linalg · SparseMatrix¶

29 accepted declarations. Python and Rust forms, contracts, evidence, failure boundaries, and checked usages are kept together below.

Worked example¶

The complete checked program Apply and multiply canonical sparse exact operators uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Apply and multiply canonical sparse exact operators."""

from noether import Z
from noether.linalg import SparseMatrix, Vector


def main() -> None:
    operator = SparseMatrix.from_triplets(
        Z,
        (3, 3),
        [(0, 0, 2), (0, 2, -1), (1, 1, 3), (2, 0, 4)],
    )
    vector = Vector.from_values(Z, [5, 7, 11])
    image = operator.apply(vector)
    assert image.to_values() == [-1, 21, 20]
    assert (operator @ operator).nnz == 4
    print(f"A v = {image.to_values()}; nnz(A^2) = {(operator @ operator).nnz}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/05_sparse_exact_operators.py.

`linalg.SparseMatrix`¶

A canonical sparse matrix over one explicit coefficient context.

PythonRust

class SparseMatrix

noether::linalg::SparseMatrix · Direct Rust declaration

pub struct SparseMatrix<R: Ring> { /* private fields */ }

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/05_sparse_exact_operators.py:10 · examples/05_sparse_exact_operators.py:6 · validation/unit/commalg/test_quotient_facade.py:179 · validation/unit/commalg/test_quotient_facade.py:18 · validation/unit/commalg/test_quotient_facade.py:191 · validation/unit/commalg/test_quotient_facade.py:192

`linalg.SparseMatrix.add`¶

Add another compatible value to this value.

Detailed contract

Add sparse matrices with equal contexts and shapes. Returns the argument unchanged.

PythonRust

(self, other: SparseMatrix[R]) -> SparseMatrix[R]

noether::linalg::SparseMatrix::add · Direct Rust declaration

pub fn add(&self, rhs: &Self) -> Result<Self, LinalgError>
fn add(self, rhs: &SparseMatrix<R>) -> Self::Output

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/infra/test_discovery.py:211 · validation/unit/infra/test_public_api_index.py:293

`linalg.SparseMatrix.getitem`¶

Return the entry selected by the supplied index.

Detailed contract

Materialize one coefficient, failing when its index is outside the shape.

PythonRust

(self, index: tuple[int, int]) -> int | _Fraction | ResidueClass | FiniteFieldElement | PadicElement | PadicLocalFieldElement | QadicElement | RealBall | ComplexBall | PolynomialScalar | QuotientScalar

noether::linalg::SparseMatrix::get · Direct Rust declaration

pub fn get(&self, row: usize, col: usize) -> Result<R::Element, IndexError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

`linalg.SparseMatrix.matmul`¶

Multiply this value by another compatible value.

Detailed contract

Compose two sparse matrices by exact sparse matrix multiplication.

PythonRust

(self, other: SparseMatrix[R]) -> SparseMatrix[R]

noether::linalg::SparseMatrix::matmul · Direct Rust declaration

pub fn matmul(&self, rhs: &Self) -> Result<Self, LinalgError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/infra/test_discovery.py:199 · validation/unit/infra/test_discovery.py:213 · validation/unit/infra/test_docs_site_generator.py:146 · validation/unit/infra/test_docs_site_generator.py:149 · validation/unit/infra/test_docs_site_generator.py:150 · validation/unit/infra/test_docs_site_generator.py:152

`linalg.SparseMatrix.mul`¶

Multiply this value by another compatible value.

PythonRust

(self, scalar: int | _Fraction | ResidueClass | FiniteFieldElement | PadicElement | PadicLocalFieldElement | QadicElement | RealBall | ComplexBall | PolynomialScalar | QuotientScalar) -> SparseMatrix[R]

noether::linalg::SparseMatrix::mul · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/infra/test_public_api_index.py:214

`linalg.SparseMatrix.neg`¶

Return the additive inverse of this value.

