the matrix and returns the largest one.

Examples

use qfall_math::integer::{MatPolyOverZ, Z};
use std::str::FromStr;

let mat = MatPolyOverZ::from_str("[[1  2, 1  3],[1  2, 0]]").unwrap();

let eucl_norm = mat.norm_l_infty_infty();

// max{2, 3} = 3
assert_eq!(Z::from(3), eucl_norm);

impl MatPolyOverZ

pub fn is_identity(&self) -> bool

Checks if a MatPolyOverZ is a identity matrix, i.e. all entries on the diagonal are the constant polynomial 1 and 0 elsewhere.

Returns true if the matrix is the identity and false otherwise.

Examples

use std::str::FromStr;
use qfall_math::integer::MatPolyOverZ;

let matrix = MatPolyOverZ::from_str("[[1  1, 0],[0, 1  1]]").unwrap();

assert!(matrix.is_identity());

pub fn is_square(&self) -> bool

Checks if a MatPolyOverZ is a square matrix, i.e. the number of rows and columns is identical.

Returns true if the number of rows and columns is identical.

Examples

use std::str::FromStr;
use qfall_math::integer::MatPolyOverZ;

let matrix = MatPolyOverZ::from_str("[[1  1, 0],[0, 1  1]]").unwrap();
let check = matrix.is_square();

pub fn is_zero(&self) -> bool

Checks if a MatPolyOverZ is a zero matrix, i.e. all entries are the constant polynomial 0 everywhere.

Returns true if the matrix is zero and false otherwise.

Examples

use std::str::FromStr;
use qfall_math::integer::MatPolyOverZ;

let matrix = MatPolyOverZ::from_str("[[0, 0],[0, 0]]").unwrap();
let check = matrix.is_zero();

pub fn is_symmetric(&self) -> bool

Checks if a MatPolyOverZ is symmetric.

Returns true if we have a_ij == a_ji for all i,j.

Examples

use qfall_math::integer::MatPolyOverZ;

let value = MatPolyOverZ::identity(2,2);
assert!(value.is_symmetric());

pub fn rank(&self) -> Z

Returns the rank of the matrix.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let matrix = MatPolyOverZ::from_str("[[1  1, 0, 0],[0, 0, 1  1]]").unwrap();

let rank = matrix.rank();

impl MatPolyOverZ

pub fn reduce_by_poly(&mut self, modulus: &PolyOverZ)

Entrywise reduces a matrix of polynomials by a polynomial modulus. The modulus must have a leading coefficient of 1, else the function will panic.

Parameters:

• modulus: Specifies the polynomial by which self is reduced

Examples

use qfall_math::integer::{MatPolyOverZ, PolyOverZ};
use std::str::FromStr;

let mut a = MatPolyOverZ::from_str("[[4  0 1 2 3, 3  0 1 1]]").unwrap();
let modulus = PolyOverZ::from_str("3  0 1 1").unwrap();

a.reduce_by_poly(&modulus);

assert_eq!(MatPolyOverZ::from_str("[[2  0 2, 0]]").unwrap(), a);

Panics …

• if the modulus does not have a leading coefficient of 1.

impl MatPolyOverZ

pub fn sample_binomial( num_rows: impl TryInto<i64> + Display, num_cols: impl TryInto<i64> + Display, max_degree: impl TryInto<i64> + Display, n: impl Into<Z>, p: impl Into<Q>, ) -> Result<Self, MathError>

Outputs a MatPolyOverZ instance with entries chosen according to the binomial distribution parameterized by n and p.

Parameters:

• num_rows: specifies the number of rows the new matrix should have
• num_cols: specifies the number of columns the new matrix should have
• max_degree: specifies the maximum length of all polynomials in the matrix, i.e. the maximum number of coefficients any polynomial in the matrix can have
• n: specifies the number of trials
• p: specifies the probability of success

Returns a new MatPolyOverZ instance with entries chosen according to the binomial distribution or a MathError if n < 0, p ∉ (0,1), n does not fit into an i64, or the dimensions of the matrix were chosen too small.

Examples

use qfall_math::integer::MatPolyOverZ;

let sample = MatPolyOverZ::sample_binomial(2, 2, 5, 2, 0.5).unwrap();

Errors and Failures

• Returns a MathError of type InvalidIntegerInput if n < 0 or p ∉ (0,1).
• Returns a MathError of type ConversionError if n does not fit into an i64.

Panics …

• if the provided number of rows and columns are not suited to create a matrix. For further information see MatPolyOverZ::new.

pub fn sample_binomial_with_offset( num_rows: impl TryInto<i64> + Display, num_cols: impl TryInto<i64> + Display, max_degree: impl TryInto<i64> + Display, offset: impl Into<Z>, n: impl Into<Z>, p: impl Into<Q>, ) -> Result<Self, MathError>

Outputs a MatPolyOverZ instance with entries chosen according to the binomial distribution parameterized by n and p with given offset.

Parameters:

• num_rows: specifies the number of rows the new matrix should have
• num_cols: specifies the number of columns the new matrix should have
• max_degree: specifies the maximum length of all polynomials in the matrix, i.e. the maximum number of coefficients any polynomial in the matrix can have
• offset: specifies an offset applied to each sample collected from the binomial distribution
• n: specifies the number of trials
• p: specifies the probability of success

Returns a new MatPolyOverZ instance with entries chosen according to the binomial distribution or a MathError if n < 0, p ∉ (0,1), n does not fit into an i64, or the dimensions of the matrix were chosen too small.

Examples

use qfall_math::integer::MatPolyOverZ;

let sample = MatPolyOverZ::sample_binomial_with_offset(2, 2, 5, -1, 2, 0.5).unwrap();

Errors and Failures

• Returns a MathError of type InvalidIntegerInput if n < 0 or p ∉ (0,1).
• Returns a MathError of type ConversionError if n does not fit into an i64.
• Returns a MathError of type OutOfBounds if the max_degree is negative or it does not fit into an i64.

Panics …

• if the provided number of rows and columns are not suited to create a matrix. For further information see MatPolyOverZ::new.

impl MatPolyOverZ

pub fn sample_discrete_gauss( num_rows: impl TryInto<i64> + Display, num_cols: impl TryInto<i64> + Display, max_degree: impl TryInto<i64> + Display, center: impl Into<Q>, s: impl Into<Q>, ) -> Result<MatPolyOverZ, MathError>

Initializes a new matrix with dimensions num_rows x num_columns and with each entry sampled independently according to the discrete Gaussian distribution, using PolyOverZ::sample_discrete_gauss.

Parameters:

• num_rows: specifies the number of rows the new matrix should have
• num_cols: specifies the number of columns the new matrix should have
• max_degree: specifies the included maximal degree the created PolyOverZ should have
• center: specifies the positions of the center with peak probability
• s: specifies the Gaussian parameter, which is proportional to the standard deviation sigma * sqrt(2 * pi) = s

Returns a MatPolyOverZ with each entry sampled independently from the specified discrete Gaussian distribution or an error if s < 0.

Examples

use qfall_math::integer::MatPolyOverZ;

let matrix = MatPolyOverZ::sample_discrete_gauss(3, 1, 5, 0, 1.25f32).unwrap();

Errors and Failures

• Returns a MathError of type InvalidIntegerInput if s < 0.

Panics …

• if the provided number of rows and columns are not suited to create a matrix. For further information see MatPolyOverZ::new.
• if max_degree is negative, or does not fit into an i64.

pub fn sample_d( basis: &Self, k: impl Into<i64>, center: &[PolyOverQ], s: impl Into<Q>, ) -> Result<MatPolyOverZ, MathError>

SampleD samples a discrete Gaussian from the lattice with a provided basis.

We do not check whether basis is actually a basis. Hence, the callee is responsible for making sure that basis provides a suitable basis.

Parameters:

• basis: specifies a basis for the lattice from which is sampled
• k: the maximal length the polynomial can have
• center: specifies the positions of the center with peak probability
• s: specifies the Gaussian parameter, which is proportional to the standard deviation sigma * sqrt(2 * pi) = s

Returns a vector of polynomials sampled according to the discrete Gaussian distribution or an error if the basis is not a row vector, s < 0, or the number of rows of the basis and center differ.

