Symbol Index
- ! -- factorial
- != -- inequality
- # -- length, or access to elements
- #? -- check for presence of elements
- % -- a binary operator, usually used for remainder and reduction
- & -- a binary operator
- (*) -- 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
- + -- a unary or binary operator, usually used for addition
- ++ -- a binary operator, usually used for direct sum
- , -- the comma, used for separating entries in a list or sequence
- - -- a unary or binary operator, usually used for negation or subtraction
- -> -- make a function
- . -- access to elements whose key is a symbol
- .. -- a binary operator, uses include ranges; sequence of consecutive items
- .? -- check for presence of elements whose key is a symbol
- / -- a binary operator, usually used for division
- // -- a binary operator, usually used for quotient
- : -- a binary operator, uses include repetition; ideal quotients
- := -- assignment of method or new local variable
- ; -- statement separator
- < -- less than
- <- -- assignment with left side evaluated
- << -- a binary operator (file output, ...)
- <= -- less than or equal
- <==> -- a binary operator
- = -- assignment
- =!= -- strict inequality
- == -- equality
- === -- strict equality
- ===> -- a binary operator
- ==> -- a binary operator
- => -- produce an Option
- > -- greater than
- >= -- greater than or equal
- >> -- a binary operator, uses include bit shifting, or attaching optional inputs to functions
- ? -- comparison operator
- @ -- a binary operator
- @@ -- a binary operator
- \ -- a binary operator
- \\ -- a binary operator
- ^ -- a binary operator, usually used for powers
- ^** -- a binary operator, usually used for tensor or Cartesian power
- ^^ -- a binary operator
- _ -- a binary operator, used for subscripting and access to elements
- | -- a binary operator, often used for horizontal concatenation
- |- -- a binary operator
- || -- a binary operator, often used for vertical concatenation
- ~ -- a unary postfix operator
- abs -- absolute value function
- AbsoluteLinks -- load and install a package and its documentation
- accumulate -- apply binary operator repeatedly
- acos -- compute the arccosine
- addEndFunction -- add an ending function
- addHook -- add a hook function to an object for later processing
- addStartFunction -- add a startup function
- Adjacent -- the class of all adjacent expression pairs
- adjoint -- an adjoint map
- adjoint1 -- an adjoint map
- Adjust -- make or retrieve a monoid
- 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
- alarm -- set an alarm
- Algorithm
- Alignment
- all -- whether all elements satisfy a specified condition
- allGenerators -- list of all generators
- ambient -- ambient free module of a subquotient, or ambient ring
- ancestor -- whether one type is an ancestor of another
- ANCHOR -- hypertext anchor
- and -- conjunction
- annihilator -- the annihilator ideal
- any -- whether any elements satisfy a specified condition
- append -- append an element to a list
- applicationDirectory -- the path to the user's application directory
- applicationDirectorySuffix -- suffix that determines 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 elements of a table
- applyValues -- apply a function to each value
- apropos -- symbols matching a pattern
- argument -- specify the function in a scripted functor for an argument
- Array -- the class of all arrays -- [...]
- Ascending
- ascii -- ASCII character conversion
- asin -- compute the arcsine
- assert -- assert something is true
- assign -- assign a value
- AssociativeExpression -- the class of associative expressions
- atan -- compute the arctangent
- atEndOfFile -- test for end of file
- Authors -- package item: start a new package
- autoload -- arrange for a function to be loaded automatically
- backtrace -- whether a backtrace is displayed following an error message
- backupFileRegexp -- a regular expression for recognizing names of backup files
- Bag -- the class of all bags
- Bareiss
- baseFilename -- the base part of a filename or path
- BaseFunction -- function for a documented feature
- baseName -- the base name of a generator
- baseRings -- store the list of base rings of a ring
- BaseRow
- BasicList -- the class of all basic lists
- basis -- basis of all or part of a module or ring
- BasisElementLimit -- stop when this number of basis elements is obtained
- Bayer -- a Strategy option value for saturate
- BeforePrint -- top level method applied before printing results
- beginDocumentation -- package item: start documentation section
- benchmark -- accurate timing of execution
- betti -- display degrees
- BettiTally -- the class of all Betti tallies
- between -- insert something between elements of a list
- Binary
- BinaryOperation -- the class of all binary operation expressions
- binomial -- binomial coefficient
- BLOCKQUOTE -- hypertext BLOCKQUOTE item
