Macaulay2Doc : Index

• ! -- factorial
• != -- inequality
• " -- delineate a string with quotation marks
• # -- length or access to elements
• # BasicList -- length or cardinality
• # HashTable -- length or cardinality
• # Set -- length or cardinality
• # String -- length or cardinality
• #? -- check existence of value in a list, hash table, database, or string
• % -- 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
• + CC -- a unary or binary operator, usually used for addition
• + Constant -- a unary or binary operator, usually used for addition
• + QQ -- a unary or binary operator, usually used for addition
• + RR -- a unary or binary operator, usually used for addition
• + RRi -- a unary or binary operator, usually used for addition
• + ZZ -- 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
• - CC -- a unary or binary operator, usually used for negation or subtraction
• - ChainComplexMap -- a unary or binary operator, usually used for negation or subtraction
• - Constant -- a unary or binary operator, usually used for negation or subtraction
• - Expression -- the class of all expressions
• - GradedModuleMap -- a unary or binary operator, usually used for negation or subtraction
• - Holder -- a unary or binary operator, usually used for negation or subtraction
• - InfiniteNumber -- a unary or binary operator, usually used for negation or subtraction
• - List -- negation of a vector
• - Matrix -- a unary or binary operator, usually used for negation or subtraction
• - Minus -- a unary or binary operator, usually used for negation or subtraction
• - MutableMatrix -- a unary or binary operator, usually used for negation or subtraction
• - ProjectiveHilbertPolynomial -- a unary or binary operator, usually used for negation or subtraction
• - QQ -- a unary or binary operator, usually used for negation or subtraction
• - RingElement -- a unary or binary operator, usually used for negation or subtraction
• - RR -- a unary or binary operator, usually used for negation or subtraction
• - RRi -- a unary or binary operator, usually used for negation or subtraction
• - Vector -- negation of a Vector
• - VirtualTally -- negation of a VirtualTally
• - ZeroExpression -- a unary or binary operator, usually used for negation or subtraction
• - ZZ -- a unary or binary operator, usually used for negation or subtraction
• -- -- comment
• -> -- 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
• .? -- check for presence of elements whose key is a symbol
• / -- a binary operator, usually used for division
• // -- a binary operator, usually used for quotient
• /// -- delineate a string with slashes
• : -- 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, ...)
• << Thing -- print to a file
• <= -- less than or equal
• <== -- a unary and binary operator
• <=== -- a unary and binary operator
• <==> -- a binary operator
• = -- assignment
• =!= -- strict inequality
• == -- equality
• === -- strict equality
• ===> -- a binary operator
• ==> -- a binary operator
• => -- produce an Option
• > -- greater than
• > InfiniteNumber -- greater than
• > ZZ -- greater than
• >= -- greater than or equal
• >= InfiniteNumber -- greater than or equal
• >= ZZ -- greater than or equal
• >> -- a binary operator, uses include bit shifting, or attaching optional inputs to functions
• ? -- comparison operator
• ? Function -- view brief documentation of a symbol
• ? Keyword -- view brief documentation of a symbol
• ? Package -- view brief documentation of a symbol
• ? ScriptedFunctor -- view brief documentation of a symbol
• ? Symbol -- view brief documentation of a symbol
• ? Type -- view brief documentation of a symbol
• @ -- a binary operator
• @@ -- a binary operator
• \ -- a binary operator
• \\ -- a binary operator
• ^ -- 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
• ^^ -- logical exclusive-or
• _ -- a binary operator, used for subscripting and access to elements
• _* -- a unary postfix operator, used for indicating pushforward maps
• | -- a binary operator, often used for horizontal concatenation
• |- -- a binary operator
• || -- a binary operator, often used for vertical concatenation
• ~ -- a unary postfix operator
• 4ti2
• a first Macaulay2 session
• about -- search the documentation
• about(...,Body=>...) -- search the documentation
• about(Function) -- search the documentation
• about(String) -- search the documentation
• about(Symbol) -- search the documentation
• about(Type) -- search the documentation
• abs -- absolute value function
• abs(CC) -- absolute value function
• abs(QQ) -- absolute value function
• abs(RR) -- absolute value function
• abs(RRi) -- absolute value function
• abs(ZZ) -- absolute value function
• accumulate -- apply a binary operator repeatedly
• accumulate(Function,Thing) -- apply a binary operator repeatedly
• accumulate(Function,Thing,Thing) -- apply a binary operator repeatedly
• accumulate(Function,Thing,VisibleList) -- apply a binary operator repeatedly
• accumulate(Function,VisibleList) -- apply a binary operator repeatedly
• accumulate(VisibleList,Function) -- apply a binary operator repeatedly
• accumulate(VisibleList,Thing,Function) -- apply a binary operator repeatedly