Example

use qfall_math::{
    integer::MatPolyOverZ,
    rational::PolyOverQ,
};
use std::str::FromStr;

let basis = MatPolyOverZ::from_str("[[1  1, 3  0 1 -1, 2  2 2]]").unwrap();
let center = vec![PolyOverQ::default()];

let sample = MatPolyOverZ::sample_d(&basis, 3, &center, 10.5_f64).unwrap();

Errors and Failures

• Returns a MathError of type VectorFunctionCalledOnNonVector, if the basis is not a row vector.
• Returns a MathError of type InvalidIntegerInput if s < 0.
• Returns a MathError of type MismatchingMatrixDimension if the number of rows of the basis and center differ.

This function implements SampleD according to:

• [1] Gentry, Craig and Peikert, Chris and Vaikuntanathan, Vinod (2008). Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the fortieth annual ACM symposium on Theory of computing. https://dl.acm.org/doi/pdf/10.1145/1374376.1374407

Panics …

• if the polynomials have higher length than the provided upper bound k

impl MatPolyOverZ

pub fn sample_uniform( num_rows: impl TryInto<i64> + Display, num_cols: impl TryInto<i64> + Display, max_degree: impl TryInto<i64> + Display, lower_bound: impl Into<Z>, upper_bound: impl Into<Z>, ) -> Result<Self, MathError>

Outputs a MatPolyOverZ instance with polynomials as entries, whose coefficients were chosen uniform at random in [lower_bound, upper_bound).

The internally used uniform at random chosen bytes are generated by ThreadRng, which uses ChaCha12 and is considered cryptographically secure.

Parameters:

• num_rows: specifies the number of rows the new matrix should have
• num_cols: specifies the number of columns the new matrix should have
• max_degree: specifies the maximum length of all polynomials in the matrix, i.e. the maximum number of coefficients any polynomial in the matrix can have
• lower_bound: specifies the included lower bound of the interval over which is sampled
• upper_bound: specifies the excluded upper bound of the interval over which is sampled

Returns a new MatPolyOverZ instance with polynomials as entries, whose coefficients were chosen uniformly at random in [lower_bound, upper_bound) or a MathError if the interval was chosen too small or the max_degree of the polynomials is negative or too large to fit into i64.

Examples

use qfall_math::integer::MatPolyOverZ;

let matrix = MatPolyOverZ::sample_uniform(3, 3, 5, 17, 26).unwrap();

Errors and Failures

• Returns a MathError of type InvalidInterval if the given upper_bound isn’t at least larger than lower_bound.
• Returns a MathError of type OutOfBounds if the max_degree is negative or it does not fit into an i64.

Panics …

• if the provided number of rows and columns are not suited to create a matrix. For further information see MatPolyOverZ::new.

impl MatPolyOverZ

pub fn reverse_columns(&mut self)

Swaps the i-th column with the n-i-th column for all i <= n/2 of the specified matrix with n columns.

Examples

use qfall_math::integer::MatPolyOverZ;

let mut matrix = MatPolyOverZ::new(4, 3);
matrix.reverse_columns();

pub fn reverse_rows(&mut self)

Swaps the i-th row with the n-i-th row for all i <= n/2 of the specified matrix with n rows.

Examples

use qfall_math::integer::MatPolyOverZ;

let mut matrix = MatPolyOverZ::new(4, 3);
matrix.reverse_rows();

impl MatPolyOverZ

pub fn sort_by_column<T: Ord>( &self, cond_func: fn(&Self) -> Result<T, MathError>, ) -> Result<Self, MathError>

Sorts the columns of the matrix based on some condition defined by cond_func in an ascending order.

This condition is usually a norm with the described input-output behaviour.

Parameters:

• cond_func: computes values implementing Ord over the columns of the specified matrix. These values are then used to re-order / sort the rows of the matrix.

Returns an empty Ok if the action could be performed successfully. A MathError is returned if the execution of cond_func returned an error.

Examples

Use a build-in function as condition

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;
let mat = MatPolyOverZ::from_str("[[2  3 4, 1  2, 1  1]]").unwrap();
let cmp = MatPolyOverZ::from_str("[[1  1, 1  2, 2  3 4]]").unwrap();

let sorted = mat.sort_by_column(MatPolyOverZ::norm_eucl_sqrd).unwrap();

assert_eq!(cmp, sorted);

Use a custom function as condition

This function needs to take a column vector as input and output a type implementing PartialOrd

use qfall_math::{integer::{MatPolyOverZ, Z}, error::MathError, traits::{MatrixDimensions, MatrixGetEntry}};
use crate::qfall_math::traits::GetCoefficient;
use std::str::FromStr;
let mat = MatPolyOverZ::from_str("[[2  0 4, 1  2, 1  1]]").unwrap();
let cmp = MatPolyOverZ::from_str("[[2  0 4, 1  1, 1  2]]").unwrap();

fn custom_cond_func(matrix: &MatPolyOverZ) -> Result<Z, MathError> {
    let mut sum = Z::ZERO;
    for entry in matrix.get_entries_rowwise() {
        sum += entry.get_coeff(0)?;
    }
    Ok(sum)
}

let sorted = mat.sort_by_column(custom_cond_func).unwrap();

assert_eq!(cmp, sorted);

Errors and Failures

• Returns a MathError of the same type as cond_func if the execution of cond_func fails.

pub fn sort_by_row<T: Ord>( &self, cond_func: fn(&Self) -> Result<T, MathError>, ) -> Result<Self, MathError>

Sorts the rows of the matrix based on some condition defined by cond_func in an ascending order.

This condition is usually a norm with the described input-output behaviour.

Parameters:

• cond_func: computes values implementing Ord over the columns of the specified matrix. These values are then used to re-order / sort the columns of the matrix.

Returns an empty Ok if the action could be performed successfully. A MathError is returned if the execution of cond_func returned an error.

Examples

Use a build-in function as condition

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;
let mat = MatPolyOverZ::from_str("[[2  3 4],[1  2],[1  1]]").unwrap();
let cmp = MatPolyOverZ::from_str("[[1  1],[1  2],[2  3 4]]").unwrap();

let sorted = mat.sort_by_row(MatPolyOverZ::norm_infty).unwrap();

assert_eq!(cmp, sorted);

Use a custom function as condition

This function needs to take a row vector as input and output a type implementing PartialOrd

use qfall_math::{integer::{MatPolyOverZ, Z}, error::MathError, traits::{MatrixDimensions, MatrixGetEntry}};
use crate::qfall_math::traits::GetCoefficient;
use std::str::FromStr;
let mat = MatPolyOverZ::from_str("[[2  0 4],[1  2],[1  1]]").unwrap();
let cmp = MatPolyOverZ::from_str("[[2  0 4],[1  1],[1  2]]").unwrap();

fn custom_cond_func(matrix: &MatPolyOverZ) -> Result<Z, MathError> {
    let mut sum = Z::ZERO;
    for entry in matrix.get_entries_columnwise() {
        sum += entry.get_coeff(0)?;
    }
    Ok(sum)
}

let sorted = mat.sort_by_row(custom_cond_func).unwrap();

assert_eq!(cmp, sorted);

Errors and Failures

• Returns a MathError of the same type as cond_func if the execution of cond_func fails.

impl MatPolyOverZ

pub fn pretty_string( &self, nr_printed_rows: u64, nr_printed_columns: u64, ) -> String

Outputs the matrix as a String, where the upper leftmost nr_printed_rows x nr_printed_columns submatrix is output entirely as well as the corresponding entries in the last column and row of the matrix.

Parameters:

• nr_printed_rows: defines the number of rows of the upper leftmost matrix that are printed entirely
• nr_printed_columns: defines the number of columns of the upper leftmost matrix that are printed entirely

Returns a String representing the abbreviated matrix.

