Thing -- the class of all things

Types of thing :

• AtomicInt -- the class of atomic integers
• BasicList -- the class of all basic lists
• Boolean -- the class of Boolean values
• CompiledFunctionBody -- the class of all compiled function bodies
• Database -- the class of all database files
• Dictionary -- the class of all dictionaries
• File -- the class of all files
• Function -- the class of all functions
• FunctionBody -- the class of function bodies
• HashTable -- the class of all hash tables
• 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
• Pseudocode -- the class of pseudocodes
• Symbol -- the class of all symbols
• SymbolBody -- see symbolBody -- symbol bodies
• Task -- the class of all tasks
• Thing -- the class of all things

Functions and methods returning a thing :

• BasicList # ZZ -- get value from list, hash table, database, or string
• HashTable # Thing -- see BasicList # ZZ -- get value from list, hash table, database, or string
• String # ZZ -- see BasicList # ZZ -- get value from list, hash table, database, or string
• Function Thing -- function application
• taskResult(Task) -- retrieve the value returned by a task

Methods that use a thing :

• HashTable #? Thing -- see #? -- check existence of value in a list, hash table, database, or string
• Thing * List -- see * -- a binary operator, usually used for multiplication
• Thing =!= Thing -- see =!= -- strict inequality
• Thing => Thing -- see => -- produce an Option
• accumulate(Function,Thing) -- see accumulate -- apply a binary operator repeatedly
• accumulate(Function,Thing,Thing) -- see accumulate -- apply a binary operator repeatedly
• accumulate(Function,Thing,VisibleList) -- see accumulate -- apply a binary operator repeatedly
• accumulate(VisibleList,Thing,Function) -- see accumulate -- apply a binary operator repeatedly
• addHook(MutableHashTable,Thing,Function) -- see addHook -- add a hook function to an object for later processing
• append(BasicList,Thing) -- see append -- add an element to the end of a list
• apply(Thing,Function) -- apply a function to an object with an iterator
• assert(Thing) -- see assert -- check whether something is true, raise an error if not
• baseName(Thing) -- see baseName -- the base name of a generator
• between(Thing,VisibleList) -- insert something between elements of a list
• Command Thing -- see Command -- the class of all commands
• createTask(Function,Thing) -- see createTask -- create a task
• delete(Thing,BasicList) -- see delete -- delete some elements of a list
• describe(Thing) -- see describe -- real description
• dictionary(Thing) -- see dictionary -- determine the dictionary to which a symbol belongs
• makeDocumentTag(Thing) -- see DocumentTag -- the class of all document tags
• examples(Thing) -- see examples -- list the examples in documentation
• Expression != Thing -- see Expression -- the class of all expressions
• Expression % Thing -- see Expression -- the class of all expressions
• Expression & Thing -- see Expression -- the class of all expressions
• Expression - Thing -- see Expression -- the class of all expressions
• Expression .. Thing -- see Expression -- the class of all expressions
• Expression ..< Thing -- see Expression -- the class of all expressions
• Expression / Thing -- see Expression -- the class of all expressions
• Expression : Thing -- see Expression -- the class of all expressions
• Expression <== Thing -- see Expression -- the class of all expressions
• Expression <=== Thing -- see Expression -- the class of all expressions
• Expression <==> Thing -- see Expression -- the class of all expressions
• Expression ===> Thing -- see Expression -- the class of all expressions
• Expression ==> Thing -- see Expression -- the class of all expressions
• Expression @ Thing -- see Expression -- the class of all expressions
• Expression @@ Thing -- see Expression -- the class of all expressions
• Expression ^ Thing -- see Expression -- the class of all expressions
• Expression ^** Thing -- see Expression -- the class of all expressions
• Expression ^^ Thing -- see Expression -- the class of all expressions
• Expression _ Thing -- see Expression -- the class of all expressions
• Expression | Thing -- see Expression -- the class of all expressions
• Expression |- Thing -- see Expression -- the class of all expressions
• Expression || Thing -- see Expression -- the class of all expressions
• Expression and Thing -- see Expression -- the class of all expressions
• Expression or Thing -- see Expression -- the class of all expressions
• Expression Thing -- see Expression -- the class of all expressions
• Expression xor Thing -- see Expression -- the class of all expressions
• Thing != Expression -- see Expression -- the class of all expressions
• Thing % Expression -- see Expression -- the class of all expressions
• Thing & Expression -- see Expression -- the class of all expressions
• Thing - Expression -- see Expression -- the class of all expressions
• Thing .. Expression -- see Expression -- the class of all expressions
• Thing ..< Expression -- see Expression -- the class of all expressions
• Thing / Expression -- see Expression -- the class of all expressions
• Thing : Expression -- see Expression -- the class of all expressions
• Thing <== Expression -- see Expression -- the class of all expressions
• Thing <=== Expression -- see Expression -- the class of all expressions
• Thing <==> Expression -- see Expression -- the class of all expressions
• Thing ===> Expression -- see Expression -- the class of all expressions
• Thing ==> Expression -- see Expression -- the class of all expressions
• Thing @ Expression -- see Expression -- the class of all expressions
• Thing @@ Expression -- see Expression -- the class of all expressions
• Thing ^ Expression -- see Expression -- the class of all expressions
• Thing ^** Expression -- see Expression -- the class of all expressions
• Thing ^^ Expression -- see Expression -- the class of all expressions
• Thing _ Expression -- see Expression -- the class of all expressions
• Thing | Expression -- see Expression -- the class of all expressions
• Thing |- Expression -- see Expression -- the class of all expressions
• Thing || Expression -- see Expression -- the class of all expressions
• Thing and Expression -- see Expression -- the class of all expressions
• Thing Expression -- see Expression -- the class of all expressions
• Thing or Expression -- see Expression -- the class of all expressions
• Thing xor Expression -- see Expression -- the class of all expressions
• Expression * Thing (missing documentation)
• Expression ** Thing (missing documentation)
• Expression + Thing (missing documentation)
• Expression ++ Thing (missing documentation)
• Expression == Thing (missing documentation)
• << Thing -- see File << Thing -- print to a file
• File << Thing -- print to a file
• Nothing << Thing -- see File << Thing -- print to a file
• String << Thing -- see File << Thing -- print to a file
• fold(Function,Thing) -- see fold -- apply a binary operator repeatedly
• fold(Function,Thing,Thing) -- see fold -- apply a binary operator repeatedly
• fold(VisibleList,Thing,Function) -- see fold -- apply a binary operator repeatedly
• Function _ Thing -- attach the first argument to a function of two or more arguments
• help(Thing) -- see help -- view documentation nodes
• hooks(Thing) -- see hooks -- list hooks attached to a key
• IndexedVariableTable _ Thing -- see IndexedVariableTable
• IndexedVariableTable _ Thing = Thing -- see IndexedVariableTable
• IndexedVariableTable .. Thing (missing documentation)
• IndexedVariableTable ..< Thing (missing documentation)
• infoHelp(Thing) -- see infoHelp -- view documentation in Info format
• insert(ZZ,Thing,VisibleList) -- see insert -- copy a list, inserting an element
• instance(Thing,Type) -- see instance -- whether something has a certain type
• isFreeModule(Thing) -- see isFreeModule -- whether something is a free module
• isIdeal(Thing) -- see isIdeal -- whether something is an ideal
• isMember(Thing,Set) -- see isMember -- test membership in a list or set
• isMember(Thing,VisibleList) -- see isMember -- test membership in a list or set
• isModule(Thing) -- see isModule -- whether something is a module
• isMonomialIdeal(Thing) -- see isMonomialIdeal -- whether something is a monomial ideal
• isMutable(Thing) -- see isMutable -- whether something may be modified
• isPolynomialRing(Thing) -- see isPolynomialRing -- whether something is a polynomial ring
• isQuotientModule(Thing) -- see isQuotientModule -- whether something is evidently a quotient of a free module
• isRing(Thing) -- see isRing -- whether something is a ring
• isSubmodule(Thing) -- see isSubmodule -- whether a module is evidently a submodule of a free module
• List / Thing -- vector division
• methods(Thing) -- see methods -- list methods
• MonoidElement .. Thing (missing documentation)
• MonoidElement ..< Thing (missing documentation)
• MonoidElement _ Thing (missing documentation)
• net(Thing) -- see net -- format for printing, as a net
• package(Thing) -- see package -- get containing package
• peek'(ZZ,Thing) -- see peek' -- examine contents of an object
• prepend(Thing,BasicList) -- see prepend -- add an element to the beginning of a list
• Program << Thing -- run program with input redirection
• registerFinalizer(Thing,String) (missing documentation)
• remove(HashTable,Thing) -- see remove -- remove an entry from a mutable hash table, list, or database
• replace(ZZ,Thing,VisibleList) -- copy a list, replacing an element
• RingElement .. Thing (missing documentation)
• RingElement ..< Thing (missing documentation)
• RingElement _ Thing (missing documentation)
• runHooks(MutableHashTable,Thing,Thing) -- see runHooks -- run the hook functions stored in an object
• runHooks(Sequence,Thing) -- see runHooks -- run the hook functions stored in an object
• runHooks(Symbol,Thing) -- see runHooks -- run the hook functions stored in an object
• scan(Thing,Function) -- see scan -- apply a function to each element in a list or sequence
• schedule(Function,Thing) -- see schedule -- schedule a task for execution
• ScriptedFunctor ^ Thing -- see ScriptedFunctor -- the class of all scripted functors
• ScriptedFunctor _ Thing -- see ScriptedFunctor -- the class of all scripted functors
• ScriptedFunctor Thing -- see ScriptedFunctor -- the class of all scripted functors
• select(Thing,Function) -- select elements from an object with an iterator
• SelfInitializingType Thing -- see SelfInitializingType -- the class of all self initializing types
• Set #? Thing -- test set membership
• substitute(Divide,Thing) -- see substitute -- substituting values for variables
• substitute(Power,Thing) -- see substitute -- substituting values for variables
• substitute(Product,Thing) -- see substitute -- substituting values for variables
• substitute(Sum,Thing) -- see substitute -- substituting values for variables
• Symbol _ Thing -- index variable
• Symbol _ Thing = Thing -- assignment to an indexed variable
• SYNOPSIS(Thing) -- see SYNOPSIS -- a standardized synopsis for use in documentation nodes
• take(Thing,ZZ) -- see take -- Take some elements from a list or sequence.