• Acknowledgement -- acknowledgements listed in a documentation node
• Acknowledgements
• acos -- arccosine
• acos(CC) -- arccosine
• acos(RR) -- arccosine
• acos(RRi) -- arccosine
• acosh -- inverse hyperbolic cosine
• acosh(Number) -- inverse hyperbolic cosine
• acot -- compute the inverse cotangent
• acot(Number) -- compute the inverse cotangent
• acoth -- compute the hyperbolic arctangent of a number
• acoth(Constant) -- compute the hyperbolic arctangent of a number
• acoth(Number) -- compute the hyperbolic arctangent of a number
• addCancelTask -- specify that the completion of one task triggers the cancellation of another
• addCancelTask(Task,Task) -- specify that the completion of one task triggers the cancellation of another
• addDependencyTask -- schedule a task, but ensure that it will not run until another task finishes
• 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
• addHook(...,Strategy=>...) -- add a hook function to an object for later processing
• addHook(MutableHashTable,Thing,Function) -- add a hook function to an object for later processing
• addHook(Sequence,Function) -- add a hook function to an object for later processing
• addHook(Symbol,Function) -- 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 -- schedule a task upon completion of another
• addStartTask(Task,Task) -- schedule a task upon completion of another
• Adjacent -- the class of all adjacent expression pairs
• adjoint -- an adjoint map
• adjoint' -- an adjoint map
• adjoint'(Matrix,Module,Module) -- an adjoint map
• adjoint(Matrix,Module,Module) -- an adjoint map
• AffineVariety -- the class of all affine varieties
• AffineVariety * AffineVariety -- a binary operator, usually used for multiplication
• AffineVariety ** Ring -- a binary operator, usually used for tensor product or Cartesian product
• 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
• agm(CC,CC) -- arithmetic-geometric mean
• agm(RR,RR) -- arithmetic-geometric mean
• alarm -- set an alarm
• Algorithm -- an optional argument
• Alignment -- an optional argument
• all -- whether all elements satisfy a specified condition
• all(BasicList,BasicList,Function) -- whether all corresponding elements of a pair of lists satisfy a condition
• all(BasicList,Function) -- whether all elements of a list satisfy a specified condition
• all(HashTable,Function) -- whether all key/value pairs in a hash table satisfy a specified condition
• all(ZZ,Function) -- whether all elements of a list satisfy a specified condition
• allowableThreads -- the current maximum number of simultaneously running tasks
• ambient -- ambient free module of a subquotient, or ambient ring
• ambient(GaloisField) -- corresponding quotient ring
• ambient(Matrix)
• ambient(Module) -- ambient free module
• ambient(PolynomialRing) -- ambient polynomial ring
• ambient(QuotientRing) -- ambient polynomial ring
• ambient(Ring) -- ambient polynomial ring
• an example of a package
• ancestor -- whether one type is an ancestor of another
• 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 <| ... |>
• antipode -- antipode for skew commuting polynomial rings
• antipode(RingElement) -- antipode for skew commuting polynomial rings
• any -- whether any elements satisfy a specified condition
• any(BasicList,BasicList,Function) -- whether any corresponding elements of a pair of lists satisfy a condition
• any(BasicList,Function) -- whether any elements of a list satisfy a specified condition
• any(HashTable,Function) -- whether all key/value pairs in a hash table satisfy a specified condition
• any(ZZ,Function) -- whether any elements of a list satisfy a specified condition
• append -- add an element to the end of a list
• append(BasicList,Thing) -- add an element to the end of a list
• application directory -- the path to the user's application directory
• 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
• apply(BasicList,BasicList,Function) -- apply a function to pairs of elements, one from each list
• apply(BasicList,Function) -- apply a function to each element of a list
• apply(BasicList,String,Function) -- apply a function to pairs of elements, one from each list
• apply(String,BasicList,Function) -- apply a function to pairs of elements, one from each list
• apply(String,Function) -- apply a function to each element of a list
• apply(String,String,Function) -- apply a function to pairs of elements, one from each list
• apply(Thing,Function) -- apply a function to an object with an iterator
• apply(ZZ,Function) -- apply a function to {0,..., n-1}
• applyKeys -- apply a function to each key in a hash table
• applyKeys(HashTable,Function) -- apply a function to each key in a hash table
• applyKeys(HashTable,Function,Function) -- apply a function to each key in a hash table
• applyPairs -- apply a function to each pair in a hash table
• applyPairs(HashTable,Function) -- 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
• applyValues(HashTable,Function) -- apply a function to each value in a hash table
• apropos -- symbols matching a pattern
• apropos(String) -- symbols matching a pattern
• argument -- specify the function in a scripted functor for an argument
• Array -- the class of all arrays -- [...]