Example

use qfall_math::integer::MatZ;
let matrix = MatZ::identity(10, 10);

println!("Matrix: {}", matrix.pretty_string(2, 2));
// outputs the following:
// Matrix: [
//   [1, 0, , ..., 0],
//   [0, 1, , ..., 0],
//   [...],
//   [0, 0, , ..., 1]
// ]

impl MatPolyOverZ

pub fn trace(&self) -> Result<PolyOverZ, MathError>

Returns the trace of a matrix and an error, if the matrix is not square.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let matrix = MatPolyOverZ::from_str("[[1  42, 2  1 2],[1  4, 0]]").unwrap();
let trace = matrix.trace().unwrap();

Errors and Failures

• Returns a MathError of type NoSquareMatrix if the matrix is not a square matrix.

impl MatPolyOverZ

pub fn transpose(&self) -> Self

Returns the transposed form of the given matrix, i.e. rows get transformed to columns and vice versa.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat = MatPolyOverZ::from_str("[[0, 1  42],[3  17 24 42, 1  17]]").unwrap();
let cmp = MatPolyOverZ::from_str("[[0, 3  17 24 42],[1  42, 1  17]]").unwrap();

assert_eq!(mat.transpose(), cmp);

impl MatPolyOverZ

pub unsafe fn get_fmpz_poly_mat_struct(&mut self) -> &mut fmpz_poly_mat_struct

Returns a mutable reference to the field matrix of type fmpz_poly_mat_struct.

WARNING: The returned struct is part of flint_sys. Any changes to this object are unsafe and may introduce memory leaks.

This function is a passthrough to enable users of this library to use flint_sys and with that FLINT functions that might not be covered in our library yet. If this is the case, please consider contributing to this open-source project by opening a Pull Request at qfall_math to provide this feature in the future.

Safety

Any flint_sys struct and function is part of a FFI to the C-library FLINT. As FLINT is a C-library, it does not provide all memory safety features that Rust and our Wrapper provide. Thus, using functions of flint_sys can introduce memory leaks.

impl MatPolyOverZ

pub unsafe fn set_fmpz_poly_mat_struct( &mut self, flint_struct: fmpz_poly_mat_struct, )

Sets the field matrix of type fmpz_poly_mat_struct to flint_struct.

Parameters:

• flint_struct: value to set the attribute to

This function is a passthrough to enable users of this library to use flint_sys and with that FLINT functions that might not be covered in our library yet. If this is the case, please consider contributing to this open-source project by opening a Pull Request at qfall_math to provide this feature in the future.

Safety

Ensure that the old struct does not share any memory with any other structs that might be used in the future. The memory of the old struct is freed using this function.

Any flint_sys struct and function is part of a FFI to the C-library FLINT. As FLINT is a C-library, it does not provide all memory safety features that Rust and our Wrapper provide. Thus, using functions of flint_sys can introduce memory leaks.

impl MatPolyOverZ

pub fn dot_product(&self, other: &Self) -> Result<PolyOverZ, MathError>

Returns the dot product of two vectors of type MatPolyOverZ. Note that the dimensions of the two vectors are irrelevant for the dot product.

Parameters:

• other: specifies the other vector the dot product is calculated over

Returns the resulting dot_product as a PolyOverZ or an error if the given MatPolyOverZ instances aren’t vectors or have different numbers of entries.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let poly_vec_1 = MatPolyOverZ::from_str("[[4  -1 0 1 1],[2  1 2]]").unwrap();
let poly_vec_2 = MatPolyOverZ::from_str("[[4  -1 0 1 1, 1  42]]").unwrap();

let dot_prod = poly_vec_1.dot_product(&poly_vec_2).unwrap();

Errors and Failures

• Returns a MathError of type MathError::VectorFunctionCalledOnNonVector if the given MatPolyOverZ instance is not a (row or column) vector.
• Returns a MathError of type MathError::MismatchingMatrixDimension if the given vectors have different lengths.

impl MatPolyOverZ

pub fn is_row_vector(&self) -> bool

Returns true if the provided MatPolyOverZ has only one row, i.e. is a row vector. Otherwise, returns false.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let row_vec = MatPolyOverZ::from_str("[[1  1, 1  2, 1  3]]").unwrap();
let col_vec = MatPolyOverZ::from_str("[[1  1],[0],[1  3]]").unwrap();

assert!(row_vec.is_row_vector());
assert!(!col_vec.is_row_vector());

pub fn is_column_vector(&self) -> bool

Returns true if the provided MatPolyOverZ has only one column, i.e. is a column vector. Otherwise, returns false.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let row_vec = MatPolyOverZ::from_str("[[1  1, 1  2, 1  3]]").unwrap();
let col_vec = MatPolyOverZ::from_str("[[1  1],[0],[1  3]]").unwrap();

assert!(col_vec.is_column_vector());
assert!(!row_vec.is_column_vector());

pub fn is_vector(&self) -> bool

Returns true if the provided MatPolyOverZ has only one column or one row, i.e. is a vector. Otherwise, returns false.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let row_vec = MatPolyOverZ::from_str("[[1  1, 1  2, 1  3]]").unwrap();
let col_vec = MatPolyOverZ::from_str("[[1  1],[0],[1  3]]").unwrap();

assert!(row_vec.is_vector());
assert!(col_vec.is_vector());

pub fn has_single_entry(&self) -> bool

Returns true if the provided MatPolyOverZ has only one entry, i.e. is a 1x1 matrix. Otherwise, returns false.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let vec = MatPolyOverZ::from_str("[[1  1]]").unwrap();

assert!(vec.has_single_entry());

impl MatPolyOverZ

pub fn norm_eucl_sqrd(&self) -> Result<Z, MathError>

Returns the squared Euclidean norm or 2-norm of the given (row or column) vector or an error if the given MatPolyOverZ instance is not a (row or column) vector. The squared Euclidean norm for a polynomial vector is obtained by computing the sum of the squared Euclidean norms of the individual polynomials. The squared Euclidean norm for a polynomial is obtained by treating the coefficients of the polynomial as a vector and then applying the standard squared Euclidean norm.

Examples

use qfall_math::integer::{MatPolyOverZ, Z};
use std::str::FromStr;

let vec = MatPolyOverZ::from_str("[[1  1],[2  2 2],[1  3]]").unwrap();

let sqrd_2_norm = vec.norm_eucl_sqrd().unwrap();

assert_eq!(Z::from(18), sqrd_2_norm);

Errors and Failures

• Returns a MathError of type MathError::VectorFunctionCalledOnNonVector if the given MatPolyOverZ instance is not a (row or column) vector.

pub fn norm_eucl(&self) -> Result<Q, MathError>

Returns the Euclidean norm or 2-norm of the given (row or column) vector or an error if the given MatPolyOverZ instance is not a (row or column) vector.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let vec = MatPolyOverZ::from_str("[[1  2],[2  2 2],[1  2]]").unwrap();

let eucl_norm = vec.norm_eucl().unwrap();

assert_eq!(4, eucl_norm);

Errors and Failures

• Returns a MathError of type MathError::VectorFunctionCalledOnNonVector if the given MatPolyOverZ instance is not a (row or column) vector.

pub fn norm_infty(&self) -> Result<Z, MathError>

Returns the infinity norm or ∞-norm of the given (row or column) vector or an error if the given MatPolyOverZ instance is not a (row or column) vector. The infinity norm for a polynomial vector is obtained by computing the infinity norm on the vector consisting of the infinity norms of the individual polynomials. The infinity norm for a polynomial is obtained by treating the coefficients of the polynomial as a vector and then applying the standard infinity norm.

Examples

use qfall_math::integer::{MatPolyOverZ, Z};
use std::str::FromStr;

let vec = MatPolyOverZ::from_str("[[1  1],[2  2 4],[1  3]]").unwrap();

let infty_norm = vec.norm_infty().unwrap();

assert_eq!(Z::from(4), infty_norm);

Errors and Failures

• Returns a MathError of type MathError::VectorFunctionCalledOnNonVector if the given MatPolyOverZ instance is not a (row or column) vector.

Trait Implementations

impl Add<&MatPolyOverZ> for &MatPolynomialRingZq

fn add(self, other: &MatPolyOverZ) -> Self::Output

Implements the Add trait for a MatPolynomialRingZq matrix with a MatPolyOverZ matrix. Add is implemented for any combination of owned and borrowed values.

