Machine-readable contracts¶
Download every accepted Python call schema · download canonical transport schemas.
The call index covers every accepted declaration and overload. The 34 entries below are the narrower, versioned cross-process transport registry. Generic hydration is deliberately limited to these Rust-owned schemas; deserialization revalidates every mathematical value.
noether/category/SteinerCategory@1¶
Python category.SteinerCategory · Rust domain
Validated finite strong Steiner category.
Canonical JSON Schema
{
"$defs": {
"SignedBoundaryWire": {
"properties": {
"negative": {
"items": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"type": "array"
},
"positive": {
"items": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"negative",
"positive"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"atom_counts": {
"items": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"type": "array"
},
"boundaries": {
"items": {
"items": {
"$ref": "#/$defs/SignedBoundaryWire"
},
"type": "array"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"atom_counts",
"boundaries"
],
"title": "SteinerCategory",
"type": "object"
}
noether/combin/Composition@1¶
Python combin.Composition · Rust domain
A thin Python handle around Noether's canonical integer composition.
Canonical JSON Schema
noether/combin/Graph@1¶
Python combin.Graph · Rust domain
The thin Python projection of Noether's CSR graph value.
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"directed": {
"type": "boolean"
},
"edges": {
"items": {
"maxItems": 3,
"minItems": 3,
"prefixItems": [
{
"format": "uint32",
"minimum": 0,
"type": "integer"
},
{
"format": "uint32",
"minimum": 0,
"type": "integer"
},
{
"format": "int64",
"type": "integer"
}
],
"type": "array"
},
"type": "array"
},
"order": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"order",
"edges",
"directed"
],
"title": "Graph",
"type": "object"
}
noether/combin/KashiwaraCrystal@1¶
Python combin.KashiwaraCrystal · Rust domain
A thin Python handle around Noether's validated finite type-A crystal.
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"cartan_matrix": {
"items": {
"items": {
"format": "int64",
"type": "integer"
},
"type": "array"
},
"type": "array"
},
"f_edges": {
"items": {
"items": {
"format": "uint32",
"minimum": 0,
"type": [
"integer",
"null"
]
},
"type": "array"
},
"type": "array"
},
"weights": {
"items": {
"items": {
"format": "int64",
"type": "integer"
},
"type": "array"
},
"type": "array"
}
},
"required": [
"cartan_matrix",
"weights",
"f_edges"
],
"title": "KashiwaraCrystal",
"type": "object"
}
noether/combin/Matroid@1¶
Python combin.Matroid · Rust domain
A thin Python handle around Noether's validated Rust [Matroid].
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"bases": {
"items": {
"items": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"type": "array"
},
"type": "array"
},
"ground_set": {
"items": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"ground_set",
"bases"
],
"title": "Matroid",
"type": "object"
}
noether/combin/Partition@1¶
Python combin.Partition · Rust domain
A thin Python handle around Noether's canonical integer partition.
Canonical JSON Schema
noether/combin/Poset@1¶
Python combin.Poset · Rust domain
The thin Python handle around Noether's validated Rust [Poset].
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"covers": {
"items": {
"maxItems": 2,
"minItems": 2,
"prefixItems": [
{
"format": "uint32",
"minimum": 0,
"type": "integer"
},
{
"format": "uint32",
"minimum": 0,
"type": "integer"
}
],
"type": "array"
},
"type": "array"
},
"order": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"order",
"covers"
],
"title": "Poset",
"type": "object"
}
noether/combin/SymmetricFunction@1¶
Python combin.SymmetricFunction · Rust domain
A thin Python handle around Noether's exact rational symmetric function.
Canonical JSON Schema
{
"$defs": {
"Partition": {
"properties": {
"parts": {
"items": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"parts"
],
"type": "object"
},
"SymmetricTermWire": {
"properties": {
"coefficient": {
"type": "string"
},
"partition": {
"$ref": "#/$defs/Partition"
}
},
"required": [
"partition",
"coefficient"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"basis": {
"type": "string"
},
"terms": {
"items": {
"$ref": "#/$defs/SymmetricTermWire"
},
"type": "array"
}
},
"required": [
"basis",
"terms"
],
"title": "SymmetricFunction",
"type": "object"
}
noether/combin/Tableau@1¶
Python combin.Tableau · Rust domain
A thin Python handle around Noether's semistandard integer tableau.