Detailed contract

Negate every stored coefficient.

PythonRust

(self) -> SparseMatrix[R]

noether::linalg::SparseMatrix::neg · Direct Rust declaration

pub fn neg(&self) -> Result<Self, LinalgError>
fn neg(self) -> Self::Output

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

`linalg.SparseMatrix.rmul`¶

Multiply this value by a compatible value on its left.

PythonRust

(self, scalar: int | _Fraction | ResidueClass | FiniteFieldElement | PadicElement | PadicLocalFieldElement | QadicElement | RealBall | ComplexBall | PolynomialScalar | QuotientScalar) -> SparseMatrix[R]

noether::linalg::SparseMatrix · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

`linalg.SparseMatrix.sub`¶

Subtract another compatible value from this value.

Detailed contract

Subtract sparse matrices with equal contexts and shapes.

PythonRust

(self, other: SparseMatrix[R]) -> SparseMatrix[R]

noether::linalg::SparseMatrix::sub · Direct Rust declaration

pub fn sub(&self, rhs: &Self) -> Result<Self, LinalgError>
fn sub(self, rhs: &SparseMatrix<R>) -> Self::Output

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/infra/test_discovery.py:212

`linalg.SparseMatrix.apply`¶

Apply this sparse linear operator to a vector.

PythonRust

(self, vector: Vector[R]) -> Vector[R]

noether::linalg::SparseMatrix::apply · Direct Rust declaration

fn apply(&self, vector: &Vector<R>) -> Result<Vector<R>, LinalgError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/05_sparse_exact_operators.py:16 · validation/unit/commalg/test_local_algebra.py:94 · validation/unit/commalg/test_local_algebra.py:97 · validation/unit/commalg/test_polynomial_facade.py:199 · validation/unit/commalg/test_quotient_facade.py:186 · validation/unit/groups/test_weight_characters.py:39

`linalg.SparseMatrix.apply_block`¶

Apply this sparse linear operator to a dense matrix block.

PythonRust

(self, block: Matrix[R]) -> Matrix[R]

noether::linalg::SparseMatrix::apply_block · Direct Rust declaration

fn apply_block(&self, block: &Matrix<R>) -> Result<Matrix<R>, LinalgError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/infra/test_discovery.py:198 · validation/unit/linalg/test_semilinear_facade.py:22 · validation/unit/linalg/test_sparse_matrix_facade.py:113 · validation/unit/linalg/test_sparse_matrix_facade.py:65 · validation/unit/linalg/test_vector_facade.py:54

`linalg.SparseMatrix.column_indices`¶

Canonical CSR column indices.

PythonRust

(self) -> list[int]

noether::linalg::SparseMatrix::column_indices · Direct Rust declaration

pub fn column_indices(&self) -> &[usize]

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_sparse_matrix_facade.py:121 · validation/unit/linalg/test_sparse_matrix_facade.py:33

`linalg.SparseMatrix.csr`¶

Canonical (row_offsets, column_indices, values) arrays.

PythonRust

(self) -> tuple[list[int], list[int], list[int | _Fraction | ResidueClass | FiniteFieldElement | PadicElement | PadicLocalFieldElement | QadicElement | RealBall | ComplexBall | PolynomialScalar | QuotientScalar]]

noether::linalg::SparseMatrix · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_sparse_matrix_facade.py:31 · validation/unit/linalg/test_sparse_matrix_facade.py:44

`linalg.SparseMatrix.density`¶

Fraction of cells stored explicitly.

Detailed contract

Fraction of matrix cells that are explicitly stored.

PythonRust

(self) -> float

noether::linalg::SparseMatrix::density · Direct Rust declaration

pub fn density(&self) -> f64
fn density(&self) -> f64

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_sparse_matrix_facade.py:30 · validation/corpus/numthy/diagonal-quadric-local-density-sums.py:96

`linalg.SparseMatrix.from_csr`¶

Construct from canonical CSR arrays.