• Thing * Expression (missing documentation)
• Thing ** Expression (missing documentation)
• Thing + Expression (missing documentation)
• Thing ++ Expression (missing documentation)
• Thing .. IndexedVariableTable (missing documentation)
• Thing .. MonoidElement (missing documentation)
• Thing .. RingElement (missing documentation)
• Thing ..< IndexedVariableTable (missing documentation)
• Thing ..< MonoidElement (missing documentation)
• Thing ..< RingElement (missing documentation)
• Command \\ Thing -- see Thing // Function -- apply a function
• Function \\ Thing -- see Thing // Function -- apply a function
• SelfInitializingType \\ Thing -- see Thing // Function -- apply a function
• Thing // Command -- see Thing // Function -- apply a function
• Thing // Function -- apply a function
• Thing // SelfInitializingType -- see Thing // Function -- apply a function
• Thing == Expression (missing documentation)
• Thing === Thing -- strict equality
• toList(Thing) -- see toList -- create a list
• toSequence(Thing) -- see toSequence -- convert to sequence
• truncate(InfiniteNumber,Thing) (missing documentation)
• ultimate(Function,Thing) -- see ultimate -- ultimate value for an iteration
• undocumented(Thing) -- see undocumented -- declare that something need not be documented
• viewHelp(Thing) -- see viewHelp -- view online documentation in a web browser
• VirtualTally _ Thing -- get a count from a tally
• WrapperType Thing -- see WrapperType -- a class of lists with abbreviated constructors
• ZZ : Thing -- repeat an item

Fixed objects of class Thing :

• ! -- factorial
• != -- inequality
• # -- length or access to elements
• #? -- check existence of value in a list, hash table, database, or string
• % -- a binary operator, usually used for remainder and reduction
• %= -- augmented assignment for %
• & -- a binary operator
• &= -- augmented assignment for &
• (*) -- a unary postfix operator, used for indicating a graded object
• * -- a binary operator, usually used for multiplication
• ** -- a binary operator, usually used for tensor product or Cartesian product
• **= -- augmented assignment for **
• *= -- augmented assignment for *
• + -- a unary or binary operator, usually used for addition
• ++ -- a binary operator, usually used for direct sum
• ++= -- augmented assignment for ++
• += -- augmented assignment for +
• , -- the comma, used for separating entries in a list or sequence
• - -- a unary or binary operator, usually used for negation or subtraction
• -= -- augmented assignment for -
• -> -- make a function
• . -- access to elements whose key is a symbol
• .. -- a binary operator, used for sequences of consecutive items
• ..< -- a binary operator, used for sequences of consecutive items, not including the endpoint
• ..<= -- augmented assignment for ..<
• ..= -- augmented assignment for ..
• .? -- check for presence of elements whose key is a symbol
• / -- a binary operator, usually used for division
• // -- a binary operator, usually used for quotient
• //= -- augmented assignment for //
• /= -- augmented assignment for /
• : -- a binary operator, uses include repetition; ideal quotients
• := -- assignment of method or new local variable
• ; -- expression separator
• < -- less than
• <- -- assignment with left side evaluated
• << -- a binary operator (file output, ...)
• <<= -- augmented assignment for <<
• <= -- less than or equal
• <== -- a unary and binary operator
• <=== -- a unary and binary operator
• <==> -- a binary operator
• <==>= -- augmented assignment for <==>
• = -- assignment
• =!= -- strict inequality
• == -- equality
• ===> -- a binary operator
• ===>= -- augmented assignment for ===>
• ==> -- a binary operator
• ==>= -- augmented assignment for ==>
• => -- produce an Option
• > -- greater than
• >= -- greater than or equal
• >> -- a binary operator, uses include bit shifting, or attaching optional inputs to functions
• >>= -- augmented assignment for >>
• ? -- comparison operator
• ?? -- null coalescing operator
• ??= -- augmented assignment for ??
• @ -- a binary operator
• @= -- augmented assignment for @
• @@ -- a binary operator
• @@= -- augmented assignment for @@
• \ -- a binary operator
• \= -- augmented assignment for \
• \\ -- a binary operator
• \\= -- augmented assignment for \\
• ^ -- a binary operator, usually used for powers
• ^* -- a unary postfix operator, used for indicating pullback maps
• ^** -- a binary operator, usually used for tensor or Cartesian power
• ^**= -- augmented assignment for ^**
• ^= -- augmented assignment for ^
• ^^ -- logical exclusive-or
• ^^= -- augmented assignment for ^^
• _ -- a binary operator, used for subscripting and access to elements
• _* -- a unary postfix operator, used for indicating pushforward maps
• _= -- augmented assignment for _
• | -- a binary operator, often used for horizontal concatenation
• |- -- a binary operator
• |-= -- augmented assignment for |-
• |= -- augmented assignment for |
• || -- a binary operator, often used for vertical concatenation
• ||= -- augmented assignment for ||
• ~ -- a unary postfix operator
• about -- search the documentation
• abs -- absolute value function
• accumulate -- apply a binary operator repeatedly
• Acknowledgement -- acknowledgements listed in a documentation node
• acos -- arccosine
• acosh -- inverse hyperbolic cosine
• acot -- compute the inverse cotangent
• acoth -- compute the hyperbolic arctangent of a number
• addCancelTask -- see addCancelTask(Task,Task) -- specify that the completion of one task triggers the cancellation of another
• addDependencyTask -- see addDependencyTask(Task,Task) -- schedule a task, but ensure that it will not run until another task finishes
• addEndFunction -- add an ending function
• addHook -- add a hook function to an object for later processing
• GlobalHookStore -- see addHook -- add a hook function to an object for later processing
• AdditionalPaths -- list of non-standard paths to search for a program
• addStartFunction -- add a startup function
• addStartTask -- see addStartTask(Task,Task) -- schedule a task upon completion of another
• Adjacent -- the class of all adjacent expression pairs
• adjoint -- the tensor-Hom adjunction maps
• adjoint' -- see adjoint -- the tensor-Hom adjunction maps
• AffineVariety -- the class of all affine varieties
• AfterEval -- top level method applied after evaluation
• AfterNoPrint -- top level method applied after not printing
• AfterPrint -- top level method applied after printing
• agm -- arithmetic-geometric mean
• alarm -- set an alarm
• Algorithm -- an optional argument
• Alignment -- an optional argument
• all -- whether all elements satisfy a specified condition
• AllCodimensions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• ambient -- ambient free module of a subquotient, or ambient ring
• analyticSpread -- Compute the analytic spread of a module or ideal
• ancestor -- see ancestor(Type,Type) -- whether one type is an ancestor of another
• ancestors -- the ancestors of something
• and -- conjunction
• AngleBarList -- the class of lists delimited by <| ... |>
• annihilator -- the annihilator ideal
• antipode -- antipode for skew commuting polynomial rings
• any -- whether any elements satisfy a specified condition
• append -- add an element to the end of a list
• applicationDirectory -- the path to the user's application directory
• apply -- apply a function to each element
• applyKeys -- apply a function to each key in a hash table
• applyPairs -- apply a function to each pair in a hash table
• applyTable -- apply a function to each element of a table
• applyValues -- apply a function to each value in a hash table
• apropos -- symbols matching a pattern
• argument -- specify the function in a scripted functor for an argument
• Array -- the class of all arrays -- [...]