Parameters:

• other: specifies the value to add with self

Returns the addition of self and other as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::MatPolynomialRingZq;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolynomialRingZq::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]] / 3  1 2 3 mod 17").unwrap();
let mat_2 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();

let mat_3 = &mat_1 + &mat_2;

Panics …

• if the dimensions of self and other do not match for multiplication.

type Output = MatPolynomialRingZq

The resulting type after applying the + operator.

impl Add for &MatPolyOverZ

fn add(self, other: Self) -> Self::Output

Implements the Add trait for two MatPolyOverZ values. Add is implemented for any combination of MatPolyOverZ and borrowed MatPolyOverZ.

Parameters:

• other: specifies the value to add to self

Returns the sum of both numbers as a MatPolyOverZ.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();
let b: MatPolyOverZ = MatPolyOverZ::from_str("[[1  -42, 0, 2  24 42],[3  1 12 4, 1  -1, 1  17]]").unwrap();

let c: MatPolyOverZ = &a + &b;
let d: MatPolyOverZ = a + b;
let e: MatPolyOverZ = &c + d;
let f: MatPolyOverZ = c + &e;

Panics …

• if the dimensions of both matrices mismatch.

type Output = MatPolyOverZ

The resulting type after applying the + operator.

impl AddAssign<&MatPolyOverZ> for MatPolyOverZ

fn add_assign(&mut self, other: &Self)

Computes the addition of self and other reusing the memory of self.

Parameters:

• other: specifies the value to add to self

Examples

use qfall_math::integer::MatPolyOverZ;
let mut a = MatPolyOverZ::identity(2, 2);
let b = MatPolyOverZ::new(2, 2);

a += &b;
a += b;

Panics …

• if the matrix dimensions mismatch.

impl AddAssign<&MatPolyOverZ> for MatPolynomialRingZq

fn add_assign(&mut self, other: &MatPolyOverZ)

Documentation at MatPolynomialRingZq::add_assign.

impl AddAssign<MatPolyOverZ> for MatPolynomialRingZq

fn add_assign(&mut self, other: MatPolyOverZ)

Documentation at MatPolynomialRingZq::add_assign.

impl AddAssign for MatPolyOverZ

fn add_assign(&mut self, other: MatPolyOverZ)

Documentation at MatPolyOverZ::add_assign.

impl Clone for MatPolyOverZ

fn clone(&self) -> Self

Clones the given element and returns a deep clone of the MatPolyOverZ element.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a = MatPolyOverZ::from_str("[[2  0 1],[1  15]]").unwrap();
let b = a.clone();

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl CompareBase<&MatPolyOverZ> for MatNTTPolynomialRingZq

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<&MatPolyOverZ> for MatPolyOverZ

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<&MatPolyOverZ> for MatPolynomialRingZq

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<&MatZ> for MatPolyOverZ

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<&PolyOverZ> for MatPolyOverZ

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl<Integer: Into<Z>> CompareBase<Integer> for MatPolyOverZ

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<MatPolyOverZ> for MatNTTPolynomialRingZq

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<MatPolyOverZ> for MatPolynomialRingZq

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<MatZ> for MatPolyOverZ

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<PolyOverZ> for MatPolyOverZ

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase for MatPolyOverZ

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl Concatenate for &MatPolyOverZ

fn concat_vertical(self, other: Self) -> Result<Self::Output, MathError>

Concatenates self with other vertically, i.e. other is added below.

Parameters:

• other: the other matrix to concatenate with self

Returns a vertical concatenation of the two matrices or an error, if the matrices can not be concatenated vertically.

Examples

use qfall_math::traits::*;
use qfall_math::integer::MatPolyOverZ;

let mat_1 = MatPolyOverZ::new(13, 5);
let mat_2 = MatPolyOverZ::new(17, 5);

let mat_vert = mat_1.concat_vertical(&mat_2).unwrap();

Errors and Failures

• Returns a MathError of type MismatchingMatrixDimension if the matrices can not be concatenated due to mismatching dimensions.

fn concat_horizontal(self, other: Self) -> Result<Self::Output, MathError>

Concatenates self with other horizontally, i.e. other is added on the right.

Parameters:

• other: the other matrix to concatenate with self

Returns a horizontal concatenation of the two matrices or a an error, if the matrices can not be concatenated horizontally.

Examples

use qfall_math::traits::*;
use qfall_math::integer::MatPolyOverZ;

let mat_1 = MatPolyOverZ::new(17, 5);
let mat_2 = MatPolyOverZ::new(17, 6);

let mat_vert = mat_1.concat_horizontal(&mat_2).unwrap();

Errors and Failures

• Returns a MathError of type MismatchingMatrixDimension if the matrices can not be concatenated due to mismatching dimensions.

type Output = MatPolyOverZ

impl Debug for MatPolyOverZ

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for MatPolyOverZ

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Implements the deserialize option. This allows to create a MatPolyOverZ from a given Json-object.

impl Display for MatPolyOverZ

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Allows to convert a matrix of type MatPolyOverZ into a String.

Returns the Matrix in form of a String. For matrix [[0, 1 42, 2 42 24],[3 17 24 42, 1 17, 1 42]] the String looks like this [[0, 1 42, 2 42 24],[3 17 24 42, 1 17, 1 42]].

Examples

use qfall_math::integer::MatPolyOverZ;
use core::fmt;
use std::str::FromStr;

let matrix = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();
println!("{matrix}");

use qfall_math::integer::MatPolyOverZ;
use core::fmt;
use std::str::FromStr;

let matrix = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();
let matrix_string = matrix.to_string();

impl Drop for MatPolyOverZ

fn drop(&mut self)

Drops the given MatPolyOverZ value and frees the allocated memory.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;
{
    let a = MatPolyOverZ::from_str("[[2  0 1],[1  15]]").unwrap();
} // as a's scope ends here, it get's dropped

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a = MatPolyOverZ::from_str("[[2  0 1],[1  15]]").unwrap();
drop(a); // explicitly drops a's value

impl<Integer: Into<Z>> Evaluate<Integer, MatZ> for MatPolyOverZ

fn evaluate(&self, value: Integer) -> MatZ

Evaluates a MatPolyOverZ on a given input entrywise.

Parameters:

• value: the value with which to evaluate the matrix of polynomials.

Returns the evaluation of the polynomial as a MatZ.

Examples

use qfall_math::traits::*;
use qfall_math::integer::Z;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let poly = MatPolyOverZ::from_str("[[0, 1  17, 2  24 42],[2  24 42, 2  24 42, 2  24 42]]").unwrap();
let res = poly.evaluate(3);

impl From<&MatPolyOverZ> for MatPolyOverZ

fn from(value: &MatPolyOverZ) -> Self

Alias for MatPolyOverZ::clone.

impl From<&MatPolyOverZ> for String

fn from(value: &MatPolyOverZ) -> Self

Converts a MatPolyOverZ into its String representation.

Parameters:

• value: specifies the matrix that will be represented as a String

Returns a String of the form "[[row_0],[row_1],...[row_n]]".

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;
let matrix = MatPolyOverZ::from_str("[[1  17, 1  5],[2  1 7, 1  2]]").unwrap();

let string: String = matrix.into();

impl From<&MatZ> for MatPolyOverZ

fn from(matrix: &MatZ) -> Self

Creates a MatPolyOverZ with constant polynomials defined by a MatZ.

Parameters

• matrix: a matrix with constant integers.

Returns a matrix of polynomial that all have the first coefficient set to the value in the matrix.

Examples

use qfall_math::integer::{MatZ, MatPolyOverZ};

let mat_z = MatZ::identity(10, 10);
let mat_poly = MatPolyOverZ::from(&mat_z);

impl From<MatPolyOverZ> for String

fn from(value: MatPolyOverZ) -> Self

Documentation can be found at String::from for &MatPolyOverZ.

impl From<MatZ> for MatPolyOverZ

fn from(value: MatZ) -> Self

Documentation can be found at MatPolyOverZ::from for &MatZ.

impl FromCoefficientEmbedding<(&MatZ, i64)> for MatPolyOverZ

fn from_coefficient_embedding(embedding: (&MatZ, i64)) -> Self

Computes a MatPolyOverZ from a coefficient embedding. Interprets the first degree + 1 many rows of the matrix as the coefficients of the first row of polynomials. The first one containing their coefficients of degree 0, and the last one their coefficients of degree degree. It inverts the operation of MatPolyOverZ::into_coefficient_embedding.

