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commalg · CyclicHypersurfaceCover

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

commalg.CyclicHypersurfaceCover

A general cyclic cover w^m=f of projective space.

CyclicHypersurfaceCover(base: ProjectiveSpace[C], degree: int, branch: Polynomial[C])

noether::commalg::CyclicHypersurfaceCover · Direct Rust declaration

pub struct CyclicHypersurfaceCover<R: CommutativeRing> { /* 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/CyclicHypersurfaceCover@1

Executable usage: validation/unit/commalg/test_surface_facade.py:38 · validation/unit/commalg/test_surface_facade.py:85 · validation/unit/commalg/test_surface_facade.py:9 · validation/parity/commalg/test_surface_magma_parity.py:12 · validation/parity/commalg/test_surface_magma_parity.py:64 · validation/bench/surface_frobenius.py:56

commalg.CyclicHypersurfaceCover.base

Return the base recorded by this CyclicHypersurfaceCover.

Detailed contract

Base projective space.

(self) -> ProjectiveSpace[C]

noether::commalg::CyclicHypersurfaceCover::base · Direct Rust declaration

pub fn base(&self) -> &ProjectiveSpace<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/CyclicHypersurfaceCover@1

Executable usage: validation/unit/commalg/test_acceptance_workload.py:59 · validation/unit/commalg/test_acceptance_workload.py:60 · validation/unit/commalg/test_base_change.py:112 · validation/unit/commalg/test_base_change.py:113 · validation/unit/commalg/test_polynomial_ideal_facade.py:398 · validation/unit/commalg/test_polynomial_ideal_facade.py:399

commalg.CyclicHypersurfaceCover.branch

Return the branch recorded by this CyclicHypersurfaceCover.

Detailed contract

Branch hypersurface in the base projective space.

(self) -> Scheme[C]

noether::commalg::CyclicHypersurfaceCover::branch · Direct Rust declaration

pub fn branch(&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/CyclicHypersurfaceCover@1

Executable usage: validation/unit/commalg/test_polynomial_ideal_facade.py:793 · validation/unit/infra/test_slurm_handoff.py:277 · validation/unit/infra/test_slurm_handoff.py:282 · validation/parity/commalg/test_surface_magma_parity.py:61 · validation/parity/commalg/test_surface_magma_parity.py:64 · validation/bench/magma_release.py:3583

commalg.CyclicHypersurfaceCover.branch_equation

Return the branch equation recorded by this CyclicHypersurfaceCover.

Detailed contract

Homogeneous branch equation in the base coordinates.

(self) -> Polynomial[C]

noether::commalg::CyclicHypersurfaceCover::branch_equation · Direct Rust declaration

pub fn branch_equation(&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/CyclicHypersurfaceCover@1

commalg.CyclicHypersurfaceCover.cover_degree

Return the cover degree recorded by this CyclicHypersurfaceCover.

Detailed contract

Cyclic cover degree.

(self) -> int

noether::commalg::CyclicHypersurfaceCover::cover_degree · Direct Rust declaration

pub fn cover_degree(&self) -> u64
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/CyclicHypersurfaceCover@1

commalg.CyclicHypersurfaceCover.from_json

Deserialize and revalidate a CyclicHypersurfaceCover from typed JSON.

Detailed contract

Restore and revalidate this cyclic cover.

(cls, value: str) -> CyclicHypersurfaceCover[SchemeBase]

noether::commalg::CyclicHypersurfaceCover::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/CyclicHypersurfaceCover@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.CyclicHypersurfaceCover.point_counts

Compute point counts for this CyclicHypersurfaceCover.

Detailed contract

Count points over each requested relative extension degree. The operation chooses the admitted mathematical route; callers do not name a backend. Exhaustive cyclic fibers are the current correctness floor and retain an independent direct-root scan when affordable.

(self: CyclicHypersurfaceCover[FiniteField], degrees: Sequence[int]) -> PointCountSequence

noether::commalg::CyclicHypersurfaceCover::point_counts · Direct Rust declaration

pub fn point_counts<I>( &self, degrees: I, ) -> Result<PointCountSequence, PointCountError>where I: IntoIterator<Item = u64>,
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 released
Semantic ID noether/commalg/CyclicHypersurfaceCover@1

Executable usage: validation/unit/commalg/test_surface_facade.py:45 · validation/unit/commalg/test_surface_facade.py:87 · validation/parity/commalg/test_surface_magma_parity.py:65 · validation/bench/surface_frobenius.py:87

commalg.CyclicHypersurfaceCover.ramification

Return the ramification recorded by this CyclicHypersurfaceCover.

Detailed contract

Tame or wild ramification regime.

(self) -> Literal['tame', 'wild']

noether::commalg::CyclicHypersurfaceCover::ramification · Direct Rust declaration

pub fn ramification(&self) -> CyclicCoverRamification
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/CyclicHypersurfaceCover@1

commalg.CyclicHypersurfaceCover.smoothness_evidence

Compute smoothness evidence for this CyclicHypersurfaceCover.

Detailed contract

Compute smoothness evidence using the criterion valid in this regime. Tame covers check both branch smoothness and the cone Jacobian. Wild covers deliberately do not apply the tame branch criterion and rely on the direct equation Jacobian only.

(self) -> CyclicCoverSmoothnessEvidence[C]

noether::commalg::CyclicHypersurfaceCover::smoothness_evidence · Direct Rust declaration

pub fn smoothness_evidence( &self, ) -> Result<CyclicCoverSmoothnessEvidence<RationalField>, WeightedProjectiveError>
pub fn smoothness_evidence( &self, ) -> Result<CyclicCoverSmoothnessEvidence<FiniteField>, WeightedProjectiveError>
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/CyclicHypersurfaceCover@1

Executable usage: validation/unit/commalg/test_surface_facade.py:40

commalg.CyclicHypersurfaceCover.surface_cohomology

Compute surface cohomology for this CyclicHypersurfaceCover.

Detailed contract

Establish the smooth projective surface cohomology used for exact Frobenius reconstruction, when the tame cyclic-cover theorem applies.

(self: CyclicHypersurfaceCover[FiniteField]) -> SmoothProjectiveSurfaceCohomology

noether::commalg::CyclicHypersurfaceCover::surface_cohomology · Direct Rust declaration

pub fn surface_cohomology( &self, ) -> Result<SmoothProjectiveSurfaceCohomology, FrobeniusError>
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/CyclicHypersurfaceCover@1

Executable usage: validation/unit/commalg/test_surface_facade.py:61 · validation/parity/commalg/test_surface_magma_parity.py:66 · validation/bench/surface_frobenius.py:91

commalg.CyclicHypersurfaceCover.to_json

Serialize this CyclicHypersurfaceCover to its canonical typed JSON representation.

Detailed contract

Serialize this cyclic cover and its exact branch presentation.

(self) -> str

noether::commalg::CyclicHypersurfaceCover::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/CyclicHypersurfaceCover@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.CyclicHypersurfaceCover.weighted_realization

Return the weighted realization recorded by this CyclicHypersurfaceCover.

Detailed contract

Equation w^m-f=0 in its weighted projective ambient space.

(self) -> WeightedProjectiveHypersurface[C]

noether::commalg::CyclicHypersurfaceCover::weighted_realization · Direct Rust declaration

pub fn weighted_realization(&self) -> &WeightedProjectiveHypersurface<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/CyclicHypersurfaceCover@1

Executable usage: validation/unit/commalg/test_surface_facade.py:43