• arXiv -- link to an arXiv article
• Ascending -- specify ascending order
• ascii -- ASCII character conversion
• asin -- arcsine
• asinh -- inverse hyperbolic sine
• assert -- check whether something is true, raise an error if not
• associatedPrimes -- find associated primes
• AssociativeExpression -- the class of associative expressions
• atan -- compute the arctangent of a number
• atan2 -- compute an angle of a certain triangle
• atanh -- compute the hyperbolic arctangent of a number
• atEndOfFile -- see atEndOfFile(File) -- test for end of file
• AtomicInt -- the class of atomic integers
• Authors -- an optional argument
• autoload -- arrange for a function to be loaded automatically
• AuxiliaryFiles -- an optional argument
• Bag -- the class of all bags
• Bareiss
• Base
• baseFilename -- the base part of a filename or path
• BaseFunction -- the basename of a function in a documentation node
• baseName -- the base name of a generator
• baseRing -- produce the ring from which a ring was formed
• baseRings -- store the list of base rings of a ring
• BaseRow -- an optional argument
• BasicList -- the class of all basic lists
• basis -- basis or generating set of all or part of a ring, ideal or module
• BasisElementLimit -- an optional argument
• Bayer -- value of an optional argument
• BeforePrint -- top level method applied before printing results
• beginDocumentation -- start documentation section of a package
• benchmark -- accurate timing of execution
• BesselJ -- Bessel function of the first kind
• BesselY -- Bessel function of the second kind
• Beta -- Beta function
• betti -- display or modify a Betti diagram
• BettiTally -- the class of all Betti tallies
• between -- insert something between elements of a list
• BinaryOperation -- the class of all binary operation expressions
• Binomial -- value of an optional argument
• binomial -- binomial coefficient
• BKZ -- compute BKZ reduced basis instead of an LLL reduced basis
• Body -- an optional argument
• Boolean -- the class of Boolean values
• borel -- see borel(Matrix) -- make a Borel fixed submodule
• Boxes -- an optional argument
• break -- break from a loop
• cache -- a key under which to store cache tables
• CacheExampleOutput -- an optional argument
• CacheFunction -- the class of cache functions
• CacheTable -- hash tables for caching
• cacheValue -- cache values of functions in their arguments
• cancelTask -- see cancelTask(Task) -- stop a task
• canonicalBundle (missing documentation)
• capture -- evaluate Macaulay2 code and capture the output
• CatalanConstant -- Catalan's constant
• catch -- catch a thrown exception
• Caveat -- warnings or limitations listed in a documentation node
• CC -- the class of all complex numbers
• CC' -- the parent class of all rings of complex numbers
• ceiling -- ceiling function
• Center -- value of an optional argument
• centerString -- center a string or net
• Certification -- an optional argument
• ChainComplex -- the class of all chain complexes
• chainComplex -- make a chain complex
• ChainComplexMap -- the class of all maps between chain complexes
• changeBase -- change integer base
• ChangeMatrix -- an optional argument
• char -- computes the characteristic of the ring or field
• characters -- get characters from a string
• check -- perform tests of a package
• checkDegrees -- compares the degrees of generators of two modules
• CheckDocumentation -- an optional argument
• chi
• class -- class of an object
• clean -- Set to zero elements that are approximately zero
• clearAll -- forget everything
• clearEcho -- turn off echoing
• clearOutput -- forget output values
• close -- close a file
• closeIn -- close an input file
• closeOut -- close an output file
• ClosestFit -- an optional argument
• code -- display source code
• codim -- compute the codimension
• CodimensionLimit -- an optional argument
• coefficient -- coefficient of a monomial
• CoefficientRing -- an optional argument
• coefficientRing -- get the coefficient ring
• coefficients -- monomials and their coefficients
• Cofactor
• CohenEngine -- use the original Macaulay2 LLL algorithm
• CohenTopLevel -- use the Macaulay2 language LLL algorithm
• CoherentSheaf -- the class of all coherent sheaves
• cohomology -- general cohomology functor
• coimage -- coimage of a map
• cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
• collectGarbage -- collect the garbage in memory
• columnAdd -- add a multiple of one column to another
• columnate -- arrange strings in columns
• columnMult -- multiply a column by a ring element
• columnPermute -- permute some columns
• columnRankProfile -- find the column rank profile of a mutable matrix
• columnSwap -- interchange columns
• combine -- combine hash tables
• Command -- the class of all commands
• commandInterpreter -- the top level command interpreter
• commandLine -- the command line arguments
• commonest -- the most common elements of a list or tally
• commonRing -- find smallest containing ring
• comodule -- submodule to quotient module
• compareExchange -- compares and possibly exchanges the value of an atomic integer
• CompiledFunction -- the class of all compiled functions
• CompiledFunctionBody -- the class of all compiled function bodies
• CompiledFunctionClosure -- the class of all compiled function closures
• Complement -- a Strategy option value
• complement -- see complement(Matrix) -- find the minimal generators for cokernel of a matrix (low level form)
• complete
• CompleteIntersection -- value of an optional argument
• ComplexField -- the class of all complex fields
• components -- list the components of a direct sum
• compose -- composition as a pairing on Hom-modules
• compositions -- list the compositions of an integer
• compress -- extract nonzero columns from a matrix
• concatenate -- join strings
• conductor -- the conductor of a finite ring map
• ConductorElement -- Specifies a particular non-zerodivisor in the conductor.
• cone -- mapping cone or polyhedral cone
• Configuration -- an optional argument
• conjugate -- complex conjugate
• connectionCount -- the number of connections
• Consequences -- side-effects of a function in a documentation node
• Constant
• Constants -- an optional argument
• content -- the content of a polynomial
• continue -- continue with the next iteration of a loop
• contract -- contract one matrix by another
• contract' -- see contract'(Matrix,Matrix) -- contract a matrix by a matrix, the dual notion
• Contributors -- non-author contributors listed in a documentation node
• conwayPolynomial -- provide a Conway polynomial
• copy -- copy an object
• copyDirectory -- see copyDirectory(String,String)
• copyFile -- see copyFile(String,String)
• copyright -- a string containing the copyright notice for Macaulay2
• cos -- compute the cosine
• cosh -- compute the hyperbolic cosine
• cot -- cotangent
• cotangentSheaf -- cotangent sheaf of a projective variety
• coth -- hyperbolic cotangent
• cover -- get the covering free module
• coverMap -- see coverMap(Module) -- the surjective map from a free module to a module corresponding to the generators
• cpuTime -- seconds of cpu time used since Macaulay2 began
• createTask -- create a task
• csc -- cosecant
• csch -- hyperbolic cosecant
• currentColumnNumber -- current column number of the current input file
• currentDirectory -- current working directory
• currentFileDirectory -- the directory containing the current input file
• currentFileName -- the current source file
• Layout -- see currentLayout -- relative locations of Macaulay2 files
• currentPosition -- the current position in the current source file
• currentRowNumber -- current row number of the current input file
• currentTime -- get the current time
• Database -- the class of all database files
• Date -- an optional argument
• dd -- differential in a chain complex
• debug -- open the private dictionary of a package
• DebuggingMode -- an optional argument
• Decompose -- value of an optional argument
• decompose
• deepSplice -- remove all levels of subsequences from a sequence or list
• Default -- value of an optional argument
• default -- default member of a family
• Degree -- specify the degree of a map
• degree
• DegreeGroup -- an optional argument
• degreeGroup (missing documentation)
• degreeLength -- the length of the degree vector
• DegreeLift -- an optional argument
• DegreeLimit -- an optional argument
• DegreeMap -- an optional argument
• DegreeOrder -- sort primarily by degree
• DegreeRank -- an optional argument
• Degrees -- an optional argument
• degrees -- degrees of generators
• degreesMonoid -- see degreesRing -- the ring or monoid of degrees
• degreesRing -- the ring or monoid of degrees
• delete -- delete some elements of a list
• demark -- insert a string between elements of a list of strings
• denominator -- denominator of a fraction
• Dense -- an optional argument
• Density -- an optional argument
• depth -- depth of a net
• Descending -- specify descending order
• Descent
• Describe -- the class of the output of describe
• describe -- real description
• determinant -- determinant of a matrix
• diagonalMatrix -- make a diagonal matrix
• diameter -- diameter of an interval
• Dictionary -- the class of all dictionaries
• dictionary -- determine the dictionary to which a symbol belongs
• diff -- differentiate or take difference
• diff' -- see diff'(Matrix,Matrix) -- differentiate a matrix by a matrix, the dual notion
• difference -- difference
• Digamma -- Digamma function
• dim -- compute the Krull dimension
• DirectSum (missing documentation)
• directSum -- direct sum of modules or maps
• disassemble -- disassemble pseudocode or a function
• discriminant -- see discriminant(RingElement,RingElement)
• dismiss -- dismiss a package
• distinguished -- Compute the distinguished subvarieties of a pullback, intersection or cone
• Divide -- the class of all divide expressions
• divideByVariable -- divide all columns by a (power of a) variable
• DivideConquer -- an optional argument
• DividedPowers -- Option for inverseSystem
• do -- loop control
• doc -- a simple documentation function
• docTemplate -- see doc -- a simple documentation function
• multidoc -- see doc -- a simple documentation function
• docExample -- an example of a documentation string
• document -- create a documentation node
• DocumentTag -- the class of all document tags
• makeDocumentTag -- see DocumentTag -- the class of all document tags
• drop -- drop some elements from a list or sequence.