Canonical JSON Schema
noether/combin/Tree@1¶
Python combin.Tree · Rust domain
A rooted tree over graph-core's CSR graph.
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"edges": {
"items": {
"maxItems": 2,
"minItems": 2,
"prefixItems": [
{
"format": "uint32",
"minimum": 0,
"type": "integer"
},
{
"format": "uint32",
"minimum": 0,
"type": "integer"
}
],
"type": "array"
},
"type": "array"
},
"order": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"root": {
"format": "uint32",
"minimum": 0,
"type": "integer"
}
},
"required": [
"order",
"edges",
"root"
],
"title": "Tree",
"type": "object"
}
noether/commalg/PolynomialHomomorphism@1¶
Python commalg.PolynomialHomomorphism · Rust domain
A checked polynomial-ring homomorphism with explicit endpoints and images.
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"coefficient_map": true,
"images": {
"items": true,
"type": "array"
},
"source": true,
"target": true,
"type": {
"type": "string"
}
},
"required": [
"type",
"source",
"target",
"coefficient_map",
"images"
],
"title": "PolynomialHomomorphismWire",
"type": "object"
}
noether/commalg/RationalFunctionFieldMap@1¶
Python commalg.RationalFunctionFieldMap · Rust domain
A checked coefficientwise map between finite rational-function fields.
Canonical JSON Schema
{
"$defs": {
"FiniteFieldWire": {
"properties": {
"characteristic": {
"type": "string"
},
"modulus": {
"items": {
"format": "uint64",
"minimum": 0,
"type": "integer"
},
"type": [
"array",
"null"
]
},
"type": {
"type": "string"
}
},
"required": [
"type",
"characteristic"
],
"type": "object"
},
"FiniteRationalFunctionFieldWire": {
"properties": {
"coefficient_ring": {
"$ref": "#/$defs/FiniteFieldWire"
},
"type": {
"type": "string"
},
"variable": {
"type": "string"
}
},
"required": [
"type",
"coefficient_ring",
"variable"
],
"type": "object"
},
"PrimeSubfieldEmbeddingWire": {
"properties": {
"source": {
"$ref": "#/$defs/FiniteFieldWire"
},
"target": {
"$ref": "#/$defs/FiniteFieldWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"source",
"target"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"coefficient_map": {
"$ref": "#/$defs/PrimeSubfieldEmbeddingWire"
},
"source": {
"$ref": "#/$defs/FiniteRationalFunctionFieldWire"
},
"target": {
"$ref": "#/$defs/FiniteRationalFunctionFieldWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"source",
"target",
"coefficient_map"
],
"title": "RationalFunctionFieldMapWire",
"type": "object"
}
noether/groups/PolynomialGlRepresentation@1¶
Python groups.PolynomialGlRepresentation · Rust domain
The irreducible polynomial representation of GL indexed by a partition.
Canonical JSON Schema
{
"$defs": {
"Partition": {
"properties": {
"parts": {
"items": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"parts"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"partition": {
"$ref": "#/$defs/Partition"
},
"rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"rank",
"partition"
],
"title": "PolynomialGlRepresentation",
"type": "object"
}
noether/groups/WeightCharacter@1¶
Python groups.WeightCharacter · Rust domain
A finite formal character on an explicit weight lattice.
Canonical JSON Schema
{
"$defs": {
"WeightBasisConventionWire": {
"oneOf": [
{
"enum": [
"standard"
],
"type": "string"
},
{
"additionalProperties": false,
"properties": {
"type_a_fundamental": {
"properties": {
"degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"degree"
],
"type": "object"
}
},
"required": [
"type_a_fundamental"
],
"type": "object"
}
]
},
"WeightLattice": {
"properties": {
"basis_names": {
"items": {
"type": "string"
},
"type": "array"
},
"convention": {
"$ref": "#/$defs/WeightBasisConventionWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"basis_names",
"convention"
],
"type": "object"
},
"WeightMultiplicitySchema": {
"properties": {
"multiplicity": {
"type": "string"
},
"weight": {
"items": {
"type": "string"
},
"type": "array"
}
},
"required": [
"weight",
"multiplicity"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"lattice": {
"$ref": "#/$defs/WeightLattice"
},
"terms": {
"items": {
"$ref": "#/$defs/WeightMultiplicitySchema"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"lattice",
"terms"
],
"title": "WeightCharacter",
"type": "object"
}
noether/groups/WeightLattice@1¶
Python groups.WeightLattice · Rust domain
A free weight lattice with a named basis and an explicit basis convention.