- BODY -- hypertext BODY item
- BOLD -- hypertext BOLD item
- Boolean -- the class of Boolean values
- borel -- make a Borel fixed submodule
- Boxes
- BR -- line break
- br -- line break
- break -- break from a loop
- buildHomeDirectory -- the directory where the Macaulay 2 program is being built
- cache -- a key under which to store cache tables
- CacheTable -- hash tables for caching
- cacheValue -- cache values of functions in their arguments
- CallLimit -- trace a function each time it's run
- capture -- evaluate Macaulay 2 code and capture the output (under development)
- catch -- catch a thrown exception
- Caveat -- warnings
- CC -- the class of all complex numbers
- CCC -- high-precision complex numbers
- CDATA -- hypertext CDATA element
- ceiling -- ceiling function
- Center
- centerString -- center a string or net
- ChainComplex -- the class of all chain complexes
- chainComplex -- make a chain complex
- ChainComplexMap -- the class of all maps between chain complexes
- ChangeMatrix -- whether to produce the change of basis matrix
- char -- computes the characteristic of a field or ring
- characters -- get characters from a string
- check -- perform tests of a package
- CheckDocumentation -- load and install a package and its documentation
- class -- class of an object
- 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
- CODE -- hypertext CODE item
- code -- display source code
- codim -- compute the codimension
- CodimensionLimit -- stop when this codimension is reached
- coefficient -- coefficient of a monomial
- CoefficientRing
- coefficientRing -- get the coefficient ring
- coefficients -- monomials and their coefficients
- Cofactor
- 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
- columnSwap -- interchange columns
- combine -- combine hash tables
- Command -- the class of all commands
- commandInterpreter -- the top level command interpreter
- commandLine -- the command line arguments
- COMMENT -- hypertext COMMENT element
- comodule -- submodule to quotient module
- compactMatrixForm -- global flag for compact printing
- CompiledFunction -- the class of all compiled functions
- CompiledFunctionBody -- the class of all compiled function bodies
- CompiledFunctionClosure -- the class of all compiled function closures
- complement -- find the minimal generators for cokernel of a matrix (low level form)
- complete
- CompleteIntersection -- provide a hint when computing a radical
- components -- list the components of a direct sum
- compositions -- compositions of an integer
- compress -- extract nonzero columns from a matrix
- concatenate -- join strings
- conductor -- compute the conductor of a finite ring map
- cone -- mapping cone of a chain map
- conjugate -- complex conjugate
- connectionCount -- the number of connections
- Consequences -- side-effects of a function
- content -- the content of a polynomial
- continue -- continue with the next iteration of a loop
- contract -- contract one matrix by another
- contract' -- contract a matrix by a matrix, the dual notion
- copy -- copy an object
- copyDirectory
- copyFile
- copyright -- a string containing the copyright notice for Macaulay 2
- cos -- compute the cosine
- cosh -- compute the hyperbolic cosine
- cotangentSheaf -- cotangent sheaf of a projective variety
- cover -- get the covering free module
- coverMap -- the surjective map from a free module to a module corresponding to the generators
- currentDirectory -- current working directory
- currentFileDirectory -- the directory containing the current input file
- currentFileName -- the current source file
- currentLineNumber -- current line number of the current input file
- currentPackage -- the current package
- currentString -- evaluate a string
- currentTime -- get the current time
- Database -- the class of all database files
- Date -- package item: start a new package
- DD -- hypertext DD element
- dd -- differential in a chain complex
- debug -- open private dictionary of a package
- debugError -- a function to debug
- DebuggingMode
- debuggingMode -- whether to enter the debugger when an error occurs
- debugLevel -- current level debugging
- deepSplice -- remove subsequences
- Degree
- degree
- degreeLength -- the number of degrees
- DegreeLimit -- compute up to a certain degree
- DegreeMap
- DegreeOrder -- sort primarily by degree
- DegreeRank -- make or retrieve a monoid
- Degrees -- make or retrieve a monoid
- degrees -- degrees of generators
- degreesMonoid -- get the monoid of degrees
- degreesRing -- the ring of degrees
- delete -- delete elements of a list
- demark -- insert a string between elements of a list of strings
- denominator -- denominator of a fraction
- Dense
- depth -- depth of a net
- Descending -- specify descending order
- describe -- real description
- Description
- determinant -- determinant of a matrix
- diagonalMatrix -- make a diagonal matrix
