linalg · DistributedMatrix¶

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

Worked example¶

The complete checked program Calculate trace and norm in a concrete quadratic finite field uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Calculate trace and norm in a concrete quadratic finite field."""

from noether.numthy import FiniteField


def main() -> None:
    field = FiniteField.extension(5, 2)
    generator = field.generator()
    assert generator**2 + field(4) * generator + field(2) == field.zero()
    assert generator.trace() == field(1)
    assert generator.norm() == field(2)
    print(f"{field}: Tr(a)={generator.trace()}, Nm(a)={generator.norm()}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/08_finite_field_extensions.py.

`linalg.DistributedMatrix`¶

A dense exact F_2 matrix distributed over an explicit MPI world.

PythonRust

class DistributedMatrix

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

Executable usage: examples/distributed/f2_linear_algebra.py:21 · examples/distributed/f2_linear_algebra.py:28 · examples/distributed/f2_linear_algebra.py:33 · examples/distributed/f2_linear_algebra.py:46 · examples/distributed/f2_linear_algebra.py:6 · validation/unit/infra/test_discovery.py:207

`linalg.DistributedMatrix.add`¶

Add another compatible value to this value.

PythonRust

(self, other: DistributedMatrix[FiniteField]) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

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

`linalg.DistributedMatrix.matmul`¶

Multiply this value by another compatible value.

PythonRust

(self, other: DistributedMatrix[FiniteField]) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

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.DistributedMatrix.sub`¶

Subtract another compatible value from this value.

PythonRust

(self, other: DistributedMatrix[FiniteField]) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

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

`linalg.DistributedMatrix.collect`¶

Collect a packed matrix on one root under an explicit byte ceiling.

PythonRust

(self, *, root: int=0, max_bytes: int) -> Matrix[FiniteField] | None

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:40 · validation/unit/infra/test_slurm_handoff.py:694 · validation/bench/sage_power_series.py:297

`linalg.DistributedMatrix.cols`¶

Return the cols recorded by this DistributedMatrix.

PythonRust

(self) -> int

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

Executable usage: examples/distributed/f2_linear_algebra.py:56 · validation/unit/infra/test_mpi_scale_report.py:51 · validation/unit/infra/test_mpi_scale_report.py:77 · validation/unit/infra/test_slurm_handoff.py:115 · validation/unit/infra/test_slurm_handoff.py:123 · validation/unit/infra/test_slurm_handoff.py:355

`linalg.DistributedMatrix.distribute`¶

Collectively scatter one root-owned local matrix without unpacking its packed F_2 storage.

PythonRust

(cls, world: World, *, root: int=0, matrix: Matrix[FiniteField] | None=None, max_bytes: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:21

`linalg.DistributedMatrix.echelon`¶

Collective row echelon form and rank.

PythonRust

(self) -> tuple[DistributedMatrix[FiniteField], int]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:49 · examples/distributed/f2_linear_algebra.py:51 · validation/unit/infra/test_mpi_scale_report.py:150 · validation/unit/infra/test_mpi_scale_report.py:156 · validation/unit/infra/test_mpi_scale_report.py:316 · validation/unit/infra/test_mpi_scale_report.py:326

`linalg.DistributedMatrix.equals`¶

Collective exact equality without gathering either matrix.

PythonRust

(self, other: DistributedMatrix[FiniteField]) -> bool

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:24 · examples/distributed/f2_linear_algebra.py:29 · examples/distributed/f2_linear_algebra.py:30 · examples/distributed/f2_linear_algebra.py:31 · examples/distributed/f2_linear_algebra.py:33 · examples/distributed/f2_linear_algebra.py:35

`linalg.DistributedMatrix.extract_bits`¶

Collectively extract at most 64 packed row bits.

PythonRust

(self, row: int, col_start: int, count: int) -> int

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:23

`linalg.DistributedMatrix.field`¶

Exact coefficient field (F_2 in v0.2).

PythonRust

(self) -> FiniteField

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

Executable usage: examples/08_finite_field_extensions.py:10 · examples/08_finite_field_extensions.py:11 · examples/08_finite_field_extensions.py:12 · examples/08_finite_field_extensions.py:13 · examples/08_finite_field_extensions.py:14 · examples/08_finite_field_extensions.py:3

`linalg.DistributedMatrix.flip`¶

Collective owned toggle of one coefficient.

PythonRust

(self, row: int, col: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:24

`linalg.DistributedMatrix.get`¶

Collective read of one coefficient.