Canonical JSON Schema
{
"$defs": {
"WeightBasisConventionWire": {
"oneOf": [
{
"enum": [
"standard"
],
"type": "string"
},
{
"additionalProperties": false,
"properties": {
"type_a_fundamental": {
"properties": {
"degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"degree"
],
"type": "object"
}
},
"required": [
"type_a_fundamental"
],
"type": "object"
}
]
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"basis_names": {
"items": {
"type": "string"
},
"type": "array"
},
"convention": {
"$ref": "#/$defs/WeightBasisConventionWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"basis_names",
"convention"
],
"title": "WeightLattice",
"type": "object"
}
noether/groups/WeightLatticeMap@1¶
Python groups.WeightLatticeMap · Rust domain
A homomorphism between two explicit weight lattices.
Canonical JSON Schema
{
"$defs": {
"WeightBasisConventionWire": {
"oneOf": [
{
"enum": [
"standard"
],
"type": "string"
},
{
"additionalProperties": false,
"properties": {
"type_a_fundamental": {
"properties": {
"degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"degree"
],
"type": "object"
}
},
"required": [
"type_a_fundamental"
],
"type": "object"
}
]
},
"WeightLattice": {
"properties": {
"basis_names": {
"items": {
"type": "string"
},
"type": "array"
},
"convention": {
"$ref": "#/$defs/WeightBasisConventionWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"basis_names",
"convention"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"basis_images": {
"items": {
"items": {
"type": "string"
},
"type": "array"
},
"type": "array"
},
"source": {
"$ref": "#/$defs/WeightLattice"
},
"target": {
"$ref": "#/$defs/WeightLattice"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"source",
"target",
"basis_images"
],
"title": "WeightLatticeMap",
"type": "object"
}
noether/homalg/ExteriorAlgebra@1¶
Python homalg.ExteriorAlgebra · Rust domain
The exact exterior-algebra parent of a finite based free module.
Canonical JSON Schema
noether/homalg/ExteriorElement@1¶
Python homalg.ExteriorElement · Rust domain
A canonical sparse, possibly inhomogeneous, exact exterior-algebra element.
Canonical JSON Schema
{
"$defs": {
"ExteriorAlgebra": {
"properties": {
"source": true,
"type": {
"type": "string"
}
},
"required": [
"type",
"source"
],
"type": "object"
},
"ExteriorTermSchema": {
"properties": {
"basis": {
"items": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"type": "array"
},
"coefficient": true
},
"required": [
"basis",
"coefficient"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"algebra": {
"$ref": "#/$defs/ExteriorAlgebra"
},
"terms": {
"items": {
"$ref": "#/$defs/ExteriorTermSchema"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"algebra",
"terms"
],
"title": "ExteriorElement",
"type": "object"
}
noether/homalg/FinitelyGeneratedAbelianGroup@1¶
Python homalg.FinitelyGeneratedAbelianGroup · Rust domain
A finitely generated abelian group in canonical invariant-factor form.
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"free_rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"torsion_coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"free_rank",
"torsion_coefficients"
],
"title": "FinitelyGeneratedAbelianGroup",
"type": "object"
}
noether/homalg/ImageSubmodule@1¶
Python homalg.ImageSubmodule · Rust domain
A map-bound certificate for a complete exact image.
Canonical JSON Schema
noether/homalg/KernelSubmodule@1¶
Python homalg.KernelSubmodule · Rust domain
A map-bound certificate for a complete exact kernel.
Canonical JSON Schema
noether/homalg/ModulePowerHomomorphism@1¶
Python homalg.ModulePowerHomomorphism · Rust domain
A replay-verifiable map induced on a symmetric or exterior power.
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"induced": true,
"kind": {
"type": "string"
},
"source_map": true,
"source_power": true,
"target_power": true,
"type": {
"type": "string"
}
},
"required": [
"type",
"source_map",
"kind",
"degree",
"source_power",
"target_power",
"induced"
],
"title": "ModulePowerHomomorphism",
"type": "object"
}
noether/homalg/PresentedModulePowerHomomorphism@1¶
Python homalg.PresentedModulePowerHomomorphism · Rust domain
A replay-verifiable induced map between symmetric or exterior presentations.
