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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___Type.html" title="the class of all types">Type</a></div>
<hr/>
<div><h1>Type -- the class of all types</h1>
<div class="single"><h2>Description</h2>
<div>Everything in the system is classified, and the class that a thing belongs to is a type. A type is implemented as a hash table containing method functions for its instances.<p/>
The list of types known to the system is displayed below.</div>
</div>
<div class="waystouse"><h2>Types of type :</h2>
<ul><li><span><a href="___Header__Type.html" title="a class of lists with abbreviated constructors">HeaderType</a> -- a class of lists with abbreviated constructors</span></li>
<li><span><a href="___Monoid.html" title="the class of all monoids">Monoid</a> -- the class of all monoids</span></li>
<li><span><a href="___Ring.html" title="the class of all rings">Ring</a> -- the class of all rings</span></li>
<li><span><a href="___Ring__Family.html" title="">RingFamily</a></span></li>
<li><span><a href="___Self__Initializing__Type.html" title="the class of all self initializing types">SelfInitializingType</a> -- the class of all self initializing types</span></li>
<li><span><a href="___Wrapper__Type.html" title="a class of lists with abbreviated constructors">WrapperType</a> -- a class of lists with abbreviated constructors</span></li>
</ul>
<h2>Functions and methods returning a type :</h2>
<ul><li><span><a href="_class.html" title="class of an object">class</a> -- class of an object</span></li>
<li><span><a href="_parent.html" title="parent type of an object">parent</a> -- parent type of an object</span></li>
</ul>
<h2>Methods that use a type :</h2>
<ul><li><span><a href="_ancestor_lp__Type_cm__Type_rp.html" title="whether one type is an ancestor of another">ancestor(Type,Type)</a> -- whether one type is an ancestor of another</span></li>
<li><span>instance(Thing,Type), see <span><a href="_instance.html" title="whether something has a certain type">instance</a> -- whether something has a certain type</span></span></li>
<li><span><a href="_instances_lp__Type_rp.html" title="">instances(Type)</a></span></li>
<li><span>isQuotientOf(Type,QuotientRing), see <span><a href="_is__Quotient__Of_lp__Type_cm__Ring_rp.html" title="whether one ring is a quotient of a ring of a given type">isQuotientOf(Type,Ring)</a> -- whether one ring is a quotient of a ring of a given type</span></span></li>
<li><span><a href="_is__Quotient__Of_lp__Type_cm__Ring_rp.html" title="whether one ring is a quotient of a ring of a given type">isQuotientOf(Type,Ring)</a> -- whether one ring is a quotient of a ring of a given type</span></li>
<li><span>methods(Type), see <span><a href="_methods.html" title="list methods">methods</a> -- list methods</span></span></li>
<li><span>ofClass(Type), see <span><a href="_of__Class.html" title="English phrases for types">ofClass</a> -- English phrases for types</span></span></li>
<li><span><a href="_random_lp__Type_rp.html" title="random element of a type">random(Type)</a> -- random element of a type</span></li>
</ul>
<h2>Fixed objects of class Type :</h2>
<ul><li><span><a href="___Affine__Variety.html" title="the class of all affine varieties">AffineVariety</a> -- the class of all affine varieties</span></li>
<li><span><a href="___Array.html" title="the class of all arrays -- [...]">Array</a> -- the class of all arrays -- [...]</span></li>
<li><span><a href="___Associative__Expression.html" title="the class of associative expressions">AssociativeExpression</a> -- the class of associative expressions</span></li>
<li><span><a href="___Basic__List.html" title="the class of all basic lists">BasicList</a> -- the class of all basic lists</span></li>
<li><span><a href="___Betti__Tally.html" title="the class of all Betti tallies">BettiTally</a> -- the class of all Betti tallies</span></li>
<li><span><a href="___Boolean.html" title="the class of Boolean values">Boolean</a> -- the class of Boolean values</span></li>
<li><span><a href="___Cache__Function.html" title="the class of cache functions">CacheFunction</a> -- the class of cache functions</span></li>
<li><span><a href="___Cache__Table.html" title="hash tables for caching">CacheTable</a> -- hash tables for caching</span></li>
<li><span><a href="___Chain__Complex.html" title="the class of all chain complexes">ChainComplex</a> -- the class of all chain complexes</span></li>
<li><span><a href="___Chain__Complex__Map.html" title="the class of all maps between chain complexes">ChainComplexMap</a> -- the class of all maps between chain complexes</span></li>
