Notable mathematical lattices.

Entity["Lattice",name] or

represents an entity of type "Lattice".

[prop]

gives the value of a specified property.

[{propi,}]

gives the value of a list of properties.

EntityClass["Lattice",{propispeci,}]

represents a class of entities with values of propi defined by speci.

Sample Entities

Sample Entity Classes

Properties

  • AlternateNamesalternate names
    AutomorphismGroupOrdernumber of symmetries
    Basisbasis
    CenterDensitycenter density
    Classesclasses
    CoveringRadiuscovering radius
    CoxeterNumberCoxeter number
    CrystalFamilycrystal family
    CrystalSystemscrystal system
    Densitydensity
    Determinantdeterminant
    Dimensiondimension
    Dualdual
    EntityClassesentity classes
    Eveneven
    Extremalextremal
    GeneratorMatrixgenerator matrix
    GramMatrixGram matrix
    HermiteInvariantHermite invariant
    Imageimage
    Integralintegral
    KissingNumberkissing number
    LatticeSystemlattice system
    MinimalNormminimal squared norm
    MinimalVectorssmallest vectors
    ModularNumbermodular number
    Namename
    Nonextremalnonextremal
    Nonintegralnonintegral
    Nonunimodularnonunimodular
    Notationnotation
    Oddodd
    PackingRadiuspacking radius
    QuadraticFormquadratic form
    RadialFunctionradial function
    ThetaSeriesFunctiontheta series
    Thicknessthickness
    Unimodularunimodular
    Volumevolume

Details

  • "Lattice" entities include particular named mathematical lattices as well as members of parametrized families.
  • "Lattice" entity classes include classifications based on various mathematical properties.
  • Some properties are available for the "Lattice" entity type as a whole and can be given using the form EntityValue["Lattice",property]. Such properties include:
  • "Properties"the list of available properties
    "PropertyCanonicalNames"the standard names of available properties
    "SampleEntities"a sample list of available entities (typically of length 10)
    "SampleEntityClasses"a sample list of available entity classes (typically of length 10)
    "EntityCount"number of entities available
    "Entities"the list of available entities
    "EntityCanonicalNames"the standard names of available entities
    "EntityClasses"the list of available entity classes
    "EntityClassCanonicalNames"the standard names of available entity classes
    "PropertyClasses"the list of available property classes
    "PropertyClassCanonicalNames"the standard names of available property classes
    "PropertyCount"number of properties available
  • The following annotations can be used in the third argument of EntityValue["Lattice",property,annotation]:
  • "Source"source information for the property
    "Date"the date associated with the entity-property value (if any)
    "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values
    "EntityPropertyAssociation"an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "PropertyEntityAssociation"an association in which the specified properties are keys, and values are a nested association of entities and entity-property values
    "Dataset"a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
  • The following annotations can be used in the second argument of EntityValue[property,annotation]:
  • "Qualifiers"the list of possible qualifiers for the property
    "QualifierValues"the list of possible values that can be given to each qualifier
    "DefaultQualifierValues"the list of default values for the property's qualifiers
    "Description"a brief textual description of the property
    "Definition"a detailed textual definition of the property
    "PhysicalQuantity"the physical quantity associated with the entity-property value
    "Unit"the unit associated with the entity-property value
  • A qualifier value of Automatic indicates that an applicable format of values can be used; e.g. for the "Date" qualifier, this includes a proper date or date span.

Examples

Basic Examples  (4)

Use for entity discovery:

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Find a property value for an entity:

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Retrieve a dataset of all available properties for an entity:

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Return lattices in three dimensions:

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