PythonRust

(self, row: int, col: int) -> FiniteFieldElement

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:22 · examples/distributed/f2_linear_algebra.py:26 · examples/distributed/f2_linear_algebra.py:27 · validation/unit/commalg/test_groebner_verification_budget.py:36 · validation/unit/commalg/test_groebner_verification_budget.py:39 · validation/unit/commalg/test_groebner_verification_budget.py:41

`linalg.DistributedMatrix.global_memory_bytes`¶

Return the global memory bytes recorded by this DistributedMatrix.

PythonRust

(self) -> int | None

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

`linalg.DistributedMatrix.identity`¶

Collective identity matrix.

PythonRust

(cls, world: World, field: FiniteField, size: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/01_bezout_certificates.py:10 · examples/01_bezout_certificates.py:12 · examples/01_bezout_certificates.py:14 · examples/01_bezout_certificates.py:9 · examples/02_ball_arithmetic.py:3 · examples/distributed/f2_linear_algebra.py:20

`linalg.DistributedMatrix.inverse`¶

Collective multiplicative inverse or None when singular.

PythonRust

(self) -> DistributedMatrix[FiniteField] | None

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:37 · examples/distributed/f2_linear_algebra.py:39 · validation/unit/commalg/test_context_tower_workload.py:121 · validation/unit/commalg/test_context_tower_workload.py:122 · validation/unit/commalg/test_context_tower_workload.py:75 · validation/unit/commalg/test_context_tower_workload.py:77

`linalg.DistributedMatrix.local_memory_bytes`¶

Return the local memory bytes recorded by this DistributedMatrix.

PythonRust

(self) -> int

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

`linalg.DistributedMatrix.matmul`¶

Collective exact matrix product.

PythonRust

(self, other: DistributedMatrix[FiniteField]) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: validation/unit/infra/test_discovery.py:209 · validation/unit/infra/test_docs_site_generator.py:145 · validation/unit/infra/test_docs_site_generator.py:146 · validation/unit/infra/test_mpi_scale_report.py:168 · validation/unit/infra/test_mpi_scale_report.py:182 · validation/unit/infra/test_mpi_scale_report.py:192

`linalg.DistributedMatrix.nullspace`¶

Collective right-nullspace basis with basis vectors as columns.

PythonRust

(self) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:56 · validation/unit/infra/test_discovery.py:210 · validation/unit/infra/test_mpi_scale_report.py:152 · validation/unit/infra/test_mpi_scale_report.py:156 · validation/unit/infra/test_mpi_scale_report.py:348 · validation/unit/infra/test_mpi_scale_report.py:358

`linalg.DistributedMatrix.open`¶

Collectively reopen a process-grid-independent manifest.

PythonRust

(cls, world: World, path: str) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: validation/unit/infra/test_docs_site_generator.py:101 · validation/unit/infra/test_engine_gateway.py:85 · validation/unit/infra/test_sdist_audit.py:31 · validation/backends/graph/sage_oracle.py:47 · validation/bench/_macaulay2.py:111 · validation/bench/_magma.py:91

`linalg.DistributedMatrix.paste`¶

Collective paste into an owned copy of this matrix.

PythonRust

(self, row_start: int, col_start: int, source: DistributedMatrix[FiniteField]) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:34 · validation/unit/infra/test_discovery.py:208

`linalg.DistributedMatrix.ple_rank`¶

Collective PLE rank without retaining witnesses.

PythonRust

(self) -> int

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:55

`linalg.DistributedMatrix.pluq`¶

Collective deterministic PLUQ decomposition with P L U Q = A.

PythonRust

(self) -> DistributedPLUQFactorization[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:47 · validation/unit/infra/test_mpi_scale_report.py:150 · validation/unit/infra/test_mpi_scale_report.py:156 · validation/unit/linalg/test_acceptance_workload.py:35 · validation/unit/linalg/test_acceptance_workload.py:49 · validation/unit/linalg/test_acceptance_workload.py:78

`linalg.DistributedMatrix.process_grid`¶

Return the process grid recorded by this DistributedMatrix.

PythonRust

(self) -> tuple[int, int]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

`linalg.DistributedMatrix.random`¶

Collective process-grid-independent deterministic random matrix.