Parameters:

• embedding: the coefficient matrix and the maximal degree of the polynomials (defines how the matrix is split)

Returns a matrix of polynomials that corresponds to the embedding.

Examples

use std::str::FromStr;
use qfall_math::{
    integer::{MatZ, MatPolyOverZ},
    traits::FromCoefficientEmbedding,
};

let matrix = MatZ::from_str("[[17, 1],[3, 2],[-5, 3]]").unwrap();
let poly = MatPolyOverZ::from_coefficient_embedding((&matrix, 2));
let cmp_poly = MatPolyOverZ::from_str("[[3  17 3 -5, 3  1 2 3]]").unwrap();
assert_eq!(cmp_poly, poly);

impl FromStr for MatPolyOverZ

fn from_str(string: &str) -> Result<Self, MathError>

Creates a MatPolyOverZ matrix from a String.

Warning: Each entry is parsed as a PolyOverZ object. If an entry string starts with a correctly formatted PolyOverZ object, the rest of this entry string is ignored. This means that the entry input string "4 0 1 2 3" is the same as "4 0 1 2 3 4 5 6 7".

Parameters:

• string: the matrix of form: "[[poly_1, poly_2, poly_3],[poly_4, poly_5, poly_6]]" for a 2x3 matrix where first three polynomials are in the first row and the second three are in the second row.

Returns a MatPolyOverZ or an error if the matrix is not formatted in a suitable way, the number of rows or columns is too large (must fit into i64), the number of entries in rows is unequal, or if an entry is not formatted correctly.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let matrix = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let str_1 = "[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]";
let matrix = MatPolyOverZ::from_str(str_1).unwrap();

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let string = String::from("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]");
let matrix = MatPolyOverZ::from_str(&string).unwrap();

Errors and Failures

• Returns a MathError of type MathError::StringConversionError,
  • if the matrix is not formatted in a suitable way,
  • if the number of rows or columns is too large (must fit into i64),
  • if the number of entries in rows is unequal, or
  • if an entry is not formatted correctly. For further information see PolyOverZ::from_str.

Panics …

• if the provided number of rows and columns are not suited to create a matrix. For further information see MatPolyOverZ::new.

type Err = MathError

The associated error which can be returned from parsing.

impl IntoCoefficientEmbedding<MatZ> for &MatPolyOverZ

fn into_coefficient_embedding(self, size: impl Into<i64>) -> MatZ

Computes the coefficient embedding of the matrix of polynomials in a MatZ. Each column vector of polynomials is embedded into size many row vectors of coefficients. The first one containing their coefficients of degree 0, and the last one their coefficients of degree size - 1. It inverts the operation of MatPolyOverZ::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 matrix if size is large enough.

Examples

use std::str::FromStr;
use qfall_math::{
    integer::{MatZ, MatPolyOverZ},
    traits::IntoCoefficientEmbedding,
};

let poly = MatPolyOverZ::from_str("[[1  1, 2  1 2],[1  -1, 2  -1 -2]]").unwrap();
let embedding = poly.into_coefficient_embedding(2);
let cmp_mat = MatZ::from_str("[[1, 1],[0, 2],[-1, -1],[0, -2]]").unwrap();
assert_eq!(cmp_mat, embedding);

Panics …

• if size is not larger than the degree of the polynomial, i.e. not all coefficients can be embedded.

impl MatrixDimensions for MatPolyOverZ

fn get_num_rows(&self) -> i64

Returns the number of rows of the matrix as a i64.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::traits::*;

let matrix = MatPolyOverZ::new(5, 6);
let rows = matrix.get_num_rows();

fn get_num_columns(&self) -> i64

Returns the number of columns of the matrix as a i64.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::traits::*;

let matrix = MatPolyOverZ::new(5, 6);
let columns = matrix.get_num_columns();

impl MatrixGetEntry<PolyOverZ> for MatPolyOverZ

unsafe fn get_entry_unchecked(&self, row: i64, column: i64) -> PolyOverZ

Outputs the PolyOverZ value of a specific matrix entry without checking whether it’s part of the matrix.

Parameters:

• row: specifies the row in which the entry is located
• column: specifies the column in which the entry is located

Returns the PolyOverZ value of the matrix at the position of the given row and column.

Safety

To use this function safely, make sure that the selected entry is part of the matrix. If it is not, memory leaks, unexpected panics, etc. might occur.

Examples

use qfall_math::integer::{MatPolyOverZ, PolyOverZ};
use qfall_math::traits::*;
use std::str::FromStr;

let matrix = MatPolyOverZ::from_str("[[1  1, 1  2],[1  3, 1  4],[0, 1  6]]").unwrap();

assert_eq!(PolyOverZ::from(2), unsafe { matrix.get_entry_unchecked(0, 1) });
assert_eq!(PolyOverZ::from(4), unsafe { matrix.get_entry_unchecked(1, 1) });

fn get_entry( &self, row: impl TryInto<i64> + Display, column: impl TryInto<i64> + Display, ) -> Result<T, MathError>

Returns the value of a specific matrix entry.

fn get_entries(&self) -> Vec<Vec<T>>

Outputs a Vec<Vec<T>> containing all entries of the matrix s.t. any entry in row i and column j can be accessed via entries[i][j] if entries = matrix.get_entries.

fn get_entries_rowwise(&self) -> Vec<T>

Outputs a Vec<T> containing all entries of the matrix in a row-wise order, i.e. a matrix [[2, 3, 4],[5, 6, 7]] can be accessed via this function in this order [2, 3, 4, 5, 6, 7].

fn get_entries_columnwise(&self) -> Vec<T>

Outputs a Vec<T> containing all entries of the matrix in a column-wise order, i.e. a matrix [[2, 3, 4],[5, 6, 7]] can be accessed via this function in this order [2, 5, 3, 6, 4, 7].

impl MatrixGetSubmatrix for MatPolyOverZ

unsafe fn get_submatrix_unchecked( &self, row_1: i64, row_2: i64, col_1: i64, col_2: i64, ) -> Self

Returns a deep copy of the submatrix defined by the given parameters and does not check the provided dimensions. There is also a safe version of this function that checks the input.

Parameters: row_1: the starting row of the submatrix row_2: the ending row of the submatrix col_1: the starting column of the submatrix col_2: the ending column of the submatrix

Returns the submatrix from (row_1, col_1) to (row_2, col_2)(exclusively).

Examples

use qfall_math::{integer::MatPolyOverZ, traits::MatrixGetSubmatrix};
use std::str::FromStr;

let mat = MatPolyOverZ::identity(3, 3);

let sub_mat_1 = mat.get_submatrix(0, 2, 1, 1).unwrap();
let sub_mat_2 = mat.get_submatrix(0, -1, 1, -2).unwrap();
let sub_mat_3 = unsafe{mat.get_submatrix_unchecked(0, 3, 1, 2)};

let e_2 = MatPolyOverZ::from_str("[[0],[1  1],[0]]").unwrap();
assert_eq!(e_2, sub_mat_1);
assert_eq!(e_2, sub_mat_2);
assert_eq!(e_2, sub_mat_3);

Safety

To use this function safely, make sure that the selected submatrix is part of the matrix. If it is not, memory leaks, unexpected panics, etc. might occur.

fn get_row( &self, row: impl TryInto<i64> + Display + Clone, ) -> Result<Self, MathError>

Outputs the row vector of the specified row.

unsafe fn get_row_unchecked(&self, row: i64) -> Self

Outputs the row vector of the specified row.

fn get_column( &self, column: impl TryInto<i64> + Display + Clone, ) -> Result<Self, MathError>

Outputs the column vector of the specified column.

unsafe fn get_column_unchecked(&self, column: i64) -> Self

Outputs the column vector of the specified column.

fn get_submatrix( &self, row_1: impl TryInto<i64> + Display, row_2: impl TryInto<i64> + Display, col_1: impl TryInto<i64> + Display, col_2: impl TryInto<i64> + Display, ) -> Result<Self, MathError>

Returns a deep copy of the submatrix defined by the given parameters. All entries starting from (row_1, col_1) to (row_2, col_2)(inclusively) are collected in a new matrix. Note that row_1 >= row_2 and col_1 >= col_2 must hold after converting negative indices. Otherwise the function will panic.

fn get_rows(&self) -> Vec<Self>

Outputs a Vec containing all rows of the matrix in order. Use this function for simple iteration over the rows of the matrix.

fn get_columns(&self) -> Vec<Self>

Outputs a Vec containing all columns of the matrix in order. Use this function for simple iteration over the columns of the matrix.

impl MatrixSetEntry<&PolyOverZ> for MatPolyOverZ

unsafe fn set_entry_unchecked( &mut self, row: i64, column: i64, value: &PolyOverZ, )

Sets the value of a specific matrix entry according to a given value of type PolyOverZ without checking whether the coordinate is part of the matrix.