• Array | Array -- join lists, sequences or arrays
• Ascending -- specify ascending order
• ascii -- ASCII character conversion
• ascii(List) -- ASCII character conversion
• ascii(String) -- ASCII character conversion
• asin -- arcsine
• asin(CC) -- arcsine
• asin(RR) -- arcsine
• asin(RRi) -- arcsine
• asinh -- inverse hyperbolic sine
• asinh(Number) -- inverse hyperbolic sine
• assert -- check whether something is true, raise an error if not
• assert(Expression) -- check whether something is true, raise an error if not
• assert(Thing) -- check whether something is true, raise an error if not
• assigning values
• associative algebras
• AssociativeExpression -- the class of associative expressions
• atan -- compute the arctangent of a number
• atan(CC) -- compute the arctangent of a number
• atan(RR) -- compute the arctangent of a number
• atan(RRi) -- compute the arctangent of a number
• atan2 -- compute an angle of a certain triangle
• atan2(RR,RR) -- compute an angle of a certain triangle
• atan2(RRi,RRi) -- compute an angle of a certain triangle
• atanh -- compute the hyperbolic arctangent of a number
• atanh(Constant) -- compute the hyperbolic arctangent of a number
• atanh(Number) -- compute the hyperbolic arctangent of a number
• atEndOfFile -- test for end of file
• atEndOfFile(File) -- test for end of file
• Authors -- an optional argument
• authors of Macaulay2 packages
• autoload -- arrange for a function to be loaded automatically
• autoload(Symbol,String) -- arrange for a function to be loaded automatically
• AuxiliaryFiles -- an optional argument
• backtrace -- whether a backtrace is displayed following an error message
• Bag -- the class of all bags
• Bag ? Bag -- the class of all bags
• Bareiss
• 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
• baseName(Holder) -- the base name of a generator
• baseName(IndexedVariable) -- the base name of a generator
• baseName(IndexedVariableTable) -- the base name of a generator
• baseName(RingElement) -- the base name of a generator
• baseName(Subscript) -- the base name of a generator
• baseName(Symbol) -- the base name of a generator
• baseName(Thing) -- the base name of a generator
• baseRing -- produce the ring from which a ring was formed
• baseRing(Ring) -- produce the ring from which a ring was formed
• baseRings -- store the list of base rings of a ring
• BaseRow -- an optional argument
• basic arithmetic of matrices
• basic commutative algebra
• basic construction, source and target of a ring map
• basic rings of numbers
• BasicList -- the class of all basic lists
• BasicList # ZZ -- get value from list, hash table, database, or string
• BasicList #? ZZ -- check existence of value in a list, hash table, database, or string
• basis -- basis or generating set of all or part of a ring, ideal or module
• basis(...,Degree=>...) -- basis or generating set of all or part of a ring, ideal or module
• basis(...,Limit=>...) -- basis or generating set of all or part of a ring, ideal or module
• basis(...,SourceRing=>...) -- basis or generating set of all or part of a ring, ideal or module
• basis(...,Strategy=>...) -- basis or generating set of all or part of a ring, ideal or module
• basis(...,Truncate=>...) -- basis or generating set of all or part of a ring, ideal or module
• basis(...,Variables=>...) -- basis or generating set of all or part of a ring, ideal or module
• basis(Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,InfiniteNumber,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,InfiniteNumber,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,InfiniteNumber,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,InfiniteNumber,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,List,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,List,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,List,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,List,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,ZZ,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,ZZ,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,ZZ,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,ZZ,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,InfiniteNumber,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,InfiniteNumber,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,InfiniteNumber,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,InfiniteNumber,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,List,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,List,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,List,