- Dictionary -- the class of all dictionaries
- dictionary -- determine the dictionary to which a symbol belongs
- dictionaryPath
- diff -- differentiate or take difference
- diff' -- differentiate a matrix by a matrix, the dual notion
- difference -- difference
- dim -- compute the Krull dimension
- directSum -- direct sum of modules or maps
- disassemble -- disassemble pseudocode or a function
- dismiss -- dismiss a package
- Dispatch -- make a new method function
- DIV -- a hypertext division
- DIV1 -- a single-spaced paragraph separator
- Divide -- the class of all divide expressions
- divideByVariable -- divide all columns by a (power of a) variable
- DivideConquer
- DL -- hypertext DL element
- do -- loop control
- document -- package item: documentation node
- DocumentTag -- the class of all document tags
- Down -- monomial ordering
- drop -- drop some elements from a list or sequence
- DT -- hypertext DT element
- dual -- dual module or map
- dumpdata -- dump state of the system to a file
- eagonNorthcott -- Eagon-Northcott complex of a matrix of linear forms
- echoOff -- turn off echoing
- echoOn -- turn on echoing
- edit -- edit source code
- eigenvalues -- find eigenvalues of a matrix over RR or CC
- eigenvectors -- find eigenvectors of a matrix over RR or CC
- elements -- list of elements
- Eliminate -- elimination order
- EliminationOrder -- use the natural elmination order in a pushForward1 computation
- else -- condition testing
- EM -- hypertext EM item
- Email -- package item: start a new package
- encapDirectory -- encapsulated installation directory
- Encapsulate
- 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
- engineDebugLevel -- current engine debugging level
- 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
- error -- deliver error message
- errorCode -- the pseudocode that produced an error
- errorDepth -- set the error printing depth
- euler -- Euler characteristic
- eulers -- list the sectional Euler characteristics
- even -- tell whether an integer is even
- EXAMPLE -- hypertext EXAMPLE item
- ExampleItem -- a type of hypertext for holding example inputs awaiting outputs
- examples -- list the examples in documentation
- Exclude
- exec -- execute another program
- exit -- exit the program
- exp -- exponential function
- exponents -- list the exponents in a polynomial
- export -- package item: export functions
- exportMutable -- package item: export writable variables
- 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
- F4 -- set the Groebner basis algorithm
- factor -- factor a ring element or a ZZ-module
- false
- Fano -- Fano scheme
- Faugere -- set the Groebner basis algorithm
- File -- the class of all files
- fileDictionaries -- local dictionaries for loaded files
- fileExists -- whether a file exists
- fileExitHooks -- a list of hooks (functions) to execute when the current file has been loaded
- fileLength -- the length of a file
- fileMode -- set or get file mode
- FilePosition -- the class of all file positions
- fileTime -- get or set file modified time
- findFiles -- find files recursively
- FindOne -- find a primitive element
- findSynonyms -- find synonyms of symbols
- First
- first -- first element of a list
- firstkey -- get the first key
- fittingIdeal -- Fitting ideal of a module
- flagLookup -- flag a symbol
- flatten -- flatten a list by unnesting lists
- Flexible
- flip -- matrix of commutativity of tensor product
- floor -- floor function
- flush -- flush output to file
- fold -- apply binary operator repeatedly
- FollowLinks
- for -- for loops
- forceGB -- declare that the columns of a matrix are a Groebner basis
- ForestNode -- a type of basic list used to represent a forest, i.e., a list of rooted trees
- fork -- fork the process
- Format
- format -- format a string
- frac -- construct a fraction field
- fraction
- FractionField -- the class of all fraction fields
- frames -- get the frames associated to a closure
- from -- loop control
- 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
- gb -- compute a Groebner basis
- GBDegrees
- gbTrace -- provide tracing output during various computations in the engine.
- gcd -- greatest common divisor
- gcdCoefficients -- gcd with coefficients
- 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
- 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
- getWWW -- get a web page
- GF -- make a finite field
- GLex -- graded lexicographic ordering
- Global -- monomial ordering
- global -- get a global symbol
- 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
- 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
- graphIdeal -- the ideal of the graph of the regular map corresponding to a ring map
- graphRing -- the coordinate ring of the graph of the regular map corresponding to a ring map
- Grassmannian -- the Grassmannian of linear subspaces of a vector space
- GRevLex -- graded reverse lexicographical monomial order.