Canonical JSON Schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"induced": true,
"kind": {
"type": "string"
},
"source_map": true,
"source_power": true,
"target_power": true,
"type": {
"type": "string"
}
},
"required": [
"type",
"source_map",
"kind",
"degree",
"source_power",
"target_power",
"induced"
],
"title": "PresentedModulePowerHomomorphism",
"type": "object"
}
noether/numthy/FiniteFieldEmbedding@1¶
Python numthy.FiniteFieldEmbedding · Rust domain
An explicitly presented embedding between compatible finite fields.
Canonical JSON Schema
{
"$defs": {
"FiniteFieldElementWire": {
"properties": {
"coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"field": {
"$ref": "#/$defs/FiniteFieldWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"field",
"coefficients"
],
"type": "object"
},
"FiniteFieldWire": {
"properties": {
"characteristic": {
"type": "string"
},
"modulus": {
"items": {
"format": "uint64",
"minimum": 0,
"type": "integer"
},
"type": [
"array",
"null"
]
},
"type": {
"type": "string"
}
},
"required": [
"type",
"characteristic"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"generator_image": {
"$ref": "#/$defs/FiniteFieldElementWire"
},
"source": {
"$ref": "#/$defs/FiniteFieldWire"
},
"target": {
"$ref": "#/$defs/FiniteFieldWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"source",
"target",
"generator_image"
],
"title": "FiniteFieldEmbeddingWire",
"type": "object"
}
noether/root/IntegerFiniteFieldMap@1¶
Python IntegerFiniteFieldMap · Rust domain
The canonical unital map from the integers into one finite field.
Canonical JSON Schema
{
"$defs": {
"FiniteFieldWire": {
"properties": {
"characteristic": {
"type": "string"
},
"modulus": {
"items": {
"format": "uint64",
"minimum": 0,
"type": "integer"
},
"type": [
"array",
"null"
]
},
"type": {
"type": "string"
}
},
"required": [
"type",
"characteristic"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"target": {
"$ref": "#/$defs/FiniteFieldWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"target"
],
"title": "IntegerFiniteFieldMapWire",
"type": "object"
}
noether/root/IntegerRationalEmbedding@1¶
Python IntegerRationalEmbedding · Rust domain
The canonical embedding of the integers into the rationals.
Canonical JSON Schema
noether/root/IntegerReduction@1¶
Python IntegerReduction · Rust domain
Canonical reduction from the integers into one residue ring.
Canonical JSON Schema
{
"$defs": {
"ResidueRingWire": {
"properties": {
"modulus": {
"type": "string"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"modulus"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"target": {
"$ref": "#/$defs/ResidueRingWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"target"
],
"title": "IntegerReductionWire",
"type": "object"
}
noether/root/PrimeSubfieldEmbedding@1¶
Python PrimeSubfieldEmbedding · Rust domain
The checked canonical embedding of a prime field into an extension field.
Canonical JSON Schema
{
"$defs": {
"FiniteFieldWire": {
"properties": {
"characteristic": {
"type": "string"
},
"modulus": {
"items": {
"format": "uint64",
"minimum": 0,
"type": "integer"
},
"type": [
"array",
"null"
]
},
"type": {
"type": "string"
}
},
"required": [
"type",
"characteristic"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"source": {
"$ref": "#/$defs/FiniteFieldWire"
},
"target": {
"$ref": "#/$defs/FiniteFieldWire"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"source",
"target"
],
"title": "PrimeSubfieldEmbeddingWire",
"type": "object"
}
noether/topology/EilenbergMacLaneIntegralCohomology@1¶
Python topology.EilenbergMacLaneIntegralCohomology · Rust domain
Exact bounded additive integral cohomology of a symbolic K(A,n).