PythonRust

(cls, world: World, field: FiniteField, rows: int, cols: int, *, seed: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	seeded
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/19_permutation_groups.py:16 · examples/19_permutation_groups.py:17 · examples/19_permutation_groups.py:18 · examples/distributed/f2_linear_algebra.py:46 · examples/distributed/f2_linear_algebra.py:47 · examples/distributed/f2_linear_algebra.py:48

`linalg.DistributedMatrix.rank`¶

Collective mathematical rank without retaining witnesses.

PythonRust

(self) -> int

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/38_exact_linear_systems.py:78 · examples/distributed/f2_linear_algebra.py:34 · examples/distributed/f2_linear_algebra.py:54 · examples/distributed/f2_linear_algebra.py:55 · examples/distributed/f2_linear_algebra.py:60 · validation/unit/combin/test_acceptance_workload.py:74

`linalg.DistributedMatrix.ring`¶

Alias for the exact coefficient field.

PythonRust

(self) -> FiniteField

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

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.DistributedMatrix.rows`¶

Return the rows recorded by this DistributedMatrix.

PythonRust

(self) -> int

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

Executable usage: examples/distributed/f2_linear_algebra.py:56 · validation/unit/combin/test_acceptance_workload.py:36 · validation/unit/combin/test_acceptance_workload.py:37 · validation/unit/combinatorics/test_tableau_rsk.py:15 · validation/unit/combinatorics/test_tableau_rsk.py:42 · validation/unit/combinatorics/test_tableau_rsk.py:43

`linalg.DistributedMatrix.rref`¶

Collective reduced row echelon form and rank.

PythonRust

(self) -> tuple[DistributedMatrix[FiniteField], int]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:50 · validation/unit/infra/test_mpi_scale_report.py:150 · validation/unit/infra/test_mpi_scale_report.py:156 · validation/unit/infra/test_mpi_scale_report.py:316 · validation/unit/infra/test_mpi_scale_report.py:328 · validation/unit/infra/test_mpi_scale_report.py:339

`linalg.DistributedMatrix.set`¶

Collective owned update of one coefficient.

PythonRust

(self, row: int, col: int, value: FiniteFieldElement) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:24 · validation/unit/combinatorics/test_matroid.py:83 · validation/unit/combinatorics/test_matroid.py:85 · validation/unit/geometry/test_acceptance_workload.py:42 · validation/unit/geometry/test_geometry_facade.py:82 · validation/unit/geometry/test_polytope_facade.py:32

`linalg.DistributedMatrix.shape`¶

Return the shape recorded by this DistributedMatrix.

PythonRust

(self) -> tuple[int, int]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

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.DistributedMatrix.solve_left`¶

Collectively solve self @ X = right or return None.

PythonRust

(self, right: DistributedMatrix[FiniteField]) -> DistributedMatrix[FiniteField] | None

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:36

`linalg.DistributedMatrix.submatrix`¶

Collective owned half-open submatrix.

PythonRust

(self, row_start: int, col_start: int, row_end: int, col_end: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:32

`linalg.DistributedMatrix.swap_cols`¶

Collective owned column interchange.

PythonRust

(self, first: int, second: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:25

`linalg.DistributedMatrix.swap_rows`¶

Collective owned row interchange.

PythonRust

(self, first: int, second: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:25

`linalg.DistributedMatrix.tile_shape`¶

Return the tile shape recorded by this DistributedMatrix.

PythonRust

(self) -> tuple[int, int]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

`linalg.DistributedMatrix.transpose`¶

Collective owned transpose.

PythonRust

(self) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

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.DistributedMatrix.world`¶

Explicit MPI world retained by the matrix.

PythonRust

(self) -> World

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	attached / bounded

Executable usage: examples/distributed/f2_linear_algebra.py:11 · examples/distributed/f2_linear_algebra.py:14 · examples/distributed/f2_linear_algebra.py:15 · examples/distributed/f2_linear_algebra.py:20 · examples/distributed/f2_linear_algebra.py:21 · examples/distributed/f2_linear_algebra.py:28

`linalg.DistributedMatrix.write`¶

Collectively write a process-grid-independent packed manifest.

PythonRust

(self, path: str) -> None

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: validation/unit/infra/test_repository_hygiene.py:145 · validation/unit/infra/test_repository_hygiene.py:233 · validation/unit/infra/test_repository_hygiene.py:234

`linalg.DistributedMatrix.xor_row`¶

Collective owned row replacement row[dst] += row[src] over F2.

PythonRust

(self, dst: int, src: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

Executable usage: examples/distributed/f2_linear_algebra.py:25

`linalg.DistributedMatrix.zeros`¶

Collective zero matrix.