- GroebnerBasis -- the class of all Groebner bases
- 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
- HEAD -- hypertext HEAD item
- HEADER1 -- hypertext HEADER1 item
- HEADER2 -- hypertext HEADER2 item
- HEADER3 -- hypertext HEADER3 item
- HEADER4 -- hypertext HEADER4 item
- HEADER5 -- hypertext HEADER5 item
- HEADER6 -- hypertext HEADER6 item
- HeaderType -- a class of lists with abbreviated constructors
- Heading
- Headline -- make a headline for a documentation node
- Heft -- make or retrieve a monoid
- height -- height of a net
- help -- help command
- Hermitian
- HH -- general homology and cohomology functor
- hh -- Hodge numbers of a smooth projective variety
- Hilbert
- hilbertFunction -- compute 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
- homeDirectory -- the home directory of the user
- HomePage -- package item: start a new package
- Homogeneous
- Homogeneous2 -- set the Groebner basis algorithm
- homogenize -- homogenize with respect to a variable
- homology -- general homology functor
- homomorphism -- get the homomorphism from element of Hom
- horizontalJoin -- join nets or strings horizontally
- HorizontalSpace
- HR -- hypertext HR element (horizontal rule)
- hr -- horizontal rule
- HREF -- hypertext link
- HTML -- hypertext item
- html -- convert hypertext to html format
- Hypertext -- the class of mark-up lists used with hypertext
- hypertext -- prepare hypertext for display
- HypertextContainer -- the class of mark-up lists that can contain paragraphs
- HypertextParagraph -- the class of mark-up lists that constitute separate paragraphs
- ICfractions -- Compute the fractions integral over a domain.
- ICmap -- natural map from an affine domain into its integral closure.
- id -- identity map
- Ideal -- the class of all ideals
- ideal -- make an ideal
- identity -- the identity function
- if -- condition testing
- IgnoreExampleErrors
- ii -- square root of -1
- image -- image of a map
- imaginaryPart -- imaginary part
- IMG -- hypertext IMG item
- ImmutableType -- the class of immutable types
- in -- a keyword used in for-loops
- incomparable -- a result indicating incomparability
- independentSets -- some maximal independent subsets of variables modulo an ideal
- indeterminate -- an indeterminate number
- IndeterminateNumber -- the class of all indeterminate numbers
- index -- numeric index of a ring variable
- indexComponents -- specify keys for components of a direct sum
- IndexedVariable -- the class of all indexed variables
- indices -- indices of a polynomial; also components for a direct sum
- inducedMap -- compute an induced map
- inducesWellDefinedMap -- whether a map is well defined
- InfiniteNumber -- the class of all infinite numbers
- infinity -- infinity
- info -- convert hypertext to info format
- InfoDirSection -- package item: start a new package
- infoHelp -- view online doc with info
- Inhomogeneous
- input -- read Macaulay 2 commands and echo
- Inputs -- inputs for a function
- installAssignmentMethod -- install methods assignment to the value of an operator
- installMethod -- install methods
- installPackage -- load and install a package and its documentation
- InstallPrefix
- instance -- whether something has a certain type
- integralClosure -- compute the integral closure of a ring
- integrate -- numerical integration
- IntermediateMarkUpType -- the class of intermediate mark-up types
- interpreterDepth -- nesting depth of the interpreter
- intersect -- compute an intersection
- inverse -- compute the inverse
- InverseMethod -- compute reciprocals
- Inverses -- make or retrieve a monoid
- 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
- isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
- 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
- isField -- whether something is a 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
- isInjective -- whether a map is injective
- isInputFile -- whether a file is open for input
- isIsomorphism -- whether a map is an isomorphism
- isListener -- whether a file is open for listening
- isModule -- whether something is a module
- isMonomialIdeal -- whether something is a monomial ideal
- isNormal -- determine whether a reduced ring is normal
- isOpen -- whether a file or database is open
- isOutputFile -- whether a file is open for output
- isPolynomialRing -- whether someting is a polynomial ring
- isPrime -- whether a integer, polynomial, or ideal is prime
- isPrimitive -- whether an element is a primitive element of a finite field
- 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 -- whether a file has data available for reading
- isRegularFile -- whether a file is a regular file
- isRing -- whether something is a ring
- isSkewCommutative -- whether a ring has skew commuting variables
- isSquareFree -- whether something is square free monomial ideal
- isSubmodule -- whether a module is evidently a submodule of a free module
- isSubset -- whether one object is a subset of another
- isSurjective -- whether a map is surjective
- isTable -- whether something is a rectangular list of lists
- isUnit -- whether a ring element is a unit
- isWellDefined -- whether a map is well defined
- ITALIC -- hypertext italic font
- Iterate -- a Strategy option value for saturate
- jacobian -- the Jacobian matrix of partial derivatives
- join -- join lists
- kernel -- kernel of a ringmap, matrix, or chain complex
- Key -- key of a documentation node
- keys -- keys used in a hash table
- Keyword -- the class of all keywords
- kill -- kill a process
- koszul
- LABEL -- hypertext label item
- last -- last element of a list
- LATER -- a hypertext element for lazy evaluation
- LAYOUT -- relative locations of Macaulay 2 files
- leadCoefficient -- the leading coefficient
- leadComponent -- the leading component of a vector or matrix
- leadMonomial -- the leading monomial
- leadTerm -- get the greatest term
- Left
- length -- length
- LengthLimit -- stop when the resolution reaches this length
- Lex -- lexicographical monomial order.