<li><span><a href="___Coherent__Sheaf.html" title="the class of all coherent sheaves">CoherentSheaf</a> -- the class of all coherent sheaves</span></li>
<li><span><a href="___Compiled__Function.html" title="the class of all compiled functions">CompiledFunction</a> -- the class of all compiled functions</span></li>
<li><span><a href="___Compiled__Function__Body.html" title="the class of all compiled function bodies">CompiledFunctionBody</a> -- the class of all compiled function bodies</span></li>
<li><span><a href="___Compiled__Function__Closure.html" title="the class of all compiled function closures">CompiledFunctionClosure</a> -- the class of all compiled function closures</span></li>
<li><span><a href="___Complex__Field.html" title="the class of all complex fields">ComplexField</a> -- the class of all complex fields</span></li>
<li><span><a href="___Constant.html" title="">Constant</a></span></li>
<li><span><a href="___Database.html" title="the class of all database files">Database</a> -- the class of all database files</span></li>
<li><span><a href="___Descent.html" title="">Descent</a></span></li>
<li><span><a href="___Dictionary.html" title="the class of all dictionaries">Dictionary</a> -- the class of all dictionaries</span></li>
<li><span><a href="___Document__Tag.html" title="the class of all document tags">DocumentTag</a> -- the class of all document tags</span></li>
<li><span><a href="___Engine__Ring.html" title="the class of rings handled by the engine">EngineRing</a> -- the class of rings handled by the engine</span></li>
<li><span><a href="___Expression.html" title="the class of all expressions">Expression</a> -- the class of all expressions</span></li>
<li><span><a href="___File.html" title="the class of all files">File</a> -- the class of all files</span></li>
<li><span><a href="___File__Position.html" title="the class of all file positions">FilePosition</a> -- the class of all file positions</span></li>
<li><span><a href="___Forest__Node.html" title="a type of basic list used to represent a forest, i.e., a list of rooted trees">ForestNode</a> -- a type of basic list used to represent a forest, i.e., a list of rooted trees</span></li>
<li><span><a href="___Fraction__Field.html" title="the class of all fraction fields">FractionField</a> -- the class of all fraction fields</span></li>
<li><span><a href="___Function.html" title="the class of all functions">Function</a> -- the class of all functions</span></li>
<li><span><a href="___Function__Body.html" title="the class of function bodies">FunctionBody</a> -- the class of function bodies</span></li>
<li><span><a href="___Function__Closure.html" title="the class of all function closures">FunctionClosure</a> -- the class of all function closures</span></li>
<li><span><a href="___Galois__Field.html" title="the class of all Galois fields">GaloisField</a> -- the class of all Galois fields</span></li>
<li><span><a href="___General__Ordered__Monoid.html" title="the class of all ordered free commutative monoids">GeneralOrderedMonoid</a> -- the class of all ordered free commutative monoids</span></li>
<li><span><a href="___Global__Dictionary.html" title="the class of all global dictionaries">GlobalDictionary</a> -- the class of all global dictionaries</span></li>
<li><span><a href="___Graded__Module.html" title="the class of all graded modules">GradedModule</a> -- the class of all graded modules</span></li>
<li><span><a href="___Graded__Module__Map.html" title="the class of all maps between graded modules">GradedModuleMap</a> -- the class of all maps between graded modules</span></li>
<li><span><a href="___Groebner__Basis.html" title="the class of all Gröbner bases">GroebnerBasis</a> -- the class of all Gröbner bases</span></li>
<li><span><a href="___Groebner__Basis__Options.html" title="">GroebnerBasisOptions</a></span></li>
<li><span><a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> -- the class of all hash tables</span></li>
<li><span><a href="___Header__Type.html" title="a class of lists with abbreviated constructors">HeaderType</a> -- a class of lists with abbreviated constructors</span></li>
<li><span><a href="___Ideal.html" title="the class of all ideals">Ideal</a> -- the class of all ideals</span></li>
<li><span><a href="___Immutable__Type.html" title="the class of immutable types">ImmutableType</a> -- the class of immutable types</span></li>
<li><span><a href="___Indeterminate__Number.html" title="the class of all indeterminate numbers">IndeterminateNumber</a> -- the class of all indeterminate numbers</span></li>
<li><span><a href="___Indexed__Variable.html" title="the class of all indexed variables">IndexedVariable</a> -- the class of all indexed variables</span></li>