• dual -- dual module or map
• Dynamic
• eagonNorthcott -- see eagonNorthcott(Matrix) -- Eagon-Northcott complex of a matrix of linear forms
• echoOff -- turn off echoing
• echoOn -- turn on echoing
• edit -- edit source code
• effCone (missing documentation)
• effGenerators (missing documentation)
• eigenvalues -- find eigenvalues of a matrix
• eigenvectors -- find eigenvectors of a matrix over RR or CC
• eint -- exponential integral
• elapsedTime -- time a computation using time elapsed
• elapsedTiming -- time a computation using time elapsed
• elements -- list of elements
• Eliminate -- elimination order
• eliminate
• else -- condition testing
• End -- module of endomorphisms
• end -- stop loading a file
• endl -- end an output line
• endPackage -- end a new package
• Engine -- specify whether a ring is handled by the engine
• EngineRing -- the class of rings handled by the engine
• entries -- lists the entries of a matrix
• environment -- the environment variables
• Equation -- the class of all equation expressions
• erase -- remove a global symbol
• erf -- error function
• erfc -- complementary error function
• error -- deliver error message
• euler -- Euler characteristic
• EulerConstant -- the Euler-Mascheroni constant
• eulers -- list the sectional Euler characteristics
• even -- tell whether an integer is even
• EXAMPLE -- hypertext EXAMPLE item
• ExampleFiles -- data files corresponding to a documentation node
• examples -- list the examples in documentation
• exchange -- exchange the value of an atomic integer
• Exclude -- an optional argument
• exec -- execute another program
• exit -- exit the program
• exp -- exponential function
• expectedReesIdeal -- symmetric algebra ideal plus jacobian dual
• expm1 -- exponential minus 1
• exponents -- the exponents of a polynomial
• export -- export symbols from a package
• exportFrom -- export symbols from a package's private dictionary
• exportMutable -- export mutable symbols from a package
• Expression -- the class of all expressions
• expression -- convert to an expression
• Ext -- compute an Ext module
• extend -- extend a module map to a chain map, if possible
• exteriorPower -- exterior power
• factor -- factor a ring element or a ZZ-module
• false
• Fano -- Fano scheme
• FastNonminimal -- compute a non-minimal graded free resolution
• File -- the class of all files
• fileDictionaries -- local dictionaries for loaded files
• fileExecutable
• fileExists -- whether a file exists
• fileLength -- the length of a file
• fileMode -- set or get file mode
• FileName -- an optional argument
• FilePosition -- the class of all file positions
• fileReadable
• fileTime -- get or set file modified time
• fileWritable
• fillMatrix -- fill a mutable matrix with random numbers
• findFiles -- find files recursively
• findHeft -- find a heft vector for a list of degrees
• FindOne -- find a primitive element
• findProgram -- load external program
• findSynonyms -- see findSynonyms(Symbol) -- find synonyms of symbols
• First -- an optional argument
• first -- first element of a list
• firstkey -- get the first key
• fittingIdeal -- Fitting ideal of a module
• flagLookup -- flag a symbol
• FlatMonoid
• flatten -- flatten a nested list or a matrix
• flattenRing -- write a ring as a (quotient of a) polynomial ring
• flip -- isomorphism map of commutativity of tensor product
• floor -- floor function
• flush -- flush output to file
• fold -- apply a binary operator repeatedly
• FollowLinks -- an optional argument
• for -- for loops
• forceGB -- declare that the columns of a matrix are a Gröbner basis
• fork -- fork the process
• format -- format a string or a real number
• formation -- recover the methods used to make a module
• fpLLL (missing documentation)
• frac -- construct a fraction field
• fraction
• FractionField -- the class of all fraction fields
• frames -- get the frames associated to a closure
• from -- loop control
• fromDividedPowers -- Translates from divided power monomial basis to ordinary monomial basis
• fromDual -- Ideal from inverse system
• Function -- the class of all functions
• FunctionApplication -- the class of all function application expressions
• FunctionBody -- the class of function bodies
• functionBody -- get the body of a function
• FunctionClosure -- the class of all function closures
• GaloisField -- the class of all Galois fields
• Gamma -- Gamma function
• gb -- compute a Gröbner basis
• Homogeneous2 -- see gb -- compute a Gröbner basis
• LinearAlgebra -- see gb -- compute a Gröbner basis
• Sugarless -- see gb -- compute a Gröbner basis
• Toric -- see gb -- compute a Gröbner basis
• UseSyzygies -- see gb -- compute a Gröbner basis
• GBDegrees -- an optional argument
• gbRemove -- remove Gröbner basis
• gbSnapshot -- the Gröbner basis matrix as so far computed
• gcd -- greatest common divisor
• gcdCoefficients -- gcd with coefficients
• gcdLLL -- compute the gcd of integers, and small multipliers
• GCstats -- information about the status of the garbage collector
• genera -- list of the successive linear sectional arithmetic genera
• GeneralOrderedMonoid -- the class of all ordered free commutative monoids
• generateAssertions -- generate assert statements from experimental input
• generator -- provide a single generator
• generators -- provide matrix or list of generators
• Generic -- an optional argument
• genericMatrix -- make a generic matrix of variables
• genericSkewMatrix -- make a generic skew symmetric matrix of variables
• genericSymmetricMatrix -- make a generic symmetric matrix
• genus -- arithmetic genus
• get -- get the contents of a file
• getc -- get a byte
• getChangeMatrix -- get the change of basis matrix
• getenv -- get value of environment variable
• getGlobalSymbol -- create a global symbol in a global dictionary
• getNetFile -- get the sequence of completed lines (nets) from a net file
• getNonUnit -- retrieve a previously discovered non-unit
• getPrimeWithRootOfUnity -- find a prime p with a primitive n-th root of unity r in ZZ/p
• getSymbol -- make a global user symbol from a string
• getWWW -- get a web page
• GF -- make a finite field
• Givens -- use Givens rotations instead of Gram-Schmidt during LLL
• GLex -- graded lexicographic ordering
• global -- get a global symbol
• globalAssign -- global assignment, in function form
• globalAssignFunction -- the standard method for the global assignment hook
• GlobalAssignHook -- hook for assignment to global variables
• globalAssignment -- install standard global assignment method
• globalAssignmentHooks -- assignment hooks for global symbols
• GlobalDictionary -- the class of all global dictionaries
• globalReleaseFunction -- the standard method for the global variable release hook
• GlobalReleaseHook
• GlobalSectionLimit (missing documentation)
• Gorenstein -- Constructing Gorenstein Rings and Modules
• GradedModule -- the class of all graded modules
• gradedModule -- make a graded module
• GradedModuleMap -- the class of all maps between graded modules
• gradedModuleMap -- make a map of graded modules
• gramm (missing documentation)
• graphIdeal -- see graphIdeal(RingMap) -- the ideal of the graph of the regular map corresponding to a ring map
• graphRing -- see graphRing(RingMap) -- the coordinate ring of the graph of the regular map corresponding to a ring map
• Grassmannian -- see Grassmannian(ZZ,ZZ) -- the Grassmannian of linear subspaces of a vector space
• GRevLex -- graded reverse lexicographical monomial order.