- LI -- hypertext list item
- lift -- lift to another ring
- liftable -- whether a ring element can be lifted to another ring
- Limit -- specify how many to compute
- Linear -- a Strategy option value for saturate
- LinearAlgebra -- set the Groebner basis algorithm
- lineNumber -- current line number
- lines -- split a string into lines
- LINK -- a hypertext LINK element
- linkFile -- make a new link to a file
- List -- the class of all lists -- {...}
- list -- loop control
- listForm -- convert to list form
- listLocalSymbols -- compact display of symbols and their values
- listSymbols -- compact display of symbols and their values
- listUserSymbols -- display the user's symbols
- LITERAL -- hypertext literal text
- load -- read Macaulay 2 commands
- loaddata -- load state of the system from a file
- loadDepth -- the load depth
- LoadDocumentation -- when loading a package, load the documentation, too
- loadedFiles
- loadedPackages
- loadPackage -- load a package
- local -- get a local symbol
- localDictionaries -- get local dictionaries
- LocalDictionary -- the class of all local dictionaries
- locate -- locate source code
- log -- logarithm function
- LongPolynomial
- lookup -- look up methods
- lookupCount -- reference count for a symbol
- LowerBound -- the class of lower bound objects
- LU -- LU decomposition
- Macaulay2
- makeDirectory -- make a directory
- MakeDocumentation
- makeDocumentTag -- convert a documentation key to a documentation tag
- MakeInfo
- MakeLinks -- load and install a package and its documentation
- makePackageIndex
- Manipulator -- the class of all file manipulators
- map -- make a map
- MarkUpType -- the class of mark-up types used with hypertext
- MarkUpTypeWithOptions -- the class of mark-up types used with hypertext, with option handling
- 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 -- maximum of elements of a list
- maxPosition -- position of largest element
- member -- test membership in a list or set
- memoize -- record results of function evaluation for future use
- MENU -- hypertext menu item
- merge -- merge hash tables
- mergePairs -- merge sorted lists of pairs
- META -- a hypertext META element
- method -- make a new method function
- MethodFunction -- a type of method function
- MethodFunctionWithOptions -- a type of method function
- methodOptions -- recover the options used when a method function was created
- methods -- list methods
- min -- minimum of elements of a list
- mingens -- minimal generator matrix
- mingle -- mingle elements of several lists
- MinimalGenerators
- MinimalMatrix -- set the matrix of minimal generators
- minimalPresentation -- compute a minimal presentation
- minimalPresentationMap -- compute a minimal presentation of a quotient ring
- minimalPresentationMapInv -- compute a minimal presentation of a quotient ring
- minimalPrimes -- minimal associated primes of an ideal
- Minimize
- minimizeFilename -- minimize a file name
- minors -- ideal generated by minors
- MinorsComputation -- the class of all minors computations
- minPosition -- position of smallest element
- minprimes -- compute the minimal primes
- Minus -- the class of all minus expressions
- minus -- additive inverse
- mkdir
- mod -- reduce modulo an integer
- modifyRing -- make a copy of a ring, with some features changed
- Module -- the class of all modules
- module -- make or get a module
- ModuleMap -- the class of all maps between modules
- modulo -- find the pre-image of a map (low level version)
- Monoid -- the class of all monoids
- monoid -- make or retrieve a monoid
- MonoidElement -- the class of all monoid elements
- monomialCurveIdeal -- make the ideal of a monomial curve
- MonomialIdeal -- the class of all monomial ideals handled by the engine
- monomialIdeal -- make a monomial ideal
- MonomialOrder -- monomial ordering
- Monomials -- whether to display the number of monomial
- monomials -- matrix of monomials in a ring element or matrix
- MonomialSize -- make or retrieve a monoid
- monomialSubideal -- find the largest monomial ideal in an ideal
- moveFile
- mutable -- whether something may be modified
- MutableHashTable -- the class of all mutable hash tables
- mutableIdentity -- make a mutable identity matrix
- MutableList -- the class of all mutable lists
- MutableMatrix -- the class of all mutable matrices
- mutableMatrix -- make a mutable matrix
- mutableZero -- make a mutable matrix filled with zeroes
- Name -- package item: start a new package
- NCLex -- Non-commutative lexicographical order.