Detailed contract

Construct a canonical CSR matrix from its component arrays. The arrays must already be canonical: row offsets are nondecreasing, columns are strictly increasing within each row, and no value is zero.

PythonRust

(cls, ring: _SparseContext, shape: tuple[int, int], row_offsets: Iterable[int], column_indices: Iterable[int], values: Iterable[int | _Fraction | ResidueClass | FiniteFieldElement | PadicElement | PadicLocalFieldElement | QadicElement | RealBall | ComplexBall | PolynomialScalar | QuotientScalar]) -> SparseMatrix[_SparseContext]

noether::linalg::SparseMatrix::from_csr · Direct Rust declaration

pub fn from_csr( ring: R, rows: usize, cols: usize, row_offsets: Vec<usize>, column_indices: Vec<usize>, values: Vec<R::Element>, ) -> Result<Self, LinalgError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_sparse_matrix_facade.py:117 · validation/unit/linalg/test_sparse_matrix_facade.py:163 · validation/unit/linalg/test_sparse_matrix_facade.py:53

`linalg.SparseMatrix.from_dense`¶

Losslessly convert a supported dense facade matrix.

Detailed contract

Losslessly convert a dense matrix into canonical sparse form.

PythonRust

(cls, matrix: Matrix[_SparseContext]) -> SparseMatrix[_SparseContext]

noether::linalg::SparseMatrix::from_dense · Direct Rust declaration

pub fn from_dense(matrix: &Matrix<R>) -> Result<Self, LinalgError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/commalg/test_quotient_facade.py:191 · validation/unit/linalg/test_sparse_matrix_facade.py:115 · validation/unit/linalg/test_sparse_matrix_facade.py:41 · validation/unit/numthy/test_padic_local_field_facade.py:206

`linalg.SparseMatrix.from_json`¶

Deserialize and revalidate a sparse matrix.

Detailed contract

Deserialize and revalidate a sparse matrix and its coefficient context.

PythonRust

(cls, value: str) -> SparseMatrix[_SparseContext]

noether::linalg::SparseMatrix::from_json · Direct Rust declaration

pub fn from_json(value: &str) -> Result<Self, NoetherError>where R: for<'de> Deserialize<'de>, R::Element: for<'de> Deserialize<'de>,

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106 · validation/unit/combin/test_graph_facade.py:25 · validation/unit/combinatorics/test_kashiwara_crystal.py:32

`linalg.SparseMatrix.from_triplets`¶

Construct from (row, column, coefficient) triplets.

Detailed contract

Construct a canonical sparse matrix from coordinate triplets. Repeated coordinates are added in input order. Entries whose combined coefficient is exactly zero are omitted.

PythonRust

(cls, ring: IntegerRing, shape: tuple[int, int], entries: Iterable[tuple[int, int, int]]) -> SparseMatrix[IntegerRing]
(cls, ring: RationalField, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | _Fraction]]) -> SparseMatrix[RationalField]
(cls, ring: ResidueRing, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | ResidueClass]]) -> SparseMatrix[ResidueRing]
(cls, ring: FiniteField, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | FiniteFieldElement]]) -> SparseMatrix[FiniteField]
(cls, ring: PadicRing, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | PadicElement]]) -> SparseMatrix[PadicRing]
(cls, ring: PadicField, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | PadicElement]]) -> SparseMatrix[PadicField]
(cls, ring: QadicRing, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | QadicElement]]) -> SparseMatrix[QadicRing]
(cls, ring: QadicField, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | QadicElement]]) -> SparseMatrix[QadicField]
(cls, ring: PadicLocalField, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | PadicLocalFieldElement]]) -> SparseMatrix[PadicLocalField]
(cls, ring: PadicLocalFieldOrder, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | PadicLocalFieldElement]]) -> SparseMatrix[PadicLocalFieldOrder]
(cls, ring: RealBallField, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | _Fraction | RealBall]]) -> SparseMatrix[RealBallField]
(cls, ring: ComplexBallField, shape: tuple[int, int], entries: Iterable[tuple[int, int, int | _Fraction | ComplexBall]]) -> SparseMatrix[ComplexBallField]
(cls, ring: PolynomialRing[_PolynomialCoefficientContext], shape: tuple[int, int], entries: Iterable[tuple[int, int, Polynomial[_PolynomialCoefficientContext] | PolynomialScalar]]) -> SparseMatrix[PolynomialRing[_PolynomialCoefficientContext]]
(cls, ring: QuotientRing[C], shape: tuple[int, int], entries: Iterable[tuple[int, int, QuotientElement[C] | Polynomial[C]]]) -> SparseMatrix[QuotientRing[C]]