PythonRust

(cls, world: World, field: FiniteField, rows: int, cols: int) -> DistributedMatrix[FiniteField]

noether::linalg::DistributedMatrix · Python projection

Python projection convenience; no separate Rust item

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	MPI-enabled build (`distributed` feature)
Domain implementation crates	noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL	released

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 · DistributedMatrix¶

Worked example¶

linalg.DistributedMatrix¶

linalg.DistributedMatrix.__add__¶

linalg.DistributedMatrix.__matmul__¶

linalg.DistributedMatrix.__sub__¶

linalg.DistributedMatrix.collect¶

linalg.DistributedMatrix.cols¶

linalg.DistributedMatrix.distribute¶

linalg.DistributedMatrix.echelon¶

linalg.DistributedMatrix.equals¶

linalg.DistributedMatrix.extract_bits¶

linalg.DistributedMatrix.field¶

linalg.DistributedMatrix.flip¶

linalg.DistributedMatrix.get¶

linalg.DistributedMatrix.global_memory_bytes¶

linalg.DistributedMatrix.identity¶

linalg.DistributedMatrix.inverse¶

linalg.DistributedMatrix.local_memory_bytes¶

linalg.DistributedMatrix.matmul¶

linalg.DistributedMatrix.nullspace¶

linalg.DistributedMatrix.open¶

linalg.DistributedMatrix.paste¶

linalg.DistributedMatrix.ple_rank¶

linalg.DistributedMatrix.pluq¶

linalg.DistributedMatrix.process_grid¶

linalg.DistributedMatrix.random¶

linalg.DistributedMatrix.rank¶

linalg.DistributedMatrix.ring¶

linalg.DistributedMatrix.rows¶

linalg.DistributedMatrix.rref¶

linalg.DistributedMatrix.set¶

linalg.DistributedMatrix.shape¶

linalg.DistributedMatrix.solve_left¶

linalg.DistributedMatrix.submatrix¶

linalg.DistributedMatrix.swap_cols¶

linalg.DistributedMatrix.swap_rows¶

linalg.DistributedMatrix.tile_shape¶

linalg.DistributedMatrix.transpose¶

linalg.DistributedMatrix.world¶

linalg.DistributedMatrix.write¶

linalg.DistributedMatrix.xor_row¶

linalg.DistributedMatrix.zeros¶

`linalg.DistributedMatrix`¶

`linalg.DistributedMatrix.add`¶

`linalg.DistributedMatrix.matmul`¶

`linalg.DistributedMatrix.sub`¶

`linalg.DistributedMatrix.collect`¶

`linalg.DistributedMatrix.cols`¶

`linalg.DistributedMatrix.distribute`¶

`linalg.DistributedMatrix.echelon`¶

`linalg.DistributedMatrix.equals`¶

`linalg.DistributedMatrix.extract_bits`¶

`linalg.DistributedMatrix.field`¶

`linalg.DistributedMatrix.flip`¶

`linalg.DistributedMatrix.get`¶

`linalg.DistributedMatrix.global_memory_bytes`¶

`linalg.DistributedMatrix.identity`¶

`linalg.DistributedMatrix.inverse`¶

`linalg.DistributedMatrix.local_memory_bytes`¶

`linalg.DistributedMatrix.matmul`¶

`linalg.DistributedMatrix.nullspace`¶

`linalg.DistributedMatrix.open`¶

`linalg.DistributedMatrix.paste`¶

`linalg.DistributedMatrix.ple_rank`¶

`linalg.DistributedMatrix.pluq`¶

`linalg.DistributedMatrix.process_grid`¶

`linalg.DistributedMatrix.random`¶

`linalg.DistributedMatrix.rank`¶

`linalg.DistributedMatrix.ring`¶

`linalg.DistributedMatrix.rows`¶

`linalg.DistributedMatrix.rref`¶

`linalg.DistributedMatrix.set`¶

`linalg.DistributedMatrix.shape`¶

`linalg.DistributedMatrix.solve_left`¶

`linalg.DistributedMatrix.submatrix`¶

`linalg.DistributedMatrix.swap_cols`¶

`linalg.DistributedMatrix.swap_rows`¶

`linalg.DistributedMatrix.tile_shape`¶

`linalg.DistributedMatrix.transpose`¶

`linalg.DistributedMatrix.world`¶

`linalg.DistributedMatrix.write`¶

`linalg.DistributedMatrix.xor_row`¶

`linalg.DistributedMatrix.zeros`¶