Canonical JSON Schema
{
"$defs": {
"EilenbergMacLaneIntegralHomology": {
"properties": {
"groups": {
"items": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": "array"
},
"max_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"space": {
"$ref": "#/$defs/EilenbergMacLaneSpace"
},
"strategy": {
"type": "string"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"space",
"max_degree",
"groups",
"strategy"
],
"type": "object"
},
"EilenbergMacLaneSpace": {
"properties": {
"delooping_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"group": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"group",
"delooping_degree"
],
"type": "object"
},
"FinitelyGeneratedAbelianGroup": {
"properties": {
"free_rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"torsion_coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"free_rank",
"torsion_coefficients"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"groups": {
"items": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": "array"
},
"homology": {
"$ref": "#/$defs/EilenbergMacLaneIntegralHomology"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"homology",
"groups"
],
"title": "EilenbergMacLaneIntegralCohomology",
"type": "object"
}
noether/topology/EilenbergMacLaneIntegralCohomologyPresentation@1¶
Python topology.EilenbergMacLaneIntegralCohomologyPresentation · Rust domain
Complete integral cohomology-ring presentation of a symbolic K(A,n).
Canonical JSON Schema
{
"$defs": {
"EilenbergMacLaneIntegralCohomologyGeneratorWire": {
"properties": {
"degree": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"display_name": {
"type": "string"
},
"id": {
"type": "string"
},
"origin": {
"$ref": "#/$defs/EilenbergMacLaneIntegralGeneratorOriginWire"
}
},
"required": [
"id",
"degree",
"display_name",
"origin"
],
"type": "object"
},
"EilenbergMacLaneIntegralCohomologyRelationTermWire": {
"properties": {
"coefficient": {
"type": "string"
},
"exponents": {
"items": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"coefficient",
"exponents"
],
"type": "object"
},
"EilenbergMacLaneIntegralCohomologyRelationWire": {
"properties": {
"terms": {
"items": {
"$ref": "#/$defs/EilenbergMacLaneIntegralCohomologyRelationTermWire"
},
"type": "array"
}
},
"required": [
"terms"
],
"type": "object"
},
"EilenbergMacLaneIntegralGeneratorOriginWire": {
"oneOf": [
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "free_fundamental_class",
"type": "string"
}
},
"required": [
"kind",
"component"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "integral_bockstein",
"type": "string"
},
"modulus": {
"type": "string"
}
},
"required": [
"kind",
"component",
"modulus"
],
"type": "object"
},
{
"properties": {
"kind": {
"const": "cyclic_tor_class",
"type": "string"
},
"left_component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"order": {
"type": "string"
},
"right_component": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"kind",
"left_component",
"right_component",
"order"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "second_delooping_fundamental_class",
"type": "string"
}
},
"required": [
"kind",
"component"
],
"type": "object"
}
]
},
"EilenbergMacLaneSpace": {
"properties": {
"delooping_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"group": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"group",
"delooping_degree"
],
"type": "object"
},
"FinitelyGeneratedAbelianGroup": {
"properties": {
"free_rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"torsion_coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"free_rank",
"torsion_coefficients"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"coefficient_ring": {
"type": "string"
},
"generators": {
"items": {
"$ref": "#/$defs/EilenbergMacLaneIntegralCohomologyGeneratorWire"
},
"type": "array"
},
"graded_commutative": {
"type": "boolean"
},
"relations": {
"items": {
"$ref": "#/$defs/EilenbergMacLaneIntegralCohomologyRelationWire"
},
"type": "array"
},
"space": {
"$ref": "#/$defs/EilenbergMacLaneSpace"
},
"strategy": {
"type": "string"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"space",
"coefficient_ring",
"graded_commutative",
"generators",
"relations",
"strategy"
],
"title": "EilenbergMacLaneIntegralCohomologyPresentation",
"type": "object"
}
noether/topology/EilenbergMacLaneIntegralHomology@1¶
Python topology.EilenbergMacLaneIntegralHomology · Rust domain
Exact bounded integral homology of a symbolic K(A,n).
Canonical JSON Schema
{
"$defs": {
"EilenbergMacLaneSpace": {
"properties": {
"delooping_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"group": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"group",
"delooping_degree"
],
"type": "object"
},
"FinitelyGeneratedAbelianGroup": {
"properties": {
"free_rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"torsion_coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"free_rank",
"torsion_coefficients"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"groups": {
"items": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": "array"
},
"max_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"space": {
"$ref": "#/$defs/EilenbergMacLaneSpace"
},
"strategy": {
"type": "string"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"space",
"max_degree",
"groups",
"strategy"
],
"title": "EilenbergMacLaneIntegralHomology",
"type": "object"
}
noether/topology/EilenbergMacLaneModularCohomology@1¶
Python topology.EilenbergMacLaneModularCohomology · Rust domain
A complete prime-field cohomology presentation of a symbolic K(A,n).
