Crate amari_enumerative 

Amari Enumerative Geometry

This crate provides enumerative geometry capabilities for the Amari mathematical library. It implements intersection theory, Schubert calculus, and tools for counting geometric configurations such as curves, surfaces, and higher-dimensional varieties.

Features

• Intersection Theory: Chow rings, intersection multiplicities, and Bezout’s theorem
• Schubert Calculus: Computations on Grassmannians and flag varieties
• Littlewood-Richardson Coefficients: Complete LR coefficient computation
• Gromov-Witten Theory: Curve counting and quantum cohomology
• Tropical Geometry: Tropical curve counting and correspondence theorems
• Moduli Spaces: Computations on moduli spaces of curves and surfaces
• Namespace/Capabilities: Geometric access control via Schubert calculus
• Phantom Types: Compile-time verification of mathematical properties

Usage

use amari_enumerative::{ProjectiveSpace, ChowClass, IntersectionRing};

// Create projective 2-space
let p2 = ProjectiveSpace::new(2);

// Define two curves
let cubic = ChowClass::hypersurface(3);
let quartic = ChowClass::hypersurface(4);

// Compute intersection number (Bezout's theorem)
let intersection = p2.intersect(&cubic, &quartic);
assert_eq!(intersection.multiplicity(), 12); // 3 * 4 = 12

Schubert Calculus Example

use amari_enumerative::{SchubertCalculus, SchubertClass, IntersectionResult};

// How many lines meet 4 general lines in projective 3-space?
let mut calc = SchubertCalculus::new((2, 4)); // Gr(2,4)
let sigma_1 = SchubertClass::new(vec![1], (2, 4)).unwrap();

let classes = vec![sigma_1.clone(), sigma_1.clone(), sigma_1.clone(), sigma_1.clone()];
let result = calc.multi_intersect(&classes);

assert_eq!(result, IntersectionResult::Finite(2)); // Answer: 2 lines!

Phantom Types for Compile-Time Verification

The crate provides zero-cost phantom types for compile-time verification:

• ValidPartition / UnvalidatedPartition: Partition validity states
• Semistandard / LatticeWord: Tableau property markers
• Granted / Pending / Revoked: Capability grant states
• Transverse / Excess / Deficient: Intersection dimension states
• FitsInBox / UnverifiedBox: Grassmannian containment states

Re-exports

pub use geometric_algebra::quantum_k_theory;

pub use geometric_algebra::signatures;

pub use geometric_algebra::GeometricProjectiveSpace;

pub use geometric_algebra::GeometricSchubertClass;

pub use geometric_algebra::GeometricVariety;

pub use gromov_witten::CurveClass as GWCurveClass;

pub use gromov_witten::GromovWittenInvariant;

pub use gromov_witten::QuantumCohomology;

pub use higher_genus::AdvancedCurveCounting;

pub use higher_genus::DTInvariant;

pub use higher_genus::HigherGenusCurve;

pub use higher_genus::JacobianData;

pub use higher_genus::PTInvariant;

pub use intersection::AlgebraicVariety;

pub use intersection::ChowClass;

pub use intersection::Constraint;

pub use intersection::Grassmannian;

pub use intersection::IntersectionNumber;

pub use intersection::IntersectionPoint;

pub use intersection::IntersectionRing;

pub use intersection::MockMultivector;

pub use intersection::ProjectiveSpace;

pub use intersection::QuantumProduct;

pub use moduli_space::CurveClass;

pub use moduli_space::ModuliSpace;

pub use moduli_space::TautologicalClass;

pub use performance::CurveBatchProcessor;

pub use performance::FastIntersectionComputer;

pub use performance::MemoryPool;

pub use performance::SparseSchubertMatrix;

pub use performance::WasmPerformanceConfig;

pub use schubert::FlagVariety;

pub use schubert::IntersectionResult;

pub use schubert::SchubertCalculus;

pub use schubert::SchubertClass;

pub use littlewood_richardson::lr_coefficient;

pub use littlewood_richardson::schubert_product;

pub use littlewood_richardson::Partition;

pub use littlewood_richardson::SkewShape;

pub use littlewood_richardson::SkewTableau;

pub use namespace::capability_accessible;

pub use namespace::namespace_intersection;

pub use namespace::Capability;

pub use namespace::CapabilityId;

pub use namespace::Namespace;

pub use namespace::NamespaceBuilder;

pub use namespace::NamespaceError;

pub use namespace::NamespaceIntersection;

pub use namespace::QuantumCapability;

pub use tropical_curves::verify_mikhalkin_gw;

pub use tropical_curves::MikhalkinResult;

pub use tropical_curves::TropicalCurve;