- needs -- read Macaulay 2 commands if necessary
- needsPackage -- load a package if not already loaded
- Net -- the class of all nets and strings
- net -- format for printing, as a net
- NetFile -- the class of all net files
- netTable -- 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
- newPackage -- package item: start a new package
- nextkey -- the next key in a database
- NonAssociativeProduct -- the class of all nonassociative product expressions
- NonLinear -- use the algorithm which doesn't assume that the ring map is linear
- NoPrint -- top level method for non-printing results
- not -- negation
- Nothing -- the empty class
- notify -- whether to notify the user when a file is loaded
- notImplemented -- print an 'not implemented' error message
- null -- the unique member of the empty class
- nullaryMethods
- nullhomotopy -- make a null homotopy
- Number -- the class of all numbers
- number -- count how many elements of a list satisfy a condition
- numColumns -- number of columns in a mutable matrix
- numerator -- numerator of a fraction
- numeric -- convert to floating point
- numgens -- the number of generators
- numRows -- number of rows in a mutable matrix
- odd -- tell whether an integer is odd
- of -- a keyword
- ofClass -- English phrases for types
- on -- trace a function each time it's run
- OneExpression -- the class all one expressions
- OO -- the structure sheaf
- oo -- the last output value
- ooo -- the next to the last output value
- oooo -- the third to the last output value
- openDatabase -- open a database file
- openDatabaseOut -- open a database file for writing
- openFiles -- list the open files
- openIn -- open an input file
- openInOut -- open an input output file
- openListener -- open a port for listening
- openOut -- open an output file
- operatorAttributes
- Option -- the class of all pairs x => y
- Options
- 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
- OutputDictionary -- the dictionary for output values
- Outputs -- outputs for a function
- override -- override default values for optional arguments
- pack -- pack elements of a list into shorter ones
- Package -- the class of all packages
- package -- get containing package
- PackageDictionary -- the dictionary for names of packages
- PackagePrefix
- pad -- pad a string with spaces
- pager -- display with paging
- PairLimit -- stop when this number of pairs is handled
- pairs -- list the pairs in a hash table
- PairsRemaining -- whether to display the number of S-pairs remaining
- PARA -- hypertext paragraph container
- parent -- parent type of an object
- part -- sum of monomials of a polynomial of a given degree
- Partition -- a type of list representing a partition of a natural number
- partitions -- list the partitions of an integer
- path -- list of directories to look in
- 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 -- the number 'pi'
- plus -- addition
- poincare -- assemble degrees into polynomial
- poincareN -- assemble degrees into polynomial
- PolynomialRing -- the class of all ordered monoid rings
- Position -- monomial ordering
- position -- find first element of a list satisfying a condition
- positions -- which elements of a list satisfy a condition
- Postfix
- Power -- the class of all power expressions
- power -- power
- PRE -- preformatted text
- precision
- Prefix
- prefixDirectory -- the prefix directory
- preimage -- preimage of an ideal under a ring map
- prepend -- add an element to the beginning of a list
- presentation -- presentation of a module or ring
- pretty -- a pretty printer
- Primary
- primaryDecomposition -- irredundant primary decomposition of an ideal
- PrimaryTag -- for internal use only: a symbol used in storing documentation
- PrimitiveElement -- specify a primitive element
- Print -- top level method for printing results
- print -- print something
- printingPrecision -- current precision for printing real numbers
- printingTimeLimit
- PrintNames -- table of printed forms of objects
- printString -- lowlevel function to print a string, net, or symbol
- printWidth
- processID -- the process identifier
- Product -- the class of all product expressions
- product
- ProductOrder -- product ordering
- profile -- profile a function
- profileSummary -- display profiling data
- 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
- promptWidth
- protect -- protect a symbol
- pruningMap
- Pseudocode -- the class of pseudocodes
- pseudocode -- produce the pseudocode for a function
- pseudoRemainder -- compute the pseudo-remainder
- pushForward
- pushForward1 -- the main computational component of pushForward
- PushforwardComputation -- a type of list used internally by pushForward1
- QQ -- the class of all rational numbers
- quit -- quit the program
- Quotient
- 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 -- the radical of an ideal
- random -- get a random element
- randomMutableMatrix -- a random mutable matrix of integers
- rank -- compute the rank
- read -- read from a file
- readDirectory -- read the contents of a directory
- readlink -- readlink fn
- realPart -- real part
- realpath -- convert a filename to one passing through no symbolic links
- recursionDepth -- the current recursion depth
- recursionLimit -- set the limit on recursion