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,List,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,ZZ,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,ZZ,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,ZZ,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(List,ZZ,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,InfiniteNumber,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,InfiniteNumber,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,InfiniteNumber,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,InfiniteNumber,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,List,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,List,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,List,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,List,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,Ring) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,ZZ,Ideal) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,ZZ,Matrix) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,ZZ,Module) -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,ZZ,Ring) -- 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
• BesselJ(ZZ,Constant) -- Bessel function of the first kind
• BesselJ(ZZ,Number) -- Bessel function of the first kind
• BesselY -- Bessel function of the second kind
• BesselY(ZZ,Constant) -- Bessel function of the second kind
• BesselY(ZZ,Number) -- Bessel function of the second kind
• Beta -- Beta function
• betti -- display or modify a Betti diagram
• betti(...,Minimize=>...) -- minimal betti numbers of a non-minimal free resolution
• betti(...,Weights=>...) -- view and set the weight vector of a Betti diagram
• betti(BettiTally) -- view and set the weight vector of a Betti diagram
• betti(ChainComplex) -- display or modify a Betti diagram
• betti(CoherentSheaf) -- display or modify a Betti diagram
• betti(GradedModule) -- display or modify a Betti diagram
• betti(GroebnerBasis) -- display or modify a Betti diagram
• betti(Ideal) -- display or modify a Betti diagram
• betti(Matrix) -- display or modify a Betti diagram
• betti(Module) -- display or modify a Betti diagram
• betti(MonomialIdeal) -- display or modify a Betti diagram
• BettiTally -- the class of all Betti tallies
• BettiTally ** BettiTally -- the class of all Betti tallies
• BettiTally ++ BettiTally -- the class of all Betti tallies
• BettiTally == BettiTally -- equality
• BettiTally Array -- the class of all Betti tallies
• BettiTally ZZ -- the class of all Betti tallies
• between -- insert something between elements of a list
• between(Thing,VisibleList) -- insert something between elements of a list
• Binary -- a hashtable with information about Macaulay2 operators
• binary methods
• BinaryOperation -- the class of all binary operation expressions
• Binomial -- value of an optional argument
• binomial -- binomial coefficient
• binomial(Constant,Constant) -- binomial coefficient
• binomial(Constant,Number) -- binomial coefficient
• binomial(Number,Constant) -- binomial coefficient
• binomial(Number,Number) -- binomial coefficient
• binomial(RingElement,ZZ) -- binomial coefficient
• BLAS
• blockMatrixForm -- global flag for block printing
• Body -- an optional argument
• Boolean -- the class of Boolean values
• Boolean == Boolean -- equality
• Boolean >> Function -- attaching options to a function
• Boolean xor Boolean -- exclusive disjunction
• Boost -- a collection of C++ source libraries
• borel -- make a Borel fixed submodule
• borel(Matrix) -- make a Borel fixed submodule
• borel(MonomialIdeal) -- 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
• CallLimit -- trace a function each time it's run
• cancelTask -- stop a task
• cancelTask(Task) -- stop a task
• capture -- evaluate Macaulay2 code and capture the output
• capture(...,PackageExports=>...) -- evaluate Macaulay2 code and capture the output
• capture(...,UserMode=>...) -- evaluate Macaulay2 code and capture the output
• capture(List) -- evaluate Macaulay2 code and capture the output
• capture(Net) -- evaluate Macaulay2 code and capture the output
• capture(String) -- 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 % CC -- a binary operator, usually used for remainder and reduction
• CC % QQ -- a binary operator, usually used for remainder and reduction
• CC % RR -- a binary operator, usually used for remainder and reduction
• CC % ZZ -- a binary operator, usually used for remainder and reduction
• CC * CC -- a binary operator, usually used for multiplication
• CC * QQ -- a binary operator, usually used for multiplication