• GroebnerBasis -- the class of all Gröbner bases
• groebnerBasis -- Gröbner basis, as a matrix
• GroebnerBasisOptions
• groupID -- the process group identifier
• GroupLex -- defines a ring where some variables are inverted
• GroupRevLex
• HardDegreeLimit -- compute only up to this degree
• hash -- hash code of an object
• HashTable -- the class of all hash tables
• hashTable -- make a hash table
• HeaderType -- a class of lists with abbreviated constructors
• Headline -- headline of a documentation node
• Heft -- an optional argument
• heft -- heft vector of ring or monoid
• Height -- an optional argument
• height -- height of a net
• help -- view documentation nodes
• Hermite (missing documentation)
• hermite (missing documentation)
• Hermitian -- an optional argument
• HH -- general homology and cohomology functor
• hh -- Hodge numbers of a smooth projective variety
• Hilbert -- an optional argument
• hilbertFunction -- the Hilbert function
• hilbertPolynomial -- compute the Hilbert polynomial
• hilbertSeries -- compute the Hilbert series
• hold -- hold something in a holder expression
• Holder -- the class of all holder expressions
• Hom -- module of homomorphisms
• Homogeneous -- a Strategy option value
• homogenize -- homogenize with respect to a variable
• homology -- general homology functor
• homomorphism -- get the homomorphism from element of Hom
• homomorphism' -- get the element of Hom from a homomorphism
• hooks -- list hooks attached to a key
• horizontalJoin -- join nets or strings horizontally
• HorizontalSpace -- an optional argument
• html -- convert to HTML format
• httpHeaders -- see httpHeaders(String) -- prepend http headers to a string
• Hybrid -- the class of lists encapsulating hybrid strategies
• hypertext -- prepare hypertext for display
• icFracP -- compute the integral closure in prime characteristic
• icFractions -- fractions integral over an affine domain
• icMap -- natural map from an affine domain into its integral closure
• icPIdeal -- compute the integral closure in prime characteristic of a principal ideal
• id -- identity map
• Ideal -- the class of all ideals
• ideal -- make an ideal
• idealizer -- compute Hom(I,I) as a quotient ring
• identity -- the identity function
• if -- condition testing
• IgnoreExampleErrors -- an optional argument
• ii -- the square root of -1
• image -- image of a map
• imaginaryPart -- imaginary part
• ImmutableType -- the class of immutable types
• importFrom -- import symbols to the current private dictionary
• in -- a keyword used in for-loops
• incomparable -- a result indicating incomparability
• independentSets -- some size-maximal independent subsets of variables modulo an ideal
• indeterminate -- an indeterminate number
• IndeterminateNumber -- the class of all indeterminate numbers
• Index -- Optional input for idealizer
• index -- numeric index of a ring variable
• indexComponents -- specify keys for components of a direct sum
• IndexedVariable -- the class of all indexed variables
• IndexedVariableTable
• indices -- indices of a polynomial; also components for a direct sum
• inducedMap -- compute an induced map
• inducesWellDefinedMap -- whether a map is well defined
• InexactField -- the class of inexact fields
• InexactFieldFamily -- the class of all families of inexact fields
• InexactNumber
• InexactNumber'
• InfiniteNumber -- the class of all infinite numbers
• infinity -- infinity
• info -- convert hypertext to info format
• InfoDirSection -- an optional argument
• infoHelp -- view documentation in Info format
• Inhomogeneous -- a Strategy option value
• input -- read Macaulay2 commands and echo
• Inputs -- inputs for a function in a documentation node
• insert -- copy a list, inserting an element
• installAssignmentMethod -- install methods assignment to the value of an operator
• installedPackages
• installMethod -- install methods
• installPackage -- load and install a package and its documentation
• InstallPrefix -- an optional argument
• instance -- whether something has a certain type
• instances -- see instances(Type)
• integralClosure -- integral closure of an ideal or a domain
• integrate -- numerical integration
• intersect -- compute an intersection
• intersectInP -- Compute distinguished varieties for an intersection in A^n or P^n
• Intersection -- value of an optional argument
• intersection -- compute an intersection
• interval -- construct an interval
• inverse -- compute the inverse
• inverseErf -- inverse error function
• InverseMethod -- compute reciprocals
• inversePermutation -- inverse permutation
• inverseRegularizedBeta -- inverse of the regularized beta function
• inverseRegularizedGamma -- inverse of the upper regularized gamma function
• Inverses -- an optional argument
• inverseSystem -- Inverse systems with equivariance
• Invertible -- an optional argument
• irreducibleCharacteristicSeries -- irreducible characteristic series of an ideal
• irreducibleDecomposition -- express a monomial ideal as an intersection of irreducible monomial ideals
• isAffineRing -- whether something is an affine ring
• isANumber -- whether a number is not not-a-number
• isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
• isc -- ISC lookup
• isCanceled -- see isCanceled(Task) -- whether a task has been canceled
• isCommutative -- whether a ring is commutative
• isConstant -- whether a ring element is constant
• isDirectory -- whether a file is a directory
• isDirectSum -- whether something is a direct sum
• isEmpty
• isField -- whether something is a field
• isFinite -- whether a number is finite
• isFinitePrimeField -- whether a ring is a finite prime field
• isFreeModule -- whether something is a free module
• isGlobalSymbol -- whether a global symbol with a given name exists
• isHomogeneous -- whether something is homogeneous (graded)
• isIdeal -- whether something is an ideal
• isInfinite -- whether a number is infinite
• isInjective -- whether a map is injective
• isInputFile -- see isInputFile(File) -- whether a file is open for input
• isIsomorphic -- Probabilistic test for isomorphism of modules
• isIsomorphism -- whether a map is an isomorphism
• isLiftable (missing documentation)
• isLinearType -- Determine whether module has linear type
• isListener -- see isListener(File) -- whether a file is open for listening
• isLLL -- is a basis an LLL basis?
• isMember -- test membership in a list or set
• isModule -- whether something is a module
• isMonomialIdeal -- whether something is a monomial ideal
• isMutable -- whether something may be modified
• isNormal -- determine if a reduced ring is normal
• isOpen -- whether a file or database is open
• isOutputFile -- see isOutputFile(File) -- whether a file is open for output
• isPolynomialRing -- whether something is a polynomial ring
• isPrimary -- determine whether a submodule is primary
• isPrime -- whether a integer or polynomial is prime
• isPrimitive -- whether an element is a primitive element of a finite field
• isProjective (missing documentation)
• isPseudoprime -- see isPseudoprime(ZZ) -- whether an integer is probably prime
• isQuotientModule -- whether something is evidently a quotient of a free module
• isQuotientOf -- whether one thing is a quotient of another
• isQuotientRing -- whether something is a quotient ring
• isReady -- see isReady(File) -- whether a file has data available for reading
• isReal -- whether a number is real
• isReduction -- Determine whether an ideal is a reduction
• isRegularFile -- whether a file is a regular file
• isRing -- whether something is a ring
• isSkewCommutative -- whether a ring has skew commuting variables
• isSorted -- whether a list is sorted
• isSquareFree -- whether something is square free monomial ideal
• isStandardGradedPolynomialRing -- Checks whether a ring is a polynomial ring over a field with variables of degree 1
• isSubmodule -- whether a module is evidently a submodule of a free module
• isSubquotient -- see isSubquotient(Module,Module) -- check whether a module is a subquotient of another
• isSubset -- whether one object is a subset of another
• isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
• isSurjective -- whether a map is surjective
• isTable -- whether something is a list of lists of equal length
• isUnit -- whether a ring element is a unit
• isWellDefined -- whether a map is well defined
• Iterate -- value of an optional argument
• Iterator -- class for iterators
• iterator -- get an iterator
• Jacobian
• jacobian -- the Jacobian matrix of partial derivatives
• jacobianDual -- Computes the 'jacobian dual', part of a method of finding generators for Rees Algebra ideals
• Join -- an optional argument
• join -- join lists, sequences, and iterable objects
• Jupyter -- top level printing method used in the Jupyter kernel
• Keep -- an optional argument for various functions
• KeepFiles -- whether to keep temporary files
• KeepZeroes -- an optional argument
• kernel -- kernel of a ringmap, matrix, or chain complex
• kernelLLL (missing documentation)
• kernelOfLocalization -- the kernel of the localization map
• Key -- key of a documentation node
• keys -- keys used in a hash table, dictionary, or database
• Keyword -- the class of all keywords
• Keywords -- an optional argument
• kill -- kill a process
• koszul -- Koszul complex or specific matrix in the Koszul complex
• last -- last element of a list
• lcm -- least common multiple
• leadCoefficient -- the coefficient of the leading term
• leadComponent -- the leading component(s) of a vector or matrix
• leadMonomial -- the leading monomial of a ring element
• leadTerm -- get the greatest term
• Left -- value of an optional argument
• left -- left endpoint of an interval
• length -- length of an object
• LengthLimit -- stop when the resolution reaches this length
• Lex -- lexicographical monomial order.