<li><span><a href="___Indexed__Variable__Table.html" title="">IndexedVariableTable</a></span></li>
<li><span><a href="___Inexact__Field.html" title="the class of inexact fields">InexactField</a> -- the class of inexact fields</span></li>
<li><span><a href="___Inexact__Field__Family.html" title="the class of all families of inexact fields">InexactFieldFamily</a> -- the class of all families of inexact fields</span></li>
<li><span><a href="___Inexact__Number.html" title="">InexactNumber</a></span></li>
<li><span><a href="___Inexact__Number_sq.html" title="">InexactNumber'</a></span></li>
<li><span><a href="___Infinite__Number.html" title="the class of all infinite numbers">InfiniteNumber</a> -- the class of all infinite numbers</span></li>
<li><span><a href="___Keyword.html" title="the class of all keywords">Keyword</a> -- the class of all keywords</span></li>
<li><span><tt>LibxmlAttribute</tt> (missing documentation<!-- tag: LibxmlAttribute -->)</span></li>
<li><span><tt>LibxmlNode</tt> (missing documentation<!-- tag: LibxmlNode -->)</span></li>
<li><span><a href="___List.html" title="the class of all lists -- {...}">List</a> -- the class of all lists -- {...}</span></li>
<li><span><a href="___Local__Dictionary.html" title="the class of all local dictionaries">LocalDictionary</a> -- the class of all local dictionaries</span></li>
<li><span><a href="___Manipulator.html" title="the class of all file manipulators">Manipulator</a> -- the class of all file manipulators</span></li>
<li><span><a href="___Matrix.html" title="the class of all matrices">Matrix</a> -- the class of all matrices</span></li>
<li><span><a href="___Method__Function.html" title="a type of method function">MethodFunction</a> -- a type of method function</span></li>
<li><span><a href="___Method__Function__With__Options.html" title="a type of method function">MethodFunctionWithOptions</a> -- a type of method function</span></li>
<li><span><a href="___Module.html" title="the class of all modules">Module</a> -- the class of all modules</span></li>
<li><span><a href="___Module__Map.html" title="the class of all maps between modules">ModuleMap</a> -- the class of all maps between modules</span></li>
<li><span><a href="___Monoid.html" title="the class of all monoids">Monoid</a> -- the class of all monoids</span></li>
<li><span><a href="___Monoid__Element.html" title="the class of all monoid elements">MonoidElement</a> -- the class of all monoid elements</span></li>
<li><span><a href="___Monomial__Ideal.html" title="the class of all monomial ideals handled by the engine">MonomialIdeal</a> -- the class of all monomial ideals handled by the engine</span></li>
<li><span><a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> -- the class of all mutable hash tables</span></li>
<li><span><a href="___Mutable__List.html" title="the class of all mutable lists">MutableList</a> -- the class of all mutable lists</span></li>
<li><span><a href="___Mutable__Matrix.html" title="the class of all mutable matrices">MutableMatrix</a> -- the class of all mutable matrices</span></li>
<li><span><a href="___Net.html" title="the class of all nets and strings">Net</a> -- the class of all nets and strings</span></li>
<li><span><a href="___Net__File.html" title="the class of all net files">NetFile</a> -- the class of all net files</span></li>
<li><span><a href="___Nothing.html" title="the empty class">Nothing</a> -- the empty class</span></li>
<li><span><a href="___Number.html" title="the class of all numbers">Number</a> -- the class of all numbers</span></li>
<li><span><a href="___One__Expression.html" title="the class all one expressions">OneExpression</a> -- the class all one expressions</span></li>
<li><span><a href="___Option.html" title="the class of all pairs x => y">Option</a> -- the class of all pairs x => y</span></li>
<li><span><a href="___Option__Table.html" title="the class of hash tables for optional arguments">OptionTable</a> -- the class of hash tables for optional arguments</span></li>
<li><span><a href="___Ordered__Monoid.html" title="the class of all ordered monoids">OrderedMonoid</a> -- the class of all ordered monoids</span></li>
<li><span><a href="___Package.html" title="the class of all packages">Package</a> -- the class of all packages</span></li>
<li><span><a href="___Partition.html" title="a type of list representing a partition of a natural number">Partition</a> -- a type of list representing a partition of a natural number</span></li>
<li><span><a href="___Polynomial__Ring.html" title="the class of all ordered monoid rings">PolynomialRing</a> -- the class of all ordered monoid rings</span></li>