• CC * RR -- a binary operator, usually used for multiplication
• CC * ZZ -- a binary operator, usually used for multiplication
• CC + CC -- a unary or binary operator, usually used for addition
• CC + QQ -- a unary or binary operator, usually used for addition
• CC + RR -- a unary or binary operator, usually used for addition
• CC + ZZ -- a unary or binary operator, usually used for addition
• CC - CC -- a unary or binary operator, usually used for negation or subtraction
• CC - QQ -- a unary or binary operator, usually used for negation or subtraction
• CC - RR -- a unary or binary operator, usually used for negation or subtraction
• CC - ZZ -- a unary or binary operator, usually used for negation or subtraction
• CC / CC -- a binary operator, usually used for division
• CC / QQ -- a binary operator, usually used for division
• CC / RR -- a binary operator, usually used for division
• CC / ZZ -- a binary operator, usually used for division
• CC // CC -- a binary operator, usually used for quotient
• CC // QQ -- a binary operator, usually used for quotient
• CC // RR -- a binary operator, usually used for quotient
• CC // ZZ -- a binary operator, usually used for quotient
• CC << ZZ
• CC == CC -- equality
• CC == QQ -- equality
• CC == RR -- equality
• CC == ZZ -- equality
• CC >> ZZ
• CC' -- the parent class of all rings of complex numbers
• cdd+
• ceiling -- ceiling function
• ceiling(Constant) -- ceiling function
• ceiling(Number) -- ceiling function
• Center -- value of an optional argument
• centerString -- center a string or net
• Certification -- an optional argument
• chain complexes
• ChainComplex -- the class of all chain complexes
• chainComplex -- make a chain complex
• ChainComplex ** ChainComplex -- tensor product
• ChainComplex ** ChainComplexMap -- tensor product
• ChainComplex ** GradedModule -- tensor product
• ChainComplex ** Module -- tensor product
• ChainComplex ** Ring -- a binary operator, usually used for tensor product or Cartesian product
• ChainComplex ++ ChainComplex -- direct sum
• ChainComplex == ChainComplex -- equality
• ChainComplex == ZZ -- equality
• ChainComplex ^ Array -- projection onto summand
• ChainComplex ^ ZZ -- access member, cohomological degree
• ChainComplex _ Array -- inclusion from summand
• ChainComplex _ ZZ -- component
• ChainComplex _ ZZ = Thing -- install component of chain complex
• ChainComplex Array -- degree shift
• chainComplex(GradedModule) -- make a chain complex from a graded module
• chainComplex(List) -- make a chain complex
• chainComplex(Matrix) -- make a small chain complex
• chainComplex(Ring) -- make an empty chain complex over a ring
• chainComplex(Sequence) -- make a chain complex
• ChainComplexMap -- the class of all maps between chain complexes
• ChainComplexMap * ChainComplexMap -- a binary operator, usually used for multiplication
• ChainComplexMap ** ChainComplex -- tensor product
• ChainComplexMap ** ChainComplexMap -- tensor product
• ChainComplexMap ** Module -- tensor product
• ChainComplexMap + ChainComplexMap -- a unary or binary operator, usually used for addition
• ChainComplexMap + RingElement -- a unary or binary operator, usually used for addition
• ChainComplexMap + ZZ -- a unary or binary operator, usually used for addition
• ChainComplexMap ++ ChainComplexMap -- direct sum
• ChainComplexMap - ChainComplexMap -- a unary or binary operator, usually used for negation or subtraction
• ChainComplexMap - RingElement -- a unary or binary operator, usually used for negation or subtraction
• ChainComplexMap == ChainComplexMap -- equality
• ChainComplexMap == RingElement -- equality
• ChainComplexMap == ZZ -- equality
• ChainComplexMap ^ Array -- component of map corresponding to summand of target
• ChainComplexMap ^ ZZ -- iterated composition
• ChainComplexMap _ Array -- component of map corresponding to summand of source
• ChainComplexMap _ ZZ -- component map
• ChainComplexMap _ ZZ = Thing -- install component of chain complex map
• ChainComplexMap Array -- degree shift
• changeBase -- change integer base
• changeBase(String,ZZ) -- change integer base
• changeBase(String,ZZ,ZZ) -- change integer base
• changeBase(ZZ,ZZ) -- change integer base
• ChangeMatrix -- an optional argument
• changes made for the next release
• changes to Macaulay2, by version
• changes, 1.0 and 1.1
• changes, 1.2
• changes, 1.3
• changes, 1.3.1
• changes, 1.4
• changes, 1.5
• changes, 1.6
• changes, 1.7
• changes, 1.8
• changes, 1.8.1
• changes, 1.8.2
• changes, 1.9
• changes, 1.9.1
• changes, 1.9.2
• changes, 1.10
• changes, 1.11
• changes, 1.12
• changes, 1.13
• changes, 1.14
• changes, 1.15