noether::linalg::SparseMatrix::from_triplets · Direct Rust declaration

pub fn from_triplets<I>( ring: R, rows: usize, cols: usize, entries: I, ) -> Result<Self, LinalgError>where I: IntoIterator<Item = (usize, usize, R::Element)>,

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/05_sparse_exact_operators.py:10 · validation/unit/commalg/test_quotient_facade.py:179 · validation/unit/homalg/test_chain_complex.py:185 · validation/unit/homalg/test_module_facade.py:221 · validation/unit/homalg/test_module_facade.py:628 · validation/unit/homalg/test_padic_homology_facade.py:192

`linalg.SparseMatrix.input_dimension`¶

Return the input dimension recorded by this SparseMatrix.

PythonRust

(self) -> int

noether::linalg::SparseMatrix::input_dimension · Direct Rust declaration

fn input_dimension(&self) -> usize

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_vector_facade.py:50 · validation/parity/linalg/test_exact_solution_modules_parity.py:163 · validation/parity/linalg/test_exact_solution_modules_parity.py:177 · validation/parity/linalg/test_exact_solution_modules_parity.py:200 · validation/parity/linalg/test_exact_solution_modules_parity.py:210

`linalg.SparseMatrix.nnz`¶

Number of stored exact nonzeros.

Detailed contract

Number of explicitly stored nonzero entries.

PythonRust

(self) -> int

noether::linalg::SparseMatrix::nnz · Direct Rust declaration

pub fn nnz(&self) -> usize
fn nnz(&self) -> usize

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/05_sparse_exact_operators.py:18 · examples/05_sparse_exact_operators.py:19 · validation/unit/commalg/test_quotient_facade.py:185 · validation/unit/homalg/test_module_facade.py:222 · validation/unit/linalg/test_sparse_matrix_facade.py:29 · validation/unit/linalg/test_sparse_matrix_facade.py:68

`linalg.SparseMatrix.output_dimension`¶

Return the output dimension recorded by this SparseMatrix.

PythonRust

(self) -> int

noether::linalg::SparseMatrix::output_dimension · Direct Rust declaration

fn output_dimension(&self) -> usize

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_vector_facade.py:51

`linalg.SparseMatrix.padic_smith_invariants`¶

Smith invariant valuations visible below a p-adic ring's precision cap.

Detailed contract

Compute visible Smith valuations through a fill-aware sparse workspace. CSR remains the canonical external representation. Elimination uses a mutable row-and-column map, chooses unit pivots by predicted fill, and switches to the dense correctness floor once measured density reaches the benchmarked cutover.

PythonRust

(self: SparseMatrix[PadicRing]) -> PadicSmithInvariants

noether::linalg::SparseMatrix::padic_smith_invariants · Direct Rust declaration

pub fn padic_smith_invariants( &self, ) -> Result<PadicSmithInvariants, LinalgError>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_padic_smith_facade.py:26 · validation/unit/linalg/test_padic_smith_facade.py:49 · validation/unit/linalg/test_padic_smith_facade.py:72 · validation/unit/linalg/test_padic_smith_facade.py:73 · validation/unit/linalg/test_padic_smith_facade.py:86

`linalg.SparseMatrix.ring`¶

Exact coefficient context.