- reduceHilbert -- reduce a Hilbert series expression
- regex -- regular expression matching
- regularity -- compute the Castelnuovo-Mumford regularity
- relations -- the defining relations
- relativizeFilename -- relativize a file name
- remainder -- matrix remainder
- remainder' -- matrix quotient and remainder (opposite)
- RemakeAllDocumentation -- load and install a package and its documentation
- remove -- remove an entry from a hash table
- removeDirectory -- remove a directory
- removeFile -- unlink a file
- removeHook -- remove a hook function from an object
- removeLowestDimension -- remove components of lowest dimension
- reorganize -- reorganize a database file
- Repair -- make or retrieve a monoid
- replace -- regular expression replacement
- RerunExamples
- reshape -- reshape a matrix
- Resolution -- the class of all resolution computations
- resolution -- projective resolution
- restart -- restart Macaulay 2
- return -- return from a function
- returnCode
- reverse -- reverse a list
- ReverseDictionary -- table of symbols where various types of objects are stored
- RevLex -- reverse lexicographic ordering
- Right
- 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
- RingMap -- the class of all ring maps
- rotate -- rotate a list
- round -- round a number to the nearest integer
- 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
- rowSwap -- interchange rows
- RR -- the class of all real numbers
- RRR -- high-precision real numbers
- rsort -- sort a list or matrix in reverse order
- run -- run an external command
- runHooks -- run the hook functions stored in an object
- same -- whether everything in a list is the same
- saturate -- saturation of ideal or submodule
- scan -- apply a function to each element
- scanKeys -- apply a function to each key in a hash table or database
- scanPairs -- apply a function to pairs in a hash table
- scanValues -- apply a function to each value in a hash table
- schreyerOrder -- create or obtain free modules with Schryer monomial orders
- Schubert -- find the Pluecker ideal of a Schubert variety
- ScriptedFunctor -- the class of all scripted functors
- searchPath -- search a path for a file
- SeeAlso -- crossreferences in documentation
- select -- select from a list, hash table, or string
- selectInSubring -- select columns in a subring
- SelfInitializingType -- the class of all self initializing types
- separate -- split a string into pieces
- separateRegexp -- separate a string into pieces, with separators determined by a regular expression
- Sequence -- the class of all sequences -- (...)
- sequence -- make a sequence
- Set -- the class of all sets
- set -- make a set
- setEcho -- turn on echoing
- setPrecision
- setRandomSeed -- set starting point for random number generator
- setup
- sheaf -- make a coherent sheaf
- sheafExt -- sheaf Ext of coherent sheaves
- sheafHom -- sheaf Hom
- SheafOfRings -- the class of sheaves of rings
- shield -- shield evaluation from interrupts
- show -- display various TeX, hypertext, or a URL, in an external application
- showClassStructure -- show relationship between things
- showHtml -- convert hypertext to html and display with a browser
- showStructure -- show relationship between types
- showTex -- convert to TeX and display on screen
- showUserStructure -- show relationship between types defined by user
- sin -- compute the sine
- singularLocus -- singular locus
- sinh -- compute the hyperbolic sine
- size -- the size of an object
- SkewCommutative -- make or retrieve a monoid
- sleep -- sleep for a while
- SMALL -- hypertext SMALL item
- smithNormalForm
- solve -- solve a linear equation
- someTerms -- select some terms of a polynomial
- Sort
- 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
- sourceHomeDirectory -- the directory where the source code is while Macaulay 2 is being built
- SPACE -- blank operator; often used for function application, making polynomial rings
- SPAN -- hypertext span
- SparseMonomialVectorExpression -- the class of all sparse monomial vector expressions
- SparseVectorExpression -- the class of all sparse vector expressions
- Spec -- make an affine variety
- splice -- remove subsequences
- sqrt -- square root function
- stack -- join nets or string vertically
- standardForm -- convert to standard form
- standardPairs -- find the standard pairs of a monomial ideal
- 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
- StopBeforeComputation -- initialize but do not begin the computation
- stopIfError -- whether to stop the program when an error occurs
- StopWithMinimalGenerators -- stop when minimal generators have been determined
- Strategy -- specify a computational strategy
- String -- the class of all strings
- STRONG -- hypertext STRONG item
- STYLE -- hypertext STYLE element
- SUB -- hypertext subscript
- sublists -- process interspersed sublists of a list
- submatrix
- 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
- SUBSECTION -- hypertext SUBSECTION item
- subsets -- produce all the subsets
- substitute -- substituting values for variables
- substring -- extract part of a string
- subtable -- extract a subtable from a table
- Sugarless -- set the Groebner basis algorithm
- Sum -- the class of all sum expressions
- sum -- compute the sum