• lift -- lift to another ring
• liftable -- whether lifting to another ring is possible
• Limit -- an optional argument
• limitFiles
• limitProcesses
• Linear -- value of an optional argument
• lines -- split a string into lines
• linkFile -- see linkFile(String,String) -- make a new link to a file
• List -- the class of all lists -- {...}
• list -- loop control
• listForm -- convert to list form
• listLocalSymbols -- display of local symbols and their values
• listSymbols -- compact display of symbols and their values
• listUserSymbols -- display the user's symbols
• LLL -- compute an LLL basis
• lngamma -- logarithm of the Gamma function
• load -- read Macaulay2 commands
• LoadDocumentation -- an optional argument
• loadedFiles
• loadPackage -- load a package
• Local -- an optional argument
• local -- get a local symbol
• localDictionaries -- get local dictionaries
• LocalDictionary -- the class of all local dictionaries
• localize -- localize an ideal at a prime ideal
• locate -- locate source code
• log -- logarithm function
• log1p -- logarithm of 1+x
• LongPolynomial -- a Strategy option value
• lookup -- look up methods
• lookupCount -- reference count for a symbol
• LowerBound -- the class of lower bound objects
• LUdecomposition -- LU decomposition
• makeDirectory -- see makeDirectory(String) -- make a directory
• MakeDocumentation -- an optional argument
• MakeHTML -- an optional argument
• MakeInfo -- an optional argument
• MakeLinks -- an optional argument
• makePackageIndex -- create an index of installed packages
• MakePDF -- an optional argument
• makeS2 -- compute the S2ification of a reduced ring
• Manipulator -- the class of all file manipulators
• map -- make a map
• MapExpression -- the class of map expressions
• markedGB -- see markedGB(Matrix,Matrix) -- make a marked Gröbner basis
• match -- regular expression matching
• mathML -- convert to MathML format
• Matrix -- the class of all matrices
• matrix -- make a matrix
• MatrixExpression -- the class of all matrix expressions
• max -- yields the maximum element in a list or sequence
• maxAllowableThreads -- the maximum possible number of simultaneously running tasks
• maxExponent
• MaximalRank -- an optional argument
• maxPosition -- position of the largest element
• MaxReductionCount -- an optional argument
• memoize -- record results of function evaluation for future use
• memoizeClear -- see memoize -- record results of function evaluation for future use
• memoizeValues -- see memoize -- record results of function evaluation for future use
• merge -- merge two hash tables
• mergePairs -- merge sorted lists of pairs
• Dispatch -- see method -- make a new method function
• method -- make a new method function
• TypicalValue -- see method -- make a new method function
• MethodFunction -- a type of method function
• MethodFunctionBinary -- a type of method function
• MethodFunctionSingle -- a type of method function
• MethodFunctionWithOptions -- a type of method function
• methodOptions -- see methodOptions(Function) -- recover the options used when a method function was created
• methods -- list methods
• midpoint -- midpoint of an interval
• min -- yields the minimum element in a list or sequence
• minExponent
• mingens -- minimal generator matrix
• mingle -- mingle elements of several lists
• minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• MinimalGenerators -- whether to compute minimal generators and return a trimmed set of generators
• MinimalMatrix -- an optional argument
• minimalPresentation -- compute a minimal presentation
• minimalPresentationMap -- see minimalPresentation(Ring) -- compute a minimal presentation of a quotient ring
• minimalPresentationMapInv -- see minimalPresentation(Ring) -- compute a minimal presentation of a quotient ring
• minimalPrimes -- minimal primes of an ideal
• minimalReduction -- Find a minimal reduction of an ideal
• Tries -- see minimalReduction(...,Tries=>...) -- Set the number of random tries to compute a minimal reduction
• Minimize -- an optional argument
• minimize
• minimizeFilename -- minimize a file name
• MinimumVersion -- the minimum required version of a program
• minors -- see minors(ZZ,Matrix) -- ideal generated by minors
• minPosition -- position of the smallest element
• Minus -- the class of all minus expressions
• minus -- additive inverse
• mkdir
• mod -- reduce modulo an integer
• Module -- the class of all modules
• module -- make or get a module
• modulo -- see modulo(Matrix,Matrix) -- find the pre-image (pullback) of image of a map (low level version)
• Monoid -- the class of all monoids
• monoid -- make or retrieve a monoid
• WeylAlgebra -- see monoid(...,WeylAlgebra=>...) -- specify differential operators in the ring
• MonoidElement -- the class of all monoid elements
• Monomial -- value of an optional argument
• monomialCurveIdeal -- make the ideal of a monomial curve
• MonomialIdeal -- the class of all monomial ideals handled by the engine
• monomialIdeal -- make a monomial ideal
• Down -- see MonomialOrder -- monomial ordering
• Global -- see MonomialOrder -- monomial ordering
• MonomialOrder -- monomial ordering
• Position -- see MonomialOrder -- monomial ordering
• Up -- see MonomialOrder -- monomial ordering
• Monomials -- whether to display the number of monomial
• monomials -- matrix of monomials in a ring element or matrix
• MonomialSize -- an optional argument
• monomialSubideal -- find the largest monomial ideal in an ideal
• moveFile -- see moveFile(String,String)
• multidegree -- multidegree
• multigraded -- convert a Betti tally into a multigraded Betti tally
• MultigradedBettiTally -- the class of all multigraded Betti tallies
• multiplicity -- Compute the Hilbert-Samuel multiplicity of an ideal
• MutableHashTable -- the class of all mutable hash tables
• mutableIdentity -- see mutableIdentity(Ring,ZZ) -- make a mutable identity matrix
• MutableList -- the class of all mutable lists
• MutableMatrix -- the class of all mutable matrices
• mutableMatrix -- make a mutable matrix
• nanosleep -- sleep for a given number of nanoseconds
• NCLex -- Non-commutative lexicographical order.
• needs -- read Macaulay2 commands if necessary
• needsPackage -- load a package if not already loaded
• nefCone (missing documentation)
• nefGenerators (missing documentation)
• Net -- the class of all nets and strings
• net -- format for printing, as a net
• NetFile -- the class of all net files
• netList -- see netList(VisibleList) -- a table of boxes
• new -- new objects and new types
• newClass -- set the class and parent of an object
• newCoordinateSystem -- change variables
• NewFromMethod
• newline -- the new line character sequence
• NewMethod
• newNetFile -- create a new net file
• NewOfFromMethod
• NewOfMethod
• Email -- see newPackage -- the preamble of a package
• HomePage -- see newPackage -- the preamble of a package
• Name -- see newPackage -- the preamble of a package
• newPackage -- the preamble of a package
• newRing -- make a copy of a ring, with some features changed
• next -- get the next object from an iterator
• nextkey -- the next key in a database
• nextPrime -- compute the smallest prime greater than or equal to a given number
• NoPrint -- top level method for non-printing results
• norm
• normalCone -- The normal cone of a subscheme
• not -- negation
• Nothing -- the empty class
• notImplemented -- print an 'not implemented' error message
• NTL -- use the all-integer LLL strategy from NTL library
• null -- the unique member of the empty class
• nullaryMethods
• nullhomotopy -- make a null homotopy
• nullSpace -- find the null space of a mutable matrix
• Number -- the class of all numbers
• number -- count how many elements of a list satisfy a condition
• NumberedVerticalList -- a type of visible self-initializing list that prints vertically
• numColumns -- see numColumns(Matrix) -- number of columns in a matrix or mutable matrix
• numerator -- numerator of a fraction
• numeric -- convert to floating point
• numericInterval -- converts to an interval
• numgens -- the number of generators
• numRows -- see numRows(Matrix) -- number of rows in a matrix or mutable matrix
• odd -- tell whether an integer is odd
• oeis -- OEIS lookup
• of -- a keyword
• ofClass -- English phrases for types
• CallLimit -- see on -- trace a function each time it's run
• GenerateAssertions -- see on -- trace a function each time it's run
• on -- trace a function each time it's run
• OneExpression -- the class all one expressions
• OO -- the structure sheaf
• openDatabase -- open a database file
• openDatabaseOut -- open a database file for writing
• openFiles -- list the open files
• openIn -- see openIn(String) -- open an input file
• openInOut -- open an input output file
• openListener -- see openListener(String) -- open a port for listening
• openOut -- see openOut(String) -- open an output file
• openOutAppend -- see openOutAppend(String) -- open an output file for appending
• Binary -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
• Flexible -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
• operatorAttributes -- a hashtable with information about Macaulay2 operators
• Postfix -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
• Prefix -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
• Option -- the class of all key-value pairs K => V
• OptionalComponentsPresent -- an optional argument
• Options -- an optional argument
• options -- get options
• OptionTable -- the class of hash tables for optional arguments
• or -- disjunction
• Order -- specify the order of a Hilbert series required
• order -- a key used internally
• OrderedMonoid -- the class of all ordered monoids
• Outputs -- outputs for a function in a documentation node
• override -- override default values for optional arguments
• pack -- pack elements of a list or string into several shorter lists or strings
• Package -- the class of all packages
• package -- get containing package
• PackageDictionary -- the dictionary for names of packages
• PackageExports -- an optional argument
• PackageImports -- an optional argument
• packageTemplate -- a template for a package
• pad -- pad a string or net with spaces
• pager -- display with paging
• PairLimit -- an optional argument
• pairs -- list the pairs in a hash table, dictionary, or basic list
• PairsRemaining -- whether to display the number of S-pairs remaining
• ParallelF4 (missing documentation)
• ParallelizeByDegree -- see parallelism in engine computations -- parallelism in engine computations
• parent -- parent type of an object
• Parenthesize
• part -- select terms of a polynomial by degree(s) or weight(s)
• Partition -- a type of list representing a partition of a natural number
• partition -- partition a set or list by values of a function
• partitions -- list the partitions of an integer
• parts -- display terms of a polynomial degree by degree
• pdim -- calculate the projective dimension
• peek -- examine contents of an object
• peek' -- examine contents of an object
• permanents -- ideal generated by square permanents of a matrix
• permutations -- produce all permutations of a list
• pfaffians -- ideal generated by Pfaffians
• pi
• pivots -- see pivots(Matrix) -- list of pivot locations of a matrix
• PlaneCurveSingularities -- Using the Rees Algebra to resolve plane curve singularities
• plus -- addition
• installHilbertFunction -- see poincare -- assemble degrees of a ring, module, or ideal into a polynomial
• poincare -- assemble degrees of a ring, module, or ideal into a polynomial
• poincareN -- assemble degrees into polynomial
• polarize -- given a monomial ideal, computes the squarefree monomial ideal obtained via polarization
• poly -- see poly(String) -- make a polynomial using classic Macaulay syntax
• PolynomialRing -- the class of all ordered monoid rings
• position -- the first element of a list satisfying a condition
• positions -- which elements of a list satisfy a condition
• Power -- the class of all power expressions
• power -- power
• powermod -- powers of integers mod N
• Precision -- name of an optional argument.