Detailed contract

The exact coefficient context.

PythonRust

(self) -> R

noether::linalg::SparseMatrix::ring · Direct Rust declaration

pub fn ring(&self) -> &R
fn ring(&self) -> &R

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/11_qadic_witt_vectors.py:3 · examples/13_chinese_remainder_theorem.py:10 · examples/13_chinese_remainder_theorem.py:12 · examples/13_chinese_remainder_theorem.py:9 · examples/14_weighted_polynomials.py:10 · examples/14_weighted_polynomials.py:11

`linalg.SparseMatrix.row_offsets`¶

Canonical CSR row offsets.

PythonRust

(self) -> list[int]

noether::linalg::SparseMatrix::row_offsets · Direct Rust declaration

pub fn row_offsets(&self) -> &[usize]

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/linalg/test_sparse_matrix_facade.py:120 · validation/unit/linalg/test_sparse_matrix_facade.py:32

`linalg.SparseMatrix.shape`¶

(rows, columns).

Detailed contract

(rows, columns).

PythonRust

(self) -> tuple[int, int]

noether::linalg::SparseMatrix::shape · Direct Rust declaration

pub fn shape(&self) -> (usize, usize)

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/27_weight_characters.py:19 · examples/27_weight_characters.py:8 · examples/27_weight_characters.py:9 · examples/distributed/f2_linear_algebra.py:51 · examples/distributed/f2_linear_algebra.py:52 · validation/unit/combin/test_acceptance_workload.py:38

`linalg.SparseMatrix.to_dense`¶

Losslessly materialize a dense matrix with the same context.

Detailed contract

Losslessly materialize the corresponding dense matrix.

PythonRust

(self) -> Matrix[R]

noether::linalg::SparseMatrix::to_dense · Direct Rust declaration

pub fn to_dense(&self) -> Matrix<R>

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/commalg/test_quotient_facade.py:187 · validation/unit/commalg/test_quotient_facade.py:191 · validation/unit/homalg/test_module_facade.py:223 · validation/unit/homalg/test_padic_homology_facade.py:195 · validation/unit/homalg/test_padic_homology_facade.py:210 · validation/unit/linalg/test_acceptance_workload.py:115

`linalg.SparseMatrix.to_json`¶

Serialize the coefficient context and canonical CSR arrays.

Detailed contract

Serialize the complete coefficient context and canonical CSR arrays.

PythonRust

(self) -> str

noether::linalg::SparseMatrix::to_json · Direct Rust declaration

pub fn to_json(&self) -> Result<String, NoetherError>where R: Serialize, R::Element: Serialize,

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/category/test_category.py:15 · validation/unit/combin/test_acceptance_workload.py:30 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106

`linalg.SparseMatrix.transpose`¶

Return the canonical sparse transpose.

PythonRust

(self) -> SparseMatrix[R]

noether::linalg::SparseMatrix::transpose · Direct Rust declaration

pub fn transpose(&self) -> Self

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/39_kahler_differentials.py:26 · examples/distributed/f2_linear_algebra.py:31 · validation/unit/combin/test_graph_facade.py:51 · validation/unit/commalg/test_power_series_facade.py:347 · validation/unit/commalg/test_quotient_facade.py:162 · validation/unit/infra/test_boundary_properties.py:54

`linalg.SparseMatrix.values`¶

Canonical CSR nonzero coefficients.

PythonRust

(self) -> list[int | _Fraction | ResidueClass | FiniteFieldElement | PadicElement | PadicLocalFieldElement | QadicElement | RealBall | ComplexBall | PolynomialScalar | QuotientScalar]

noether::linalg::SparseMatrix::values · Direct Rust declaration

pub fn values(&self) -> &[R::Element]

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: validation/unit/combinatorics/test_partition_types.py:3 · validation/unit/commalg/test_context_tower_workload.py:70 · validation/unit/commalg/test_context_tower_workload.py:82 · validation/unit/homalg/test_exact_submodules.py:31 · validation/unit/homalg/test_exact_submodules.py:32 · validation/unit/homalg/test_exterior_algebra.py:382

`linalg.SparseMatrix.zeros`¶

Construct a sparse zero matrix.