Canonical JSON Schema
{
"$defs": {
"AdmissibleCohomologyOperationWire": {
"oneOf": [
{
"properties": {
"kind": {
"const": "mod_two",
"type": "string"
},
"sequence": {
"items": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"kind",
"sequence"
],
"type": "object"
},
{
"properties": {
"bocksteins": {
"items": {
"type": "boolean"
},
"type": "array"
},
"kind": {
"const": "odd_primary",
"type": "string"
},
"prime": {
"format": "uint64",
"minimum": 0,
"type": "integer"
},
"reduced_powers": {
"items": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"kind",
"prime",
"bocksteins",
"reduced_powers"
],
"type": "object"
}
]
},
"EilenbergMacLaneCohomologyGeneratorWire": {
"properties": {
"degree": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"display_name": {
"type": "string"
},
"id": {
"type": "string"
},
"origin": {
"$ref": "#/$defs/EilenbergMacLaneGeneratorOriginWire"
}
},
"required": [
"id",
"degree",
"display_name",
"origin"
],
"type": "object"
},
"EilenbergMacLaneCohomologyOperationWire": {
"properties": {
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
},
"source_generator": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"target": true
},
"required": [
"operation",
"source_generator",
"target"
],
"type": "object"
},
"EilenbergMacLaneGeneratorOriginWire": {
"oneOf": [
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "fundamental_class",
"type": "string"
}
},
"required": [
"kind",
"component"
],
"type": "object"
},
{
"properties": {
"kind": {
"const": "bockstein",
"type": "string"
},
"source_generator": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"kind",
"source_generator"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "periodic_cyclic_class",
"type": "string"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"kind",
"component",
"primary_exponent"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"fundamental_class_lifts_integrally": {
"type": "boolean"
},
"kind": {
"const": "admissible_steenrod_square",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
}
},
"required": [
"kind",
"component",
"operation",
"fundamental_class_lifts_integrally"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"fundamental_class_lifts_integrally": {
"type": "boolean"
},
"kind": {
"const": "admissible_odd_primary_operation",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
}
},
"required": [
"kind",
"component",
"operation",
"fundamental_class_lifts_integrally"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "higher_bockstein",
"type": "string"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"kind",
"component",
"primary_exponent"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "admissible_steenrod_square_on_higher_primary_class",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"source_is_higher_bockstein": {
"type": "boolean"
}
},
"required": [
"kind",
"component",
"primary_exponent",
"source_is_higher_bockstein",
"operation"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "admissible_odd_primary_operation_on_higher_primary_class",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"source_is_higher_bockstein": {
"type": "boolean"
}
},
"required": [
"kind",
"component",
"primary_exponent",
"source_is_higher_bockstein",
"operation"
],
"type": "object"
}
]
},
"EilenbergMacLaneSpace": {
"properties": {
"delooping_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"group": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"group",
"delooping_degree"
],
"type": "object"
},
"FinitelyGeneratedAbelianGroup": {
"properties": {
"free_rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"torsion_coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"free_rank",
"torsion_coefficients"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"field": true,
"generators": {
"items": {
"$ref": "#/$defs/EilenbergMacLaneCohomologyGeneratorWire"
},
"type": "array"
},
"operations": {
"items": {
"$ref": "#/$defs/EilenbergMacLaneCohomologyOperationWire"
},
"type": "array"
},
"presentation": true,
"space": {
"$ref": "#/$defs/EilenbergMacLaneSpace"
},
"strategy": {
"type": "string"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"space",
"field",
"presentation",
"generators",
"operations",
"strategy"
],
"title": "EilenbergMacLaneModularCohomology",
"type": "object"
}
noether/topology/EilenbergMacLaneModularCohomologyTruncation@1¶
Python topology.EilenbergMacLaneModularCohomologyTruncation · Rust domain
A prime-field cohomology presentation exact through one degree.