• precision
• preimage -- preimage of a map
• prepend -- add an element to the beginning of a list
• presentation -- presentation of a module or ring
• pretty -- a pretty printer
• Increment -- see primaryComponent -- find a primary component corresponding to an associated prime
• primaryComponent -- find a primary component corresponding to an associated prime
• primaryDecomposition -- irredundant primary decomposition of an ideal
• PrimitiveElement -- specify a primitive element
• Print -- top level method for printing results
• print -- print something
• printerr -- print something to stderr
• printingTimeLimit
• printString -- lowlevel function to print a string, net, or symbol
• processID -- the process identifier
• Product -- the class of all product expressions
• product
• ProductOrder -- product ordering
• profile -- profile a function
• profileSummary -- display profiling data
• Program -- external program object
• programPaths -- user-defined external program paths
• ProgramRun -- result of running an external program
• Proj -- make a projective variety
• Projective -- whether to produce a projective Hilbert polynomial
• ProjectiveHilbertPolynomial -- the class of all Hilbert polynomials
• projectiveHilbertPolynomial -- Hilbert polynomial of projective space
• ProjectiveVariety -- the class of all projective varieties
• promote -- promote to another ring
• protect -- protect a symbol
• Prune -- value of an optional argument
• prune -- prune, e.g., compute a minimal presentation
• pruningMap
• Pseudocode -- the class of pseudocodes
• pseudocode -- produce the pseudocode for a function
• pseudoRemainder -- compute the pseudo-remainder
• pullback -- compute the pullback morphism
• pullbackMaps (missing documentation)
• pushForward -- see pushForward(RingMap,Module)
• pushout -- compute the pushout morphism
• pushoutMaps (missing documentation)
• QQ -- the class of all rational numbers
• QRDecomposition -- compute a QR decomposition of a real matrix
• quit -- quit the program
• Quotient -- value of an optional argument
• quotient -- quotient or division
• quotient' -- matrix quotient (opposite)
• quotientRemainder -- matrix quotient and remainder
• quotientRemainder' -- matrix quotient and remainder (opposite)
• QuotientRing -- the class of all quotient rings
• Radical -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• radical -- the radical of an ideal
• RadicalCodim1 -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• radicalContainment -- whether an element is contained in the radical of an ideal
• RaiseError -- whether to raise an error
• random -- get a random object
• randomKRationalPoint -- Pick a random K rational point on the scheme X defined by I
• randomMutableMatrix -- see randomMutableMatrix(ZZ,ZZ,RR,ZZ) -- a random mutable matrix of integers
• Range -- can be assigned a integral interval
• rank -- compute the rank
• rays -- 1-dimensional cones of a fan or polyhedral object
• read -- read from a file
• readDirectory -- read the contents of a directory
• readlink -- readlink fn
• readPackage -- read the package preamble
• RealField -- the class of all real fields
• RealFP -- use double precision real numbers
• realPart -- real part
• realpath -- convert a filename to one passing through no symbolic links
• RealQP -- use quadruple precision real numbers
• RealQP1 -- use a combination of double precision and quad precision real numbers
• RealRR -- use arbitrary precision real numbers
• RealXD -- use extended exponent real numbers
• recursionDepth -- the current recursion depth
• Reduce -- an optional argument
• reducedRowEchelonForm -- compute the reduced row echelon form of a matrix or mutable matrix over a field
• reduceHilbert -- reduce a Hilbert series expression
• reductionNumber -- Reduction number of one ideal with respect to another
• reesAlgebra -- Compute the defining ideal of the Rees Algebra
• reesIdeal -- Compute the defining ideal of the Rees Algebra
• References -- references listed in a documentation node
• POSIX -- see regex -- evaluate a regular expression search
• regex -- evaluate a regular expression search
• regexQuote -- escape special characters in regular expressions
• registerFinalizer -- register a string that will be displayed when an object is garbage collected
• regSeqInIdeal -- a regular sequence contained in an ideal
• regularity -- compute the Castelnuovo-Mumford regularity
• regularizedBeta -- regularized beta function
• regularizedGamma -- upper regularized gamma function
• relations -- the defining relations
• relativizeFilename -- relativize a file name
• Reload -- an optional argument
• remainder -- matrix remainder
• remainder' -- matrix quotient and remainder (opposite)
• RemakeAllDocumentation -- an optional argument
• remove -- remove an entry from a mutable hash table, list, or database
• removeDirectory -- remove a directory
• removeFile -- remove a file
• removeLowestDimension -- remove components of lowest dimension
• reorganize -- reorganize a database file
• replace -- replacement in strings and lists
• RerunExamples -- an optional argument
• reshape -- reshape a matrix
• Resolution -- the class of all resolution computations
• resolution -- projective resolution
• restart -- restart Macaulay2
• Result -- an optional argument
• resultant -- see resultant(RingElement,RingElement,RingElement)
• return -- return from a function
• returnCode
• Reverse -- an optional argument
• reverse -- reverse a list, sequence, or string
• RevLex -- reverse lexicographic ordering
• Right -- value of an optional argument
• right -- right endpoint of an interval
• Ring -- the class of all rings
• ring -- get the associated ring of an object
• RingElement -- the class of all ring elements handled by the engine
• RingFamily
• ringFromFractions -- find presentation for f.g. ring
• RingMap -- the class of all ring maps
• rootPath
• roots -- see roots(RingElement) -- compute the roots of a polynomial
• rootURI
• rotate -- see rotate(ZZ,VisibleList) -- rotate a list
• round -- round a number
• rowAdd -- add a multiple of one row to another
• RowExpression -- the class of all matrix expressions
• rowMult -- multiply a row by a ring element
• rowPermute -- permute some rows
• rowRankProfile -- find the row rank profile of a mutable matrix
• rowSwap -- interchange rows
• RR -- the class of all real numbers
• RR' -- the parent class of all rings of real numbers
• RRi -- the class of all real intervals
• rsort -- sort a list or matrix in reverse order
• run -- run an external command
• RunDirectory -- the directory from which to run a program
• RunExamples -- an optional argument
• runHooks -- run the hook functions stored in an object
• runLengthEncode -- see runLengthEncode(VisibleList) -- run length encoding
• runProgram -- run an external program
• same -- whether everything in a list is the same
• saturate -- saturation of ideal or submodule
• SaturationMap (missing documentation)
• scan -- apply a function to each element in a list or sequence
• scanKeys -- apply a function to each key in a hash table or database
• scanLines -- apply a function to each line of a file
• scanPairs -- apply a function to the pairs in a hash table
• scanValues -- apply a function to each value in a hash table or database
• schedule -- schedule a task for execution
• schreyerOrder -- create or obtain free modules with Schreyer monomial orders
• Schubert -- see Schubert(ZZ,ZZ,VisibleList) -- find the Plücker ideal of a Schubert variety
• ScriptedFunctor -- the class of all scripted functors
• searchPath -- see searchPath(List,String) -- search a path for a file
• sec -- secant
• sech -- hyperbolic secant
• SeeAlso -- cross-references to other documentation nodes
• seeParsing -- display parsing precedence table for Macaulay2 operators
• select -- select from a list, hash table, or string
• selectInSubring -- select columns in a subring
• selectVariables -- see selectVariables(List,PolynomialRing) -- make a subring of a polynomial ring generated by selected variables
• SelfInitializingType -- the class of all self initializing types
• separate -- split a string into substrings using a regular expression
• separateRegexp -- see separate -- split a string into substrings using a regular expression
• SeparateExec -- an optional argument
• Sequence -- the class of all sequences -- (...)