Parameters:

• row: specifies the row in which the entry is located
• column: specifies the column in which the entry is located
• value: specifies the value to which the entry is set

Safety

To use this function safely, make sure that the selected entry is part of the matrix. If it is not, memory leaks, unexpected panics, etc. might occur.

Examples

use qfall_math::integer::{MatPolyOverZ, PolyOverZ};
use qfall_math::traits::MatrixSetEntry;
use std::str::FromStr;

let mut matrix = MatPolyOverZ::new(2, 2);
let value = PolyOverZ::from_str("2  1 1").unwrap();

unsafe {
    matrix.set_entry_unchecked(0, 1, &value);
    matrix.set_entry_unchecked(1, 0, &PolyOverZ::from(2));
}

assert_eq!("[[0, 2  1 1],[1  2, 0]]", matrix.to_string());

fn set_entry( &mut self, row: impl TryInto<i64> + Display, column: impl TryInto<i64> + Display, value: T, ) -> Result<(), MathError>

Sets the value of a specific matrix entry according to a given value.

impl MatrixSetEntry<PolyOverZ> for MatPolyOverZ

fn set_entry( &mut self, row: impl TryInto<i64> + Display, column: impl TryInto<i64> + Display, value: PolyOverZ, ) -> Result<(), MathError>

Documentation can be found at MatPolyOverZ::set_entry for &PolyOverZ.

unsafe fn set_entry_unchecked( &mut self, row: i64, column: i64, value: PolyOverZ, )

Documentation can be found at MatPolyOverZ::set_entry for &PolyOverZ.

impl MatrixSetSubmatrix for MatPolyOverZ

unsafe fn set_submatrix_unchecked( &mut self, row_self_start: i64, col_self_start: i64, row_self_end: i64, col_self_end: i64, other: &Self, row_other_start: i64, col_other_start: i64, row_other_end: i64, col_other_end: i64, )

Sets the matrix entries in self to entries defined in other. The entries in self starting from (row_self_start, col_self_start) up to (row_self_end, col_self_end)are set to be the entries from the submatrix from other defined by (row_other_start, col_other_start) to (row_other_end, col_other_end) (exclusively).

Parameters: row_self_start: the starting row of the matrix in which to set a submatrix col_self_start: the starting column of the matrix in which to set a submatrix other: the matrix from where to take the submatrix to set row_other_start: the starting row of the specified submatrix col_other_start: the starting column of the specified submatrix row_other_end: the ending row of the specified submatrix col_other_end:the ending column of the specified submatrix

Examples

use qfall_math::{integer::MatPolyOverZ, traits::MatrixSetSubmatrix};
use std::str::FromStr;

let mut mat = MatPolyOverZ::identity(3, 3);

mat.set_submatrix(0, 1, &mat.clone(), 0, 0, 1, 1).unwrap();
// [[1,1,0],[0,0,1],[0,0,1]]
let mat_cmp = MatPolyOverZ::from_str("[[1  1, 1  1, 0],[0, 0, 1  1],[0, 0, 1  1]]").unwrap();
assert_eq!(mat, mat_cmp);

unsafe{ mat.set_submatrix_unchecked(2, 0, 3, 2, &mat.clone(), 0, 0, 1, 2) };
let mat_cmp = MatPolyOverZ::from_str("[[1  1, 1  1, 0],[0, 0, 1  1],[1  1, 1  1, 1  1]]").unwrap();
assert_eq!(mat, mat_cmp);

Safety

To use this function safely, make sure that the selected submatrices are part of the matrices, the submatrices are of the same dimensions and the base types are the same. If not, memory leaks, unexpected panics, etc. might occur.

fn set_row( &mut self, row_0: impl TryInto<i64> + Display, other: &Self, row_1: impl TryInto<i64> + Display, ) -> Result<(), MathError>

Sets a row of the given matrix to the provided row of other.

unsafe fn set_row_unchecked(&mut self, row_0: i64, other: &Self, row_1: i64)

Sets a row of the given matrix to the provided row of other.

fn set_column( &mut self, col_0: impl TryInto<i64> + Display, other: &Self, col_1: impl TryInto<i64> + Display, ) -> Result<(), MathError>

Sets a column of the given matrix to the provided column of other.

unsafe fn set_column_unchecked(&mut self, col_0: i64, other: &Self, col_1: i64)

Sets a column of the given matrix to the provided column of other.

fn set_submatrix( &mut self, row_self_start: impl TryInto<i64> + Display, col_self_start: impl TryInto<i64> + Display, other: &Self, row_other_start: impl TryInto<i64> + Display, col_other_start: impl TryInto<i64> + Display, row_other_end: impl TryInto<i64> + Display, col_other_end: impl TryInto<i64> + Display, ) -> Result<(), MathError>

Sets the matrix entries in self to entries defined in other. The entries in self starting from (row_self_start, col_self_start) are set to be the entries from the submatrix from other defined by (row_other_start, col_other_start) to (row_other_end, col_other_end) (inclusively). The original matrix must have sufficiently many entries to contain the defined submatrix.

impl MatrixSwaps for MatPolyOverZ

fn swap_entries( &mut self, row_0: impl TryInto<i64> + Display, col_0: impl TryInto<i64> + Display, row_1: impl TryInto<i64> + Display, col_1: impl TryInto<i64> + Display, ) -> Result<(), MathError>

Swaps two entries of the specified matrix.

Parameters:

• row_0: specifies the row, in which the first entry is located
• col_0: specifies the column, in which the first entry is located
• row_1: specifies the row, in which the second entry is located
• col_1: specifies the column, in which the second entry is located

Negative indices can be used to index from the back, e.g., -1 for the last element.

Returns an empty Ok if the action could be performed successfully. Otherwise, a MathError is returned if one of the specified entries is not part of the matrix.

Examples

use qfall_math::{integer::MatPolyOverZ, traits::MatrixSwaps};

let mut matrix = MatPolyOverZ::new(4, 3);
matrix.swap_entries(0, 0, 2, 1);

Errors and Failures

• Returns a MathError of type MathError::OutOfBounds if row or column are greater than the matrix size.

fn swap_columns( &mut self, col_0: impl TryInto<i64> + Display, col_1: impl TryInto<i64> + Display, ) -> Result<(), MathError>

Swaps two columns of the specified matrix.

Parameters:

• col_0: specifies the first column which is swapped with the second one
• col_1: specifies the second column which is swapped with the first one

Negative indices can be used to index from the back, e.g., -1 for the last element.

Returns an empty Ok if the action could be performed successfully. Otherwise, a MathError is returned if one of the specified columns is not part of the matrix.

Examples

use qfall_math::{integer::MatPolyOverZ, traits::MatrixSwaps};

let mut matrix = MatPolyOverZ::new(4, 3);
matrix.swap_columns(0, 2);

Errors and Failures

• Returns a MathError of type OutOfBounds if one of the given columns is greater than the matrix.

fn swap_rows( &mut self, row_0: impl TryInto<i64> + Display, row_1: impl TryInto<i64> + Display, ) -> Result<(), MathError>

Swaps two rows of the specified matrix.