Canonical JSON Schema
{
"$defs": {
"AdmissibleCohomologyOperationWire": {
"oneOf": [
{
"properties": {
"kind": {
"const": "mod_two",
"type": "string"
},
"sequence": {
"items": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"kind",
"sequence"
],
"type": "object"
},
{
"properties": {
"bocksteins": {
"items": {
"type": "boolean"
},
"type": "array"
},
"kind": {
"const": "odd_primary",
"type": "string"
},
"prime": {
"format": "uint64",
"minimum": 0,
"type": "integer"
},
"reduced_powers": {
"items": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"type": "array"
}
},
"required": [
"kind",
"prime",
"bocksteins",
"reduced_powers"
],
"type": "object"
}
]
},
"EilenbergMacLaneCohomologyGeneratorWire": {
"properties": {
"degree": {
"format": "uint32",
"minimum": 0,
"type": "integer"
},
"display_name": {
"type": "string"
},
"id": {
"type": "string"
},
"origin": {
"$ref": "#/$defs/EilenbergMacLaneGeneratorOriginWire"
}
},
"required": [
"id",
"degree",
"display_name",
"origin"
],
"type": "object"
},
"EilenbergMacLaneGeneratorOriginWire": {
"oneOf": [
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "fundamental_class",
"type": "string"
}
},
"required": [
"kind",
"component"
],
"type": "object"
},
{
"properties": {
"kind": {
"const": "bockstein",
"type": "string"
},
"source_generator": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"kind",
"source_generator"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "periodic_cyclic_class",
"type": "string"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"kind",
"component",
"primary_exponent"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"fundamental_class_lifts_integrally": {
"type": "boolean"
},
"kind": {
"const": "admissible_steenrod_square",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
}
},
"required": [
"kind",
"component",
"operation",
"fundamental_class_lifts_integrally"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"fundamental_class_lifts_integrally": {
"type": "boolean"
},
"kind": {
"const": "admissible_odd_primary_operation",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
}
},
"required": [
"kind",
"component",
"operation",
"fundamental_class_lifts_integrally"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "higher_bockstein",
"type": "string"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
}
},
"required": [
"kind",
"component",
"primary_exponent"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "admissible_steenrod_square_on_higher_primary_class",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"source_is_higher_bockstein": {
"type": "boolean"
}
},
"required": [
"kind",
"component",
"primary_exponent",
"source_is_higher_bockstein",
"operation"
],
"type": "object"
},
{
"properties": {
"component": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"kind": {
"const": "admissible_odd_primary_operation_on_higher_primary_class",
"type": "string"
},
"operation": {
"$ref": "#/$defs/AdmissibleCohomologyOperationWire"
},
"primary_exponent": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"source_is_higher_bockstein": {
"type": "boolean"
}
},
"required": [
"kind",
"component",
"primary_exponent",
"source_is_higher_bockstein",
"operation"
],
"type": "object"
}
]
},
"EilenbergMacLaneSpace": {
"properties": {
"delooping_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"group": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"group",
"delooping_degree"
],
"type": "object"
},
"FinitelyGeneratedAbelianGroup": {
"properties": {
"free_rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"torsion_coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"free_rank",
"torsion_coefficients"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"exact_through_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"field": true,
"generators": {
"items": {
"$ref": "#/$defs/EilenbergMacLaneCohomologyGeneratorWire"
},
"type": "array"
},
"presentation": true,
"space": {
"$ref": "#/$defs/EilenbergMacLaneSpace"
},
"strategy": {
"type": "string"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"space",
"field",
"exact_through_degree",
"presentation",
"generators",
"strategy"
],
"title": "EilenbergMacLaneModularCohomologyTruncation",
"type": "object"
}
noether/topology/EilenbergMacLaneSpace@1¶
Python topology.EilenbergMacLaneSpace · Rust domain
A symbolic Eilenberg--Mac Lane space K(A,n).
Canonical JSON Schema
{
"$defs": {
"FinitelyGeneratedAbelianGroup": {
"properties": {
"free_rank": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"torsion_coefficients": {
"items": {
"type": "string"
},
"type": "array"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"free_rank",
"torsion_coefficients"
],
"type": "object"
}
},
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"delooping_degree": {
"format": "uint",
"minimum": 0,
"type": "integer"
},
"group": {
"$ref": "#/$defs/FinitelyGeneratedAbelianGroup"
},
"type": {
"type": "string"
}
},
"required": [
"type",
"group",
"delooping_degree"
],
"title": "EilenbergMacLaneSpace",
"type": "object"
}