• changes, 1.16
• changes, 1.17
• changes, 1.18
• changes, 1.19
• changes, 1.19.1
• changes, 1.20
• changes, 1.21
• changes, 1.22
• char -- computes the characteristic of the ring or field
• char(AffineVariety) -- computes the characteristic of the ring or field
• char(InexactField) -- computes the characteristic of the ring or field
• char(ProjectiveVariety) -- computes the characteristic of the ring or field
• char(Ring) -- computes the characteristic of the ring or field
• characters -- get characters from a string
• check -- perform tests of a package
• check(...,UserMode=>...) -- perform tests of a package
• check(...,Verbose=>...) -- perform tests of a package
• check(List,Package) -- perform tests of a package
• check(List,String) -- perform tests of a package
• check(Package) -- perform tests of a package
• check(String) -- perform tests of a package
• check(ZZ,Package) -- perform tests of a package
• check(ZZ,String) -- perform tests of a package
• CheckDocumentation -- an optional argument
• checking your Macaulay2 installation -- and bookmarking the Macaulay2 documentation
• chi
• class -- class of an object
• clean -- Set to zero elements that are approximately zero
• clean(RR,Matrix) -- Set to zero elements that are approximately zero
• clean(RR,MutableMatrix) -- Set to zero elements that are approximately zero
• clean(RR,Number) -- Set to zero elements that are approximately zero
• clean(RR,RingElement) -- 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
• code(Command) -- display source code
• code(Function) -- display source code
• code(List) -- display source code
• code(Pseudocode) -- display source code
• code(Sequence) -- display source code
• code(Symbol) -- display source code
• code(TestInput) -- locate a package's tests
• code(ZZ) -- display source code
• codim -- compute the codimension
• codim(BettiTally) -- the class of all Betti tallies
• codim(CoherentSheaf) -- codimension of the support of a coherent sheaf on a projective variety
• codim(CoherentSheaf,Generic=>...)
• codim(Ideal) -- compute the codimension
• codim(Ideal,Generic=>...)
• codim(Module) -- codimension of the support of a module
• codim(Module,Generic=>...)
• codim(MonomialIdeal) -- compute the codimension
• codim(PolynomialRing) -- compute the codimension
• codim(PolynomialRing,Generic=>...)
• codim(ProjectiveVariety) -- codimension of the projective variety
• codim(ProjectiveVariety,Generic=>...)
• codim(QuotientRing) -- compute the codimension
• codim(QuotientRing,Generic=>...)
• CodimensionLimit -- an optional argument
• coefficient -- coefficient of a monomial
• CoefficientRing -- an optional argument
• coefficientRing -- get the coefficient ring
• coefficientRing(Ring) -- get the coefficient ring
• coefficients -- monomials and their coefficients
• coefficients(...,Monomials=>...) -- monomials and their coefficients
• coefficients(...,Variables=>...) -- monomials and their coefficients
• coefficients(Matrix) -- monomials and their coefficients
• coefficients(RingElement) -- monomials and their coefficients
• Cofactor
• coherent sheaves
• CoherentSheaf -- the class of all coherent sheaves
• CoherentSheaf (*) -- sum of twists
• CoherentSheaf ** CoherentSheaf -- tensor produce of coherent sheaves
• CoherentSheaf ++ CoherentSheaf -- direct sum of coherent sheaves
• CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves
• CoherentSheaf / Ideal -- quotient of coherent sheaves
• CoherentSheaf ^ ZZ -- direct sum
• CoherentSheaf ^** ZZ -- tensor power
• CoherentSheaf LowerBound -- the class of lower bound objects
• CoherentSheaf ZZ -- canonical twist of a coherent sheaf
• cohomCalg
• cohomology -- general cohomology functor
• coimage -- coimage of a map
• coimage(ChainComplexMap) -- coimage of a map
• coimage(GradedModuleMap) -- coimage of a map
• coimage(Matrix) -- coimage of a map
• coimage(RingMap) -- coimage of a map
• cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
• cokernel(ChainComplexMap) -- cokernel of a map of modules, graded modules, or chaincomplexes
• cokernel(GradedModuleMap) -- cokernel of a map of modules, graded modules, or chaincomplexes
• cokernel(Matrix) -- cokernel of a map of modules, graded modules, or chaincomplexes
• cokernel(RingElement) -- 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
• columnAdd(MutableMatrix,ZZ,Number,ZZ) -- add a multiple of one column to another
• columnAdd(MutableMatrix,ZZ,RingElement,ZZ) -- add a multiple of one column to another
• columnate -- arrange strings in columns
• columnMult -- multiply a column by a ring element