pub use tropical_curves::TropicalEdge;

pub use tropical_curves::TropicalIntersection;

pub use tropical_curves::TropicalModuliSpace;

pub use tropical_curves::TropicalPoint;

pub use phantom::BoxContainment;

pub use phantom::Deficient;

pub use phantom::Excess;

pub use phantom::FitsInBox;

pub use phantom::GrantState;

pub use phantom::Granted;

pub use phantom::IntersectionDimension;

pub use phantom::LatticeWord;

pub use phantom::PartitionValidity;

pub use phantom::Pending;

pub use phantom::Properties;

pub use phantom::Revoked;

pub use phantom::Semistandard;

pub use phantom::TableauValidity;

pub use phantom::Transverse;

pub use phantom::UnknownDimension;

pub use phantom::UnvalidatedPartition;

pub use phantom::UnverifiedBox;

pub use phantom::UnverifiedTableau;

pub use phantom::ValidLRTableau;

pub use phantom::ValidPartition;

pub use phantom::ValidSchubertClass;

pub use wdvv::WDVVEngine;

pub use localization::EquivariantLocalizer;

pub use localization::FixedPoint;

pub use localization::TorusWeights;

pub use matroid::Matroid;

pub use matroid::ValuatedMatroid;

pub use kazhdan_lusztig::flag_f_vector;

pub use kazhdan_lusztig::inverse_kl_polynomial;

pub use kazhdan_lusztig::kl_is_non_negative;

pub use kazhdan_lusztig::kl_polynomial;

pub use kazhdan_lusztig::z_polynomial;

pub use finite_field::grassmannian_poincare_polynomial;

pub use finite_field::grassmannian_points;

pub use finite_field::point_counts_over_extensions;

pub use finite_field::schubert_cell_points;

pub use finite_field::schubert_poincare_polynomial;

pub use finite_field::schubert_variety_points;

pub use finite_field::schubert_zeta_exponents;

pub use representability::column_matroid;

pub use representability::dual_fano_matroid;

pub use representability::fano_matroid;

pub use representability::has_minor;

pub use representability::is_binary;

pub use representability::is_regular;

pub use representability::is_ternary;

pub use representability::standard_representation;

pub use representability::RepresentabilityResult;

pub use weight_enumerator::extended_golay_code;

pub use weight_enumerator::gilbert_varshamov_bound;

pub use weight_enumerator::hamming_bound;

pub use weight_enumerator::hamming_code;

pub use weight_enumerator::plotkin_bound;

pub use weight_enumerator::reed_muller_code;

pub use weight_enumerator::simplex_code;

pub use weight_enumerator::singleton_bound;

pub use weight_enumerator::BinaryCode;

pub use csm::CSMClass;

pub use csm::SegreClass;

pub use operad::compose_namespaces;

pub use operad::composition_multiplicity;

pub use operad::interfaces_compatible;

pub use operad::ComposableNamespace;

pub use operad::Interface;

pub use operad::InterfaceDirection;

pub use stability::StabilityCondition;

pub use stability::Wall;

pub use stability::WallCrossingEngine;

Modules

csm

Chern-Schwartz-MacPherson (CSM) Classes

finite_field

F_q point counting on Grassmannians and Schubert varieties.

geometric_algebra

Integration between geometric algebra and enumerative geometry

gromov_witten

Gromov-Witten invariants and quantum cohomology

higher_genus

Higher genus computations and advanced enumerative geometry

intersection

Intersection theory and Chow rings

kazhdan_lusztig

Kazhdan-Lusztig polynomials of matroids.

littlewood_richardson

Littlewood-Richardson coefficient computation

localization

Equivariant Localization via the Atiyah-Bott Fixed Point Formula

matroid

Matroid Theory for Enumerative Geometry

moduli_space

Moduli spaces of curves and algebraic varieties

namespace

Namespace and Capability types for geometric access control

operad

Operadic Composition for Namespace Stacking

performance

Performance optimization module for WASM-first enumerative geometry

phantom

Phantom types for compile-time verification of enumerative geometry properties.

representability

Matroid representability over GF(2), GF(3), and GF(q).

schubert

Schubert calculus on Grassmannians and flag varieties

stability

Wall-Crossing and Bridgeland Stability

tropical_curves

Tropical curve counting and enumerative geometry

verified_contracts

Formal verification contracts for enumerative geometry

wdvv

WDVV Recursion for Genus-0 Gromov-Witten Invariants

weight_enumerator

Weight enumerators for binary linear codes.

Enums

EnumerativeError

Error types for enumerative geometry computations

Type Aliases

EnumerativeResult

Result type for enumerative geometry computations