Detailed contract

Construct the sparse zero matrix with the requested shape.

PythonRust

(cls, ring: _SparseContext, shape: tuple[int, int]) -> SparseMatrix[_SparseContext]

noether::linalg::SparseMatrix::zeros · Direct Rust declaration

pub fn zeros(ring: R, rows: usize, cols: usize) -> Self

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded
Semantic ID	noether/linalg/SparseMatrix@1

Executable usage: examples/38_exact_linear_systems.py:19 · examples/distributed/f2_linear_algebra.py:28 · validation/unit/commalg/test_power_series_facade.py:388 · validation/unit/commalg/test_quotient_facade.py:164 · validation/unit/homalg/test_exact_submodules.py:56 · validation/unit/homalg/test_module_facade.py:633

linalg · SparseMatrix¶

Worked example¶

linalg.SparseMatrix¶

linalg.SparseMatrix.__add__¶

linalg.SparseMatrix.__getitem__¶

linalg.SparseMatrix.__matmul__¶

linalg.SparseMatrix.__mul__¶

linalg.SparseMatrix.__neg__¶

linalg.SparseMatrix.__rmul__¶

linalg.SparseMatrix.__sub__¶

linalg.SparseMatrix.apply¶

linalg.SparseMatrix.apply_block¶

linalg.SparseMatrix.column_indices¶

linalg.SparseMatrix.csr¶

linalg.SparseMatrix.density¶

linalg.SparseMatrix.from_csr¶

linalg.SparseMatrix.from_dense¶

linalg.SparseMatrix.from_json¶

linalg.SparseMatrix.from_triplets¶

linalg.SparseMatrix.input_dimension¶

linalg.SparseMatrix.nnz¶

linalg.SparseMatrix.output_dimension¶

linalg.SparseMatrix.padic_smith_invariants¶

linalg.SparseMatrix.ring¶

linalg.SparseMatrix.row_offsets¶

linalg.SparseMatrix.shape¶

linalg.SparseMatrix.to_dense¶

linalg.SparseMatrix.to_json¶

linalg.SparseMatrix.transpose¶

linalg.SparseMatrix.values¶

linalg.SparseMatrix.zeros¶

`linalg.SparseMatrix`¶

`linalg.SparseMatrix.add`¶

`linalg.SparseMatrix.getitem`¶

`linalg.SparseMatrix.matmul`¶

`linalg.SparseMatrix.mul`¶

`linalg.SparseMatrix.neg`¶

`linalg.SparseMatrix.rmul`¶

`linalg.SparseMatrix.sub`¶

`linalg.SparseMatrix.apply`¶

`linalg.SparseMatrix.apply_block`¶

`linalg.SparseMatrix.column_indices`¶

`linalg.SparseMatrix.csr`¶

`linalg.SparseMatrix.density`¶

`linalg.SparseMatrix.from_csr`¶

`linalg.SparseMatrix.from_dense`¶

`linalg.SparseMatrix.from_json`¶

`linalg.SparseMatrix.from_triplets`¶

`linalg.SparseMatrix.input_dimension`¶

`linalg.SparseMatrix.nnz`¶

`linalg.SparseMatrix.output_dimension`¶

`linalg.SparseMatrix.padic_smith_invariants`¶

`linalg.SparseMatrix.ring`¶

`linalg.SparseMatrix.row_offsets`¶

`linalg.SparseMatrix.shape`¶

`linalg.SparseMatrix.to_dense`¶

`linalg.SparseMatrix.to_json`¶

`linalg.SparseMatrix.transpose`¶

`linalg.SparseMatrix.values`¶

`linalg.SparseMatrix.zeros`¶