Parameters:

• row_0: specifies the first row which is swapped with the second one
• row_1: specifies the second row which is swapped with the first one

Negative indices can be used to index from the back, e.g., -1 for the last element.

Returns an empty Ok if the action could be performed successfully. Otherwise, a MathError is returned if one of the specified rows is not part of the matrix.

Examples

use qfall_math::{integer::MatPolyOverZ, traits::MatrixSwaps};

let mut matrix = MatPolyOverZ::new(4, 3);
matrix.swap_rows(0, 2);

Errors and Failures

• Returns a MathError of type OutOfBounds if one of the given rows is greater than the matrix.

impl Mul<&MatPolyOverZ> for &MatPolynomialRingZq

fn mul(self, other: &MatPolyOverZ) -> Self::Output

Implements the Mul trait for a MatPolynomialRingZq matrix with a MatPolyOverZ matrix. Mul is implemented for any combination of owned and borrowed values.

Parameters:

• other: specifies the value to multiply with self

Returns the product of self and other as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::MatPolynomialRingZq;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolynomialRingZq::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]] / 3  1 2 3 mod 17").unwrap();
let mat_2 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();

let mat_3 = &mat_1 * &mat_2;

Panics …

• if the dimensions of self and other do not match for multiplication.

type Output = MatPolynomialRingZq

The resulting type after applying the * operator.

impl Mul<&MatPolynomialRingZq> for &MatPolyOverZ

fn mul(self, other: &MatPolynomialRingZq) -> Self::Output

Implements the Mul trait for a MatPolyOverZ matrix with a MatPolynomialRingZq matrix. Mul is implemented for any combination of owned and borrowed values.

Parameters:

• other: specifies the value to multiply with self

Returns the product of self and other as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::MatPolynomialRingZq;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();
let mat_2 = MatPolynomialRingZq::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]] / 3  1 2 3 mod 17").unwrap();

let mat_3 = &mat_1 * &mat_2;

Panics …

• if the dimensions of self and other do not match for multiplication.

type Output = MatPolynomialRingZq

The resulting type after applying the * operator.

impl Mul<&PolyOverZ> for &MatPolyOverZ

fn mul(self, scalar: &PolyOverZ) -> Self::Output

Implements the Mul trait for a MatPolyOverZ matrix with a PolyOverZ. Mul is implemented for any combination of owned and borrowed values.

Parameters:

• scalar: specifies the scalar by which the matrix is multiplied

Returns the product of self and scalar as a MatPolyOverZ.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::integer::PolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();
let poly = PolyOverZ::from_str("3  1 2 3").unwrap();

let mat_2 = &mat_1 * &poly;

type Output = MatPolyOverZ

The resulting type after applying the * operator.

impl Mul<&PolynomialRingZq> for &MatPolyOverZ

fn mul(self, scalar: &PolynomialRingZq) -> Self::Output

Implements the Mul trait for a MatPolyOverZ matrix with a PolynomialRingZq. Mul is implemented for any combination of owned and borrowed values.

Parameters:

• scalar: Specifies the scalar by which the matrix is multiplied.

Returns the product of self and scalar as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::{ModulusPolynomialRingZq, PolynomialRingZq};
use qfall_math::integer::{MatPolyOverZ, PolyOverZ};
use std::str::FromStr;

let modulus = ModulusPolynomialRingZq::from_str("4  1 0 0 1 mod 17").unwrap();
let poly_mat1 = MatPolyOverZ::from_str("[[3  0 1 1, 1  42],[0, 2  1 2]]").unwrap();
let poly = PolyOverZ::from_str("3  1 0 1").unwrap();
let poly_ring = PolynomialRingZq::from((&poly, &modulus));

let poly_ring_mat1 = &poly_mat1 * &poly_ring;

type Output = MatPolynomialRingZq

The resulting type after applying the * operator.

impl Mul<&Z> for &MatPolyOverZ

fn mul(self, scalar: &Z) -> Self::Output

Implements the Mul trait for a MatPolyOverZ matrix with a Z integer. Mul is implemented for any combination of owned and borrowed values.

Parameters:

• scalar: specifies the scalar by which the matrix is multiplied

Returns the product of self and scalar as a MatPolyOverZ.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::integer::Z;
use std::str::FromStr;

let mat_1 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();
let integer = Z::from(3);

let mat_2 = &mat_1 * &integer;

type Output = MatPolyOverZ

The resulting type after applying the * operator.

impl Mul for &MatPolyOverZ

fn mul(self, other: Self) -> Self::Output

Implements the Mul trait for two MatPolyOverZ values. Mul is implemented for any combination of MatPolyOverZ and borrowed MatPolyOverZ.

Parameters:

• other: specifies the value to multiply with self

Returns the product of self and other as a MatPolyOverZ.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();
let b: MatPolyOverZ = MatPolyOverZ::from_str("[[1  -42, 2  24 42],[1  -1, 1  17],[0, 2  1 42]]").unwrap();

let c = &a * &b;
let d = a * b;
let e = &c * d;
let f = c * &e;

Panics …

• if the dimensions of self and other do not match for multiplication.

type Output = MatPolyOverZ

The resulting type after applying the * operator.

impl MulAssign<&PolyOverZ> for MatPolyOverZ

fn mul_assign(&mut self, scalar: &PolyOverZ)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<&Z> for MatPolyOverZ

fn mul_assign(&mut self, scalar: &Z)

Computes the scalar multiplication of self and scalar reusing the memory of self.

Parameters:

• scalar: specifies the value to multiply to self

Returns the scalar of the matrix as a MatPolyOverZ.

Examples

use qfall_math::integer::{Z,PolyOverZ,MatPolyOverZ};
use std::str::FromStr;

let mut a = MatPolyOverZ::from_str("[[3  0 1 1, 1  42],[0, 2  1 2]]").unwrap();
let b = Z::from(2);
let c = PolyOverZ::from_str("2  1 -3").unwrap();

a *= &b;
a *= b;
a *= &c;
a *= c;
a *= 2;
a *= -2;

impl MulAssign<PolyOverZ> for MatPolyOverZ

fn mul_assign(&mut self, other: PolyOverZ)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<Z> for MatPolyOverZ

fn mul_assign(&mut self, other: Z)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<i16> for MatPolyOverZ

fn mul_assign(&mut self, other: i16)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<i32> for MatPolyOverZ

fn mul_assign(&mut self, other: i32)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<i64> for MatPolyOverZ

fn mul_assign(&mut self, scalar: i64)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<i8> for MatPolyOverZ

fn mul_assign(&mut self, other: i8)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<u16> for MatPolyOverZ

fn mul_assign(&mut self, other: u16)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<u32> for MatPolyOverZ

fn mul_assign(&mut self, other: u32)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<u64> for MatPolyOverZ

fn mul_assign(&mut self, scalar: u64)

Documentation at MatPolyOverZ::mul_assign.

impl MulAssign<u8> for MatPolyOverZ

fn mul_assign(&mut self, other: u8)

Documentation at MatPolyOverZ::mul_assign.

impl PartialEq for MatPolyOverZ

fn eq(&self, other: &Self) -> bool

Checks if two matrices over PolyOverZ are equal. Used by the == and != operators.

Parameters:

• other: the other value that is used to compare the elements

Returns true if the elements are equal, otherwise false.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;
let mat_1 = "[[0, 1  17, 2  24 42],[2  24 42, 2  24 42, 2  24 42]]";
let a: MatPolyOverZ = MatPolyOverZ::from_str(mat_1).unwrap();
let mat_2 = "[[1  17, 1  17, 2  24 42],[2  24 42, 2  24 42, 2  24 42]]";
let b: MatPolyOverZ = MatPolyOverZ::from_str(mat_2).unwrap();

// These are all equivalent and return false.
let compared: bool = (a == b);
let compared: bool = (&a == &b);
let compared: bool = (a.eq(&b));
let compared: bool = (MatPolyOverZ::eq(&a, &b));

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Rem<&Modulus> for &MatPolyOverZ

fn rem(self, modulus: &Modulus) -> Self::Output

Computes self mod modulus as long as modulus is greater than 1. For negative entries in self, the smallest positive representative is returned.