• sequence -- make a sequence
• serialNumber -- serial number of a dictionary, task, symbol, mutable hash table, or mutable list,
• Set -- the class of all sets
• set -- make a set
• setEcho -- turn on echoing
• setGroupID -- set the process group identifier
• setIOExclusive -- exclusive I/O for the current thread
• setIOSynchronized -- synchronized I/O for threads
• setIOUnSynchronized -- unsynchronized I/O for threads
• setRandomSeed -- set starting point for random number generator
• setup
• setupEmacs
• sheaf -- make a coherent sheaf
• SheafExpression -- the class of sheaf expressions
• sheafExt -- sheaf Ext of coherent sheaves
• sheafHom -- sheaf Hom
• SheafMap (missing documentation)
• sheafMap (missing documentation)
• SheafOfRings -- the class of sheaves of rings
• shield -- shield evaluation from interrupts
• show -- display various objects in an external viewer
• showHtml -- see show -- display various objects in an external viewer
• showTex -- see show -- display various objects in an external viewer
• showClassStructure -- display class structure
• showStructure -- display parent structure
• showUserStructure -- show parent structure for those types defined by user
• simpleDocFrob -- a sample documentation node
• SimplifyFractions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• sin -- compute the sine
• singularLocus -- singular locus
• sinh -- compute the hyperbolic sine
• size -- the size of an object
• size2 -- number of binary digits to the left of the point
• SizeLimit -- an optional argument
• SkewCommutative -- an optional argument
• sleep -- sleep for a while
• smithNormalForm -- see smithNormalForm(Matrix) -- smith normal form for a matrix over ZZ or a PID
• solve -- solve linear equation(s)
• someTerms -- select some terms of a polynomial
• Sort -- a Strategy option value
• sort -- sort a list or columns of a matrix
• sortColumns -- permutation giving sort order
• SortStrategy -- specify a strategy for sorting S-pairs
• source -- source of a map
• SourceCode -- sources displayed in a documentation node
• SourceRing -- an optional argument
• SPACE -- blank operator; often used for function application, making polynomial rings
• span -- construct smallest interval
• SparseMonomialVectorExpression -- the class of all sparse monomial vector expressions
• SparseVectorExpression -- the class of all sparse vector expressions
• Spec -- make an affine variety
• specialFiber -- Special fiber of a blowup
• specialFiberIdeal -- Special fiber of a blowup
• splice -- remove subsequences from a sequence or list
• splitWWW -- separate an http response into header and body
• sqrt -- square root function
• stack -- join nets or string vertically
• stacksProject -- link to a Stacks Project tag
• Standard -- the standard top level printing method
• standardForm -- convert to standard form
• standardPairs -- find the standard pairs of a monomial ideal
• StartWithOneMinor -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• stashValue -- stash values of functions in their arguments
• status -- status of a resolution computation
• stderr -- the standard error output file
• stdio -- the standard input output file
• step -- step by single lines in the debugger
• StopBeforeComputation -- an optional argument
• StopIteration -- stop iteration
• StopWithMinimalGenerators -- an optional argument
• store -- store the value of an atomic integer
• EisenbudHunekeVasconcelos -- see strategies for computing primary decomposition
• GTZ -- see strategies for computing primary decomposition
• ShimoyamaYokoyama -- see strategies for computing primary decomposition
• Strategy -- an optional argument
• Strict -- Forces strict equality of degrees
• String -- the class of all strings
• sublists -- process interspersed subsequences of a visible list
• submatrix
• submatrix' -- exclude rows and/or columns of a matrix
• submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
• Subnodes -- a menu of documentation nodes
• subquotient -- make a subquotient module
• SubringLimit -- stop after finding enough elements of a subring
• Subscript -- the class of all subscript expressions
• subscript -- specify the function in a scripted functor for a subscript
• subsets -- produce the subsets of a set or list
• substitute -- substituting values for variables
• substring -- extract part of a string
• subtable -- extract a subtable from a table
• Sum -- the class of all sum expressions
• sum -- compute the sum
• SumOfTwists -- the class of all sums of twists
• super -- get the ambient module
• Superscript -- the class of all superscript expressions
• superscript -- specify the function in a scripted functor for a superscript
• support -- list of variables occurring in a polynomial or matrix
• SVD -- singular value decomposition of a matrix
• switch -- copy a list, switching two elements
• sylvesterMatrix -- see sylvesterMatrix(RingElement,RingElement,RingElement)
• Symbol -- the class of all symbols
• symbol -- get a symbol
• SymbolBody -- see symbolBody -- symbol bodies
• symbolBody -- symbol bodies
• symlinkDirectory -- see symlinkDirectory(String,String) -- make symbolic links for all files in a directory tree
• symlinkFile -- make a symbolic link to a file
• symmetricAlgebra -- the symmetric algebra of a module
• symmetricAlgebraIdeal -- Ideal of the symmetric algebra of an ideal or module
• symmetricKernel -- Compute the Rees ring of the image of a matrix
• symmetricPower -- symmetric power
• synonym -- synonym for members of a class
• Heading -- see SYNOPSIS -- a standardized synopsis for use in documentation nodes
• SYNOPSIS -- a standardized synopsis for use in documentation nodes
• syz -- the syzygy matrix
• Syzygies -- an optional argument
• SyzygyLimit -- an optional argument
• SyzygyMatrix -- an optional argument
• SyzygyRows -- an optional argument
• syzygyScheme -- construct a syzygy scheme
• Table -- the class of all table expressions
• table -- make a table from a binary function
• take -- Take some elements from a list or sequence.
• Tally -- the class of all tally results
• tally -- tally the elements of a list, sequence, array, or string
• tan -- compute the tangent
• tangentCone -- see tangentCone(Ideal)
• tangentSheaf -- tangent sheaf of a projective variety
• tanh -- compute the hyperbolic tangent
• target -- target of a map
• Task -- the class of all tasks
• taskResult -- see taskResult(Task) -- retrieve the value returned by a task
• temporaryFileName -- make a temporary file name
• tensor -- tensor product
• tensorAssociativity -- associativity isomorphisms for tensor products
• TensorProduct (missing documentation)
• terms -- provide a list of terms of a polynomial
• TEST -- add a test for a package
• Test -- value of an optional argument
• testExample -- an example of a test string
• testHunekeQuestion -- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
• TestInput -- see tests -- locate a package's tests
• tests -- locate a package's tests
• tex -- convert to $\TeX$ format
• TeXmacs -- the TeXmacs top level printing method
• texMath -- convert to TeX math format
• then -- condition testing
• Thing -- the class of all things
• === -- see Thing === Thing -- strict equality
• threadVariable -- create a symbol whose value in one thread is not shared with others
• Threshold -- the LLL threshold, in interval (1/4,1]
• throw -- throw an exception
• Time -- the class of all timing results
• time -- time a computation
• times -- multiplication
• timing -- time a computation
• to -- loop control
• toAbsolutePath -- the absolute path version of a file name
• toCC -- convert to high-precision complex number
• toDividedPowers -- Translates to divided power monomial basis from ordinary monomial basis
• toDual -- finds the inverse system to an ideal up to a given degree
• toExternalString -- convert to a readable string
• toField -- see toField(Ring) -- declare that a ring is a field
• toList -- create a list
• toLower -- convert to lower case
• topCoefficients -- first variable and its coefficient of a polynomial or matrix
• topComponents -- compute top dimensional component of an ideal or module
• Tor -- Tor module
• toRR -- convert to high-precision real number
• toRRi -- construct an interval
• Torsion -- value of an optional argument
• TorsionFree (missing documentation)
• toSequence -- convert to sequence
• toString -- convert to a string
• TotalPairs -- whether to display the total number of S-pairs
• toUpper -- convert to upper case
• trace -- see trace(Matrix) -- trace of a matrix
• transpose -- transpose a table or a matrix
• Trim -- Choose whether to trim (or find minimal generators) for the ideal or module.
• trim -- minimize generators and relations
• true
• Truncate -- an optional argument
• truncate
• truncateOutput
• try -- catch an error
• tutorial -- convert documentation from tutorial format
• Type -- the class of all types
• typicalValues -- types of values returned by functions
• ultimate -- ultimate value for an iteration
• unbag -- see unbag(Bag)
• uncurry -- uncurry a function
• Undo -- an optional argument
• undocumented -- declare that something need not be documented
• uniform -- whether all elements of a list are the same class
• uninstallAllPackages
• uninstallPackage -- uninstall a package and remove its documentation
• Unique -- do not return repeated polynomial roots
• unique -- eliminate duplicates from a list
• uniquePermutations -- produce all unique permutations of a list
• Unmixed -- value of an optional argument
• unsequence -- extract the single element from a sequence of length 1
• unstack -- list the rows of a net
• UpdateOnly -- only copies of newer files should replace files
• UpperTriangular -- an optional argument
• URL -- a type representing a URL
• urlEncode -- URL encoding
• Usage -- ways to use a function in a documentation node
• use -- install or activate object
• UseCachedExampleOutput -- an optional argument
• UseHilbertFunction -- an optional argument
• UserMode -- an optional argument
• userSymbols -- a list of the user's symbols
• utf8 -- encode and decode unicode utf-8-encoded strings
• utf8check -- see utf8 -- encode and decode unicode utf-8-encoded strings
• utf8substring -- extract part of a utf8 string
• value -- evaluate
• currentString -- see value(String) -- evaluate a string
• values -- values in a hash table
• Variable -- specify a name for a variable
• VariableBaseName -- an optional argument
• Variables -- an optional argument
• Variety -- the class of all algebraic varieties
• variety -- get the variety
• vars -- variables
• Vasconcelos -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• Vector -- the class of all elements of modules that are handled by the engine
• vector -- make a vector
• VectorExpression -- the class of all vector expressions
• Verbose -- request verbose feedback
• Verbosity -- an optional argument
• Verify -- an optional argument
• versalEmbedding -- Compute a versal embedding
• Version -- an optional argument
• version -- information about this version of the program
• VerticalList -- a type of visible self-initializing list that prints vertically
• VerticalSpace -- an optional argument
• viewHelp -- view online documentation in a web browser
• VirtualTally
• VisibleList -- the class of all visible lists
• wait -- wait for child process
• WebApp -- the web app top level printing method
• wedgeProduct -- see wedgeProduct(ZZ,ZZ,Module) -- the exterior multiplication map
• weightRange -- the pair of lowest and highest weights of the monomials
• Weights -- assigning weights to the variables
• isWeylAlgebra -- see Weyl algebras
• when -- a keyword
• whichGm -- Largest Gm satisfied by an ideal
• while -- while loops
• width -- width of a file or net
• wikipedia -- link to a Wikipedia article
• Wrap -- a key for methods for wrapping printed output
• wrap
• WrapperType -- a class of lists with abbreviated constructors
• xor -- exclusive disjunction
• youngest -- the youngest member of a sequence
• zero -- whether something is zero
• ZeroExpression -- the class of all zero expressions
• zeta -- Riemann zeta function
• ZZ -- the class of all integers

For the programmer

The object Thing is a type, with no ancestor class..