Type -- the class of all types

Types of type:

• HeaderType -- a class of lists with abbreviated constructors
• Monoid -- the class of all monoids
• Ring -- the class of all rings
• RingFamily
• SelfInitializingType -- the class of all self initializing types
• WrapperType -- a class of lists with abbreviated constructors

Functions and methods returning a type:

• class(Thing) -- see class -- class of an object
• parent(Thing) -- see parent -- parent type of an object

Methods that use a type:

• ? Type -- see ? Symbol -- view brief documentation of a symbol
• about(Type) -- see about -- search the documentation
• ancestor(Type,Type) -- whether one type is an ancestor of another
• instance(Thing,Type) -- see instance -- whether something has a certain type
• instances(Type)
• isQuotientOf(Type,QuotientRing) -- see isQuotientOf(Type,Ring) -- whether one ring is a quotient of a ring of a given type
• isQuotientOf(Type,Ring) -- whether one ring is a quotient of a ring of a given type
• methods(Type) -- see methods -- list methods
• ofClass(Type) -- see ofClass -- English phrases for types
• random(Type) -- get a random object of a type
• select(BasicList,Type) -- select elements of a given type in a list

Protected objects of class Type:

• AffineVariety -- the class of all affine varieties
• AngleBarList -- the class of lists delimited by <| ... |>
• Array -- the class of all arrays -- [...]
• AssociativeExpression -- the class of associative expressions
• AtomicInt -- the class of atomic integers
• BasicList -- the class of all basic lists
• BettiTally -- the class of all Betti tallies
• Boolean -- the class of Boolean values
• CacheFunction -- the class of cache functions
• CacheTable -- hash tables for caching
• CC_* (missing documentation)
• ChainComplex -- the class of all chain complexes
• ChainComplexMap -- the class of all maps between chain complexes
• CoherentSheaf -- the class of all coherent sheaves
• CompiledFunction -- the class of all compiled functions
• CompiledFunctionBody -- the class of all compiled function bodies
• CompiledFunctionClosure -- the class of all compiled function closures
• ComplexField -- the class of all complex fields
• Cone -- the class of all rational convex polyhedral cones
• Constant
• Database -- the class of all database files
• Descent
• Dictionary -- the class of all dictionaries
• DocumentTag -- the class of all document tags
• EngineRing -- the class of rings handled by the engine
• Expression -- the class of all expressions
• Fan -- the class of all fans
• File -- the class of all files
• FilePosition -- the class of all file positions
• FractionField -- the class of all fraction fields
• Function -- the class of all functions
• FunctionBody -- the class of function bodies
• FunctionClosure -- the class of all function closures
• GaloisField -- the class of all Galois fields
• GeneralOrderedMonoid -- the class of all ordered free commutative monoids
• GlobalDictionary -- the class of all global dictionaries
• GradedModule -- the class of all graded modules
• GradedModuleMap -- the class of all maps between graded modules
• GroebnerBasis -- the class of all Gröbner bases
• GroebnerBasisOptions
• HashTable -- the class of all hash tables
• HeaderType -- a class of lists with abbreviated constructors
• Ideal -- the class of all ideals
• ImmutableType -- the class of immutable types
• IndeterminateNumber -- the class of all indeterminate numbers
• IndexedVariable -- the class of all indexed variables
• IndexedVariableTable
• InexactField -- the class of inexact fields
• InexactFieldFamily -- the class of all families of inexact fields
• InexactNumber
• InexactNumber'
• InfiniteNumber -- the class of all infinite numbers
• Keyword -- the class of all keywords
• List -- the class of all lists -- {...}
• LocalDictionary -- the class of all local dictionaries
• Manipulator -- the class of all file manipulators
• Matrix -- the class of all matrices
• MethodFunction -- a type of method function
• MethodFunctionBinary -- a type of method function
• MethodFunctionSingle -- a type of method function
• MethodFunctionWithOptions -- a type of method function
• Module -- the class of all modules
• Monoid -- the class of all monoids
• MonoidElement -- the class of all monoid elements
• MonomialIdeal -- the class of all monomial ideals handled by the engine
• MultigradedBettiTally -- the class of all multigraded Betti tallies
• MutableHashTable -- the class of all mutable hash tables
• MutableList -- the class of all mutable lists
• MutableMatrix -- the class of all mutable matrices
• Net -- the class of all nets and strings
• NetFile -- the class of all net files
• Nothing -- the empty class
• Number -- the class of all numbers
• OneExpression -- the class all one expressions
• Option -- the class of all key-value pairs K => V
• OptionTable -- the class of hash tables for optional arguments
• OrderedMonoid -- the class of all ordered monoids
• Package -- the class of all packages
• Partition -- a type of list representing a partition of a natural number
• PolyhedralComplex -- the class of all polyhedral complexes
• PolyhedralObject -- the class of all polyhedral objects in Polyhedra
• Polyhedron -- the class of all convex polyhedra
• PolynomialRing -- the class of all ordered monoid rings
• Program -- external program object
• ProgramRun -- result of running an external program
• ProjectiveHilbertPolynomial -- the class of all Hilbert polynomials
• ProjectiveVariety -- the class of all projective varieties
• Pseudocode -- the class of pseudocodes
• PseudocodeClosure -- see Pseudocode -- the class of pseudocodes
• QuotientRing -- the class of all quotient rings
• RealField -- the class of all real fields
• Resolution -- the class of all resolution computations
• Ring -- the class of all rings
• RingElement -- the class of all ring elements handled by the engine
• RingFamily
• RingMap -- the class of all ring maps
• RR_* (missing documentation)
• RRi_* (missing documentation)
• ScriptedFunctor -- the class of all scripted functors
• SelfInitializingType -- the class of all self initializing types
• Sequence -- the class of all sequences -- (...)
• Set -- the class of all sets
• SheafMap (missing documentation)
• SheafOfRings -- the class of sheaves of rings
• String -- the class of all strings
• SumOfTwists -- the class of all sums of twists
• Symbol -- the class of all symbols
• SymbolBody -- see symbolBody -- symbol bodies
• Tally -- the class of all tally results
• Task -- the class of all tasks
• Thing -- the class of all things
• Time -- the class of all timing results
• Variety -- the class of all algebraic varieties
• Vector -- the class of all elements of modules that are handled by the engine
• VirtualTally
• VisibleList -- the class of all visible lists
• WrapperType -- a class of lists with abbreviated constructors
• ZeroExpression -- the class of all zero expressions

For the programmer

The object Type is a type, with ancestor classes MutableHashTable < HashTable < Thing.