Parameters:

• modulus: specifies a non-zero integer over which the positive remainders are computed

Returns self mod modulus as a MatPolyOverZ instance.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::integer_mod_q::Modulus;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[2  1 -2],[1  42]]").unwrap();
let b = Modulus::from(24);

let c: MatPolyOverZ = &a % &b;

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<&Z> for &MatPolyOverZ

fn rem(self, modulus: &Z) -> Self::Output

Computes self mod modulus as long as modulus is greater than 1. For negative entries in self, the smallest positive representative is returned.

Parameters:

• modulus: specifies a non-zero integer over which the positive remainders are computed

Returns self mod modulus as a MatPolyOverZ instance.

Examples

use qfall_math::integer::{MatPolyOverZ, Z};
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[2  1 -2],[1  42]]").unwrap();
let b: Z = Z::from(24);

let c: MatPolyOverZ = a % b;

Panics …

• if modulus is smaller than 2.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl<Mod: Into<ModulusPolynomialRingZq>> Rem<Mod> for &MatPolyOverZ

fn rem(self, modulus: Mod) -> Self::Output

Computes self mod modulus as long as modulus is greater than 1. For negative entries in self, the smallest positive representative is returned.

Parameters:

• modulus: specifies a non-zero integer over which the positive remainders are computed

Returns self mod modulus as a MatPolyOverZ instance.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::integer_mod_q::ModulusPolynomialRingZq;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[2  1 -2],[1  42]]").unwrap();
let b = ModulusPolynomialRingZq::from_str("4  1 0 0 1 mod 24").unwrap();

let c: MatPolyOverZ = &a % &b;

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl<Mod: Into<ModulusPolynomialRingZq>> Rem<Mod> for MatPolyOverZ

fn rem(self, modulus: Mod) -> Self::Output

Computes self mod modulus as long as modulus is greater than 1. For negative entries in self, the smallest positive representative is returned.

Parameters:

• modulus: specifies a non-zero integer over which the positive remainders are computed

Returns self mod modulus as a MatPolyOverZ instance.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::integer_mod_q::ModulusPolynomialRingZq;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[2  1 -2],[1  42]]").unwrap();
let b = ModulusPolynomialRingZq::from_str("4  1 0 0 1 mod 24").unwrap();

let c: MatPolyOverZ = &a % &b;

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<i16> for MatPolyOverZ

fn rem(self, modulus: i16) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<i32> for MatPolyOverZ

fn rem(self, modulus: i32) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<i64> for MatPolyOverZ

fn rem(self, modulus: i64) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<i8> for MatPolyOverZ

fn rem(self, modulus: i8) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<u16> for MatPolyOverZ

fn rem(self, modulus: u16) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<u32> for MatPolyOverZ

fn rem(self, modulus: u32) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<u64> for MatPolyOverZ

fn rem(self, modulus: u64) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Rem<u8> for MatPolyOverZ

fn rem(self, modulus: u8) -> Self::Output

Documentation can be found at MatPolyOverZ::rem.

type Output = MatPolyOverZ

The resulting type after applying the % operator.

impl Serialize for MatPolyOverZ

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Implements the serialize option. This allows to create a Json-object from a given MatPolyOverZ.

impl Sub<&MatPolyOverZ> for &MatPolynomialRingZq

fn sub(self, other: &MatPolyOverZ) -> Self::Output

Implements the Sub trait for a MatPolynomialRingZq matrix with a MatPolyOverZ matrix. Sub is implemented for any combination of owned and borrowed values.

Parameters:

• other: specifies the value to subtract from self

Returns the subtraction of self by other as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::MatPolynomialRingZq;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolynomialRingZq::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]] / 3  1 2 3 mod 17").unwrap();
let mat_2 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();

let mat_3 = &mat_1 - &mat_2;

Panics …

• if the dimensions of self and other do not match for multiplication.

type Output = MatPolynomialRingZq

The resulting type after applying the - operator.

impl Sub<&MatPolynomialRingZq> for &MatPolyOverZ

fn sub(self, other: &MatPolynomialRingZq) -> Self::Output

Implements the Sub trait for a MatPolyOverZ matrix with a MatPolynomialRingZq matrix. Sub is implemented for any combination of owned and borrowed values.

Parameters:

• other: specifies the value to subtract from self

Returns the subtraction of self by other as a MatPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::MatPolynomialRingZq;
use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let mat_1 = MatPolyOverZ::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]]").unwrap();
let mat_2 = MatPolynomialRingZq::from_str("[[2  1 42, 1  17],[1  8, 2  5 6]] / 3  1 2 3 mod 17").unwrap();

let mat_3 = &mat_1 - &mat_2;

Panics …

• if the dimensions of self and other do not match for multiplication.

type Output = MatPolynomialRingZq

The resulting type after applying the - operator.

impl Sub for &MatPolyOverZ

fn sub(self, other: Self) -> Self::Output

Implements the Sub trait for two MatPolyOverZ values. Sub is implemented for any combination of MatPolyOverZ and borrowed MatPolyOverZ.

Parameters:

• other: specifies the value to subtract fromself

Returns the result of the subtraction as a MatPolyOverZ.

Examples

use qfall_math::integer::MatPolyOverZ;
use std::str::FromStr;

let a: MatPolyOverZ = MatPolyOverZ::from_str("[[0, 1  42, 2  42 24],[3  17 24 42, 1  17, 1  42]]").unwrap();
let b: MatPolyOverZ = MatPolyOverZ::from_str("[[1  -42, 0, 2  24 42],[3  1 12 4, 1  -1, 1  17]]").unwrap();

let c: MatPolyOverZ = &a - &b;
let d: MatPolyOverZ = a - b;
let e: MatPolyOverZ = &c - d;
let f: MatPolyOverZ = c - &e;

Panics …

• if the dimensions of both matrices mismatch.

type Output = MatPolyOverZ

The resulting type after applying the - operator.

impl SubAssign<&MatPolyOverZ> for MatPolyOverZ

fn sub_assign(&mut self, other: &Self)

Computes the subtraction of self and other reusing the memory of self.

Parameters:

• other: specifies the value to subtract from self

Examples

use qfall_math::integer::MatPolyOverZ;
let mut a = MatPolyOverZ::identity(2, 2);
let b = MatPolyOverZ::new(2, 2);

a -= &b;
a -= b;

Panics …

• if the matrix dimensions mismatch.

impl SubAssign<&MatPolyOverZ> for MatPolynomialRingZq

fn sub_assign(&mut self, other: &MatPolyOverZ)

Documentation at MatPolynomialRingZq::sub_assign.

impl SubAssign<MatPolyOverZ> for MatPolynomialRingZq

fn sub_assign(&mut self, other: MatPolyOverZ)

Documentation at MatPolynomialRingZq::sub_assign.

impl SubAssign for MatPolyOverZ

fn sub_assign(&mut self, other: MatPolyOverZ)

Documentation at MatPolyOverZ::sub_assign.

impl Tensor for MatPolyOverZ

fn tensor_product(&self, other: &Self) -> Self

Computes the tensor product of self with other.

Parameters:

• other: the value with which the tensor product is computed.

Returns the tensor product of self with other.

Examples

use qfall_math::integer::MatPolyOverZ;
use qfall_math::traits::Tensor;
use std::str::FromStr;

let mat_1 = MatPolyOverZ::from_str("[[1  1, 2  1 1]]").unwrap();
let mat_2 = MatPolyOverZ::from_str("[[1  1, 1  2]]").unwrap();

let mat_ab = mat_1.tensor_product(&mat_2);
let mat_ba = mat_2.tensor_product(&mat_1);

let res_ab = "[[1  1, 1  2, 2  1 1, 2  2 2]]";
let res_ba = "[[1  1, 2  1 1, 1  2, 2  2 2]]";
assert_eq!(mat_ab, MatPolyOverZ::from_str(res_ab).unwrap());
assert_eq!(mat_ba, MatPolyOverZ::from_str(res_ba).unwrap());

impl Eq for MatPolyOverZ