<li><span><a href="___Projective__Hilbert__Polynomial.html" title="the class of all Hilbert polynomials">ProjectiveHilbertPolynomial</a> -- the class of all Hilbert polynomials</span></li>
<li><span><a href="___Projective__Variety.html" title="the class of all projective varieties">ProjectiveVariety</a> -- the class of all projective varieties</span></li>
<li><span><a href="___Pseudocode.html" title="the class of pseudocodes">Pseudocode</a> -- the class of pseudocodes</span></li>
<li><span><a href="___Quotient__Ring.html" title="the class of all quotient rings">QuotientRing</a> -- the class of all quotient rings</span></li>
<li><span><a href="___Real__Field.html" title="the class of all real fields">RealField</a> -- the class of all real fields</span></li>
<li><span><a href="___Resolution.html" title="the class of all resolution computations">Resolution</a> -- the class of all resolution computations</span></li>
<li><span><a href="___Ring.html" title="the class of all rings">Ring</a> -- the class of all rings</span></li>
<li><span><a href="___Ring__Element.html" title="the class of all ring elements handled by the engine">RingElement</a> -- the class of all ring elements handled by the engine</span></li>
<li><span><a href="___Ring__Family.html" title="">RingFamily</a></span></li>
<li><span><a href="___Ring__Map.html" title="the class of all ring maps">RingMap</a> -- the class of all ring maps</span></li>
<li><span><a href="../../SchurRings/html/___Schur__Ring.html" title="the class of all Schur rings">SchurRing</a> -- the class of all Schur rings</span></li>
<li><span><a href="../../SchurRings/html/___Schur__Ring__Indexed__Variable__Table.html" title="">SchurRingIndexedVariableTable</a></span></li>
<li><span><a href="___Scripted__Functor.html" title="the class of all scripted functors">ScriptedFunctor</a> -- the class of all scripted functors</span></li>
<li><span><a href="___Self__Initializing__Type.html" title="the class of all self initializing types">SelfInitializingType</a> -- the class of all self initializing types</span></li>
<li><span><a href="___Sequence.html" title="the class of all sequences -- (...)">Sequence</a> -- the class of all sequences -- (...)</span></li>
<li><span><a href="___Set.html" title="the class of all sets">Set</a> -- the class of all sets</span></li>
<li><span><a href="___Sheaf__Of__Rings.html" title="the class of sheaves of rings">SheafOfRings</a> -- the class of sheaves of rings</span></li>
<li><span><a href="___String.html" title="the class of all strings">String</a> -- the class of all strings</span></li>
<li><span><a href="___Sum__Of__Twists.html" title="the class of all sums of twists">SumOfTwists</a> -- the class of all sums of twists</span></li>
<li><span><a href="___Symbol.html" title="the class of all symbols">Symbol</a> -- the class of all symbols</span></li>
<li><span><a href="___Tally.html" title="the class of all tally results">Tally</a> -- the class of all tally results</span></li>
<li><span><a href="___Thing.html" title="the class of all things">Thing</a> -- the class of all things</span></li>
<li><span><a href="___Time.html" title="the class of all timing results">Time</a> -- the class of all timing results</span></li>
<li><span><a href="___Tree__Node.html" title="a type of basic list used to represent a rooted tree">TreeNode</a> -- a type of basic list used to represent a rooted tree</span></li>
<li><span><a href="___Type.html" title="the class of all types">Type</a> -- the class of all types</span></li>
<li><span><a href="___Variety.html" title="the class of all algebraic varieties">Variety</a> -- the class of all algebraic varieties</span></li>
<li><span><a href="___Vector.html" title="the class of all elements of free modules that are handled by the engine">Vector</a> -- the class of all elements of free modules that are handled by the engine</span></li>
<li><span><a href="___Virtual__Tally.html" title="">VirtualTally</a></span></li>
<li><span><a href="___Visible__List.html" title="the class of all visible lists">VisibleList</a> -- the class of all visible lists</span></li>
<li><span><a href="___Wrapper__Type.html" title="a class of lists with abbreviated constructors">WrapperType</a> -- a class of lists with abbreviated constructors</span></li>
<li><span><a href="___Zero__Expression.html" title="the class of all zero expressions">ZeroExpression</a> -- the class of all zero expressions</span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Type.html" title="the class of all types">Type</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> < <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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