Skip to content

commalg · BlowUpChart

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

Worked example

The complete checked program Build and verify an isomorphism between two presentations of F_25 uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Build and verify an isomorphism between two presentations of F_25."""

from noether.numthy import FiniteField


def main() -> None:
    source = FiniteField.extension(5, 2)
    target = FiniteField.with_modulus(5, [2, 0, 1])
    isomorphism = source.isomorphism_to(target)
    isomorphism.verify()
    value = source.element_from_coefficients([3, 2])
    assert isomorphism.apply_inverse(isomorphism(value)) == value
    print(f"a maps to {isomorphism.generator_image}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/09_finite_field_isomorphisms.py.

commalg.BlowUpChart

One verified affine chart of a point blow-up.

class BlowUpChart

noether::commalg::BlowUpChart · Direct Rust declaration

pub struct BlowUpChart<R: Field> { /* private fields */ }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/commalg/test_scheme_facade.py:11 · validation/unit/commalg/test_scheme_facade.py:267

commalg.BlowUpChart.center

Return the center recorded by this BlowUpChart.

Detailed contract

Rational point used as the center.

(self) -> SchemePoint

noether::commalg::BlowUpChart::center · Direct Rust declaration

pub fn center(&self) -> &SchemePoint<R>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/combin/test_graph_facade.py:102 · validation/unit/commalg/test_acceptance_workload.py:104 · validation/unit/commalg/test_acceptance_workload.py:112 · validation/unit/commalg/test_acceptance_workload.py:96 · validation/unit/commalg/test_acceptance_workload.py:98 · validation/unit/commalg/test_scheme_facade.py:223

commalg.BlowUpChart.chart_index

Return the chart index recorded by this BlowUpChart.

Detailed contract

Index of the translated local coordinate chosen as exceptional coordinate.

(self) -> int

noether::commalg::BlowUpChart::chart_index · Direct Rust declaration

pub fn chart_index(&self) -> usize
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/commalg/test_scheme_facade.py:270

commalg.BlowUpChart.exceptional_divisor

Return the exceptional divisor recorded by this BlowUpChart.

Detailed contract

Scheme-theoretic intersection of the strict transform with the exceptional divisor.

(self) -> Scheme[C]

noether::commalg::BlowUpChart::exceptional_divisor · Direct Rust declaration

pub fn exceptional_divisor(&self) -> &Scheme<R>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/commalg/test_scheme_facade.py:241 · validation/unit/commalg/test_scheme_facade.py:242 · validation/unit/commalg/test_scheme_facade.py:243

commalg.BlowUpChart.from_json

Deserialize and revalidate a BlowUpChart from typed JSON.

Detailed contract

Deserialize and recheck the chartwise saturation identities.

(cls, value: str) -> BlowUpChart[FiniteField]

noether::commalg::BlowUpChart::from_json · Direct Rust declaration

pub fn from_json(value: &str) -> Result<Self, NoetherError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@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

commalg.BlowUpChart.source

Return the source recorded by this BlowUpChart.

Detailed contract

Scheme being blown up.

(self) -> Scheme[C]

noether::commalg::BlowUpChart::source · Direct Rust declaration

pub fn source(&self) -> &Scheme<R>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: examples/09_finite_field_isomorphisms.py:11 · examples/09_finite_field_isomorphisms.py:13 · examples/09_finite_field_isomorphisms.py:9 · examples/30_modules_and_resolutions.py:34 · examples/30_modules_and_resolutions.py:37 · validation/unit/category/test_acceptance_workload.py:25

commalg.BlowUpChart.source_coordinate_map

Return the source coordinate map recorded by this BlowUpChart.

Detailed contract

Pullbacks of the source ambient coordinates in this affine chart.

(self) -> list[Polynomial[C]]

noether::commalg::BlowUpChart::source_coordinate_map · Direct Rust declaration

pub fn source_coordinate_map(&self) -> &[Polynomial<R>]
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/commalg/test_scheme_facade.py:244

commalg.BlowUpChart.strict_transform

Return the strict transform recorded by this BlowUpChart.

Detailed contract

Saturation of the total transform by the exceptional coordinate.

(self) -> Scheme[C]

noether::commalg::BlowUpChart::strict_transform · Direct Rust declaration

pub fn strict_transform(&self) -> &Scheme<R>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/commalg/test_acceptance_workload.py:106 · validation/unit/commalg/test_acceptance_workload.py:107 · validation/unit/commalg/test_acceptance_workload.py:110 · validation/unit/commalg/test_acceptance_workload.py:117 · validation/unit/commalg/test_acceptance_workload.py:118 · validation/unit/commalg/test_scheme_facade.py:235

commalg.BlowUpChart.to_json

Serialize this BlowUpChart to its canonical typed JSON representation.

Detailed contract

Serialize this chart’s transform and exceptional evidence.

(self) -> str

noether::commalg::BlowUpChart::to_json · Direct Rust declaration

pub fn to_json(&self) -> Result<String, NoetherError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@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

commalg.BlowUpChart.total_transform

Return the total transform recorded by this BlowUpChart.

Detailed contract

Scheme-theoretic total transform before removing exceptional factors.

(self) -> Scheme[C]

noether::commalg::BlowUpChart::total_transform · Direct Rust declaration

pub fn total_transform(&self) -> &Scheme<R>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/commalg/test_scheme_facade.py:249

commalg.BlowUpChart.verify

Replay and verify the mathematical evidence carried by this BlowUpChart.

Detailed contract

Recheck the saturation and exceptional-intersection identities in this chart.

(self) -> None

noether::commalg::BlowUpChart::verify · Direct Rust declaration

pub fn verify(&self) -> Result<(), GeometryError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: examples/01_bezout_certificates.py:10 · examples/01_bezout_certificates.py:3 · examples/03_exact_linear_systems.py:13 · examples/03_exact_linear_systems.py:3 · examples/04_smith_normal_form.py:12 · examples/06_shortest_lattice_vectors.py:12

commalg.BlowUpChart.weak_transform

Return the weak transform recorded by this BlowUpChart.

Detailed contract

Transform after dividing by the common exceptional order.

(self) -> Scheme[C]

noether::commalg::BlowUpChart::weak_transform · Direct Rust declaration

pub fn weak_transform(&self) -> &Scheme<R>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/BlowUpChart@1

Executable usage: validation/unit/commalg/test_scheme_facade.py:238 · validation/unit/commalg/test_scheme_facade.py:250