- SumOfTwists -- the class of all sums of twists
- SUP -- hypertext superscript
- 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 occuring in a polynomial
- SVD -- singular value decomposition of a rectangular matrix over RR or CC
- Symbol -- the class of all symbols
- symbol -- get a symbol
- symlinkDirectory -- 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
- symmetricPower -- symmetric power
- synonym -- synonym for members of a class
- SYNOPSIS
- syz -- the syzygy matrix
- Syzygies -- whether to collect syzygies
- SyzygyLimit -- stop when this number of syzygies is obtained
- SyzygyMatrix -- set the syzygy matrix
- SyzygyRows -- the number rows of the syzygy matrix to collect
- syzygyScheme -- construct a syzygy scheme
- TABLE -- hypertext table
- Table -- the class of all table expressions
- table -- make a table (nested list)
- take -- take some elements from a list
- Tally -- the class of all tally results
- tally -- tally the elements of a list or sequence
- tan -- compute the tangent
- tangentSheaf -- tangent sheaf of a projective variety
- tanh -- compute the hyperbolic tangent
- target -- target of a map
- TD -- hypertext TD element
- temporaryFileName -- make a temporary file name
- tensor -- tensor product
- tensorAssociativity -- associativity isomorphisms for tensor products
- terms -- provide a list of terms of a polynomial
- TEST -- package item: register a test of the package
- TEX -- hypertext TEX item
- tex -- convert to TeX format
- texMath -- convert to TeX math format
- then -- condition testing
- Thing -- the class of all things
- throw -- throw an exception
- Time -- the class of all timing results
- time -- time a computation
- times -- multiplication
- timing -- time a computation
- TITLE -- hypertext title
- TO -- hypertext documentation link
- to -- loop control
- TO2 -- labeled hypertext documentation link
- toDual -- inverse system
- toExternalString -- convert to a readable string
- toField -- declare that a ring is a field
- TOH -- hypertext documentation link followed by a headline
- toList -- list of elements
- toLower -- convert to lower case
- topCoefficients -- first variable and its coefficient of a polynomial or matrix
- topComponents -- compute top dimensional component
- Tor -- Tor module
- toRRR -- convert to high-precision real
- toSequence -- convert to sequence
- toString -- convert to a string
- TotalPairs -- whether to display the total number of S-pairs
- toUpper -- convert to upper case
- TR -- hypertext TR element
- trace -- trace of a matrix
- transpose -- transpose a table or a matrix
- TreeNode -- a type of basic list used to represent a rooted tree
- trim -- minimize generators and relations
- true
- Truncate -- basis of all or part of a module or ring
- truncate -- truncate the module at a specified degree
- truncateOutput
- try -- catch an error
- tryHooks -- try the hook functions stored in an object
- TT -- hypertext TT item
- tutorial -- convert documentation from tutorial format
- Type -- the class of all types
- TypicalValue -- make a new method function
- typicalValues -- types of values returned by functions
- UL -- hypertext UL item
- ultimate -- ultimate value for an iteration
- unbag
- uncurry -- uncurry a function
- Undo
- undocumented
- uniform -- test whether elements of a list are of the same class
- uninstallPackage -- uninstall a package
- unique -- eliminate duplicates from a list
- Unmixed -- provide a hint when computing a radical
- unsequence -- extract the single element from a sequence of length 1
- unstack -- list the rows of a net
- Up -- monomial ordering
- UpdateOnly -- only copies of newer files should replace files
- URL -- a type representing a URL
- Usage -- shows the usage of a function
- use -- install or activate object
- UseHilbertFunction
- UserMode
- userSymbols -- a list of the user's symbols
- validate
- value -- evaluate
- values -- values in a hash table
- Variable -- specify a name for a variable
- VariableBaseName -- make or retrieve a monoid
- Variables
- Variety -- the class of all algebraic varieties
- variety -- get the variety
- vars -- variables
- Vector -- the class of all elements of free modules which are handled by the engine
- vector -- make a vector
- Verbose -- request verbose feedback
- Verify -- verify that a map is well-defined
- Version -- package item: start a new package
- version -- information about this version of the program
- VerticalList -- a type of visible self-initializing list that prints vertically
- VerticalSpace
- viewHelp -- view online doc with a web browser
- VisibleList -- the class of all visible lists
- wait -- wait for child process
- wedgeProduct -- the exterior multiplication map
- weightRange -- the pair of lowest and highest weights of the monomials
- Weights -- assigning weights to the variables
- WeylAlgebra -- make or retrieve a monoid
- when -- a keyword
- while -- while loops
- width -- width of a file or net
- Wrap -- a key for methods for wrapping printed output
- wrap
- WrapperType -- a class of lists with abbreviated constructors
- xor -- logical exclusive-or
- youngest -- the youngest member of a sequence
- zero -- whether something is zero
- ZeroExpression -- the class of all zero expressions
- ZZ -- the class of all integers