• columnMult(MutableMatrix,ZZ,Number) -- multiply a column by a ring element
• columnMult(MutableMatrix,ZZ,RingElement) -- multiply a column by a ring element
• columnPermute -- permute some columns
• columnPermute(MutableMatrix,ZZ,List) -- permute some columns
• columnRankProfile -- find the column rank profile of a mutable matrix
• columnRankProfile(MutableMatrix) -- find the column rank profile of a mutable matrix
• columnSwap -- interchange columns
• columnSwap(MutableMatrix,ZZ,ZZ) -- interchange columns
• combinatorial functions
• combine -- combine hash tables
• Command -- the class of all commands
• Command \ String -- apply a function to elements of a list
• Command \ VirtualTally -- apply a function to elements of a list
• Command \ VisibleList -- apply a function to elements of a list
• Command \\ Thing -- apply a function
• Command Thing -- 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
• commonest(Set) -- the most common elements of a list or tally
• commonest(Tally) -- the most common elements of a list or tally
• commonest(VisibleList) -- the most common elements of a list or tally
• commonRing -- find smallest containing ring
• commonRing(List) -- find smallest containing ring
• communicating with programs
• comodule -- submodule to quotient module
• comodule(Ideal) -- submodule to quotient module
• comodule(Module) -- 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 -- a Strategy option value
• complement -- find the minimal generators for cokernel of a matrix (low level form)
• complement(Matrix) -- find the minimal generators for cokernel of a matrix (low level form)
• complete
• complete(ChainComplex) -- complete the internal parts
• complete(ChainComplexMap)
• complete(GradedModule)
• CompleteIntersection -- value of an optional argument
• ComplexField -- the class of all complex fields
• components -- list the components of a direct sum
• components(ChainComplex)
• components(ChainComplexMap) -- list the components of a direct sum
• components(GradedModule) -- list the components of a direct sum
• components(GradedModuleMap) -- list the components of a direct sum
• components(Matrix) -- list the components of a direct sum
• components(Module) -- list the components of a direct sum
• compose -- composition as a pairing on Hom-modules
• compose(Module,Module,Module) -- composition as a pairing on Hom-modules
• compositions -- list the compositions of an integer
• compositions(ZZ,ZZ) -- list the compositions of an integer
• compress -- extract nonzero columns from a matrix
• compress(Matrix) -- extract nonzero columns from a matrix
• computing Groebner bases
• computing resolutions
• computing syzygies
• concatenate -- join strings
• concatenate(BasicList) -- join strings
• concatenate(Nothing) -- join strings
• concatenate(String) -- join strings
• concatenate(Symbol) -- join strings
• concatenate(ZZ) -- join strings
• concatenating matrices
• conditional execution -- if-then-else statements
• cone -- mapping cone of a chain map
• cone(ChainComplexMap) -- mapping cone of a chain map
• Configuration -- an optional argument
• conjugate -- complex conjugate
• conjugate(CC) -- complex conjugate
• conjugate(Number) -- complex conjugate
• conjugate(Partition) -- conjugate a partition
• connectionCount -- the number of connections
• Consequences -- side-effects of a function in a documentation node
• Constant
• Constant ! -- factorial
• Constant * Constant -- a binary operator, usually used for multiplication
• Constant * InexactNumber -- a binary operator, usually used for multiplication
• Constant * Number -- a binary operator, usually used for multiplication
• Constant * RingElement
• Constant + Constant -- a unary or binary operator, usually used for addition
• Constant + InexactNumber -- a unary or binary operator, usually used for addition
• Constant + Number -- a unary or binary operator, usually used for addition
• Constant + RingElement
• Constant - Constant -- a unary or binary operator, usually used for negation or subtraction
• Constant - InexactNumber -- a unary or binary operator, usually used for negation or subtraction
• Constant - Number -- a unary or binary operator, usually used for negation or subtraction
• Constant - RingElement
• Constant / Constant
• Constant / InexactNumber
• Constant / Number
• Constant / RingElement
• Constant == Constant
• Constant == InexactNumber
• Constant ^ Constant
• Constant ^ InexactNumber
• Constant ^ Number
• Constant ^ Ring -- lift to another ring
• Constant ^ RingFamily -- lift to another ring
• Constants -- an optional argument
• constructing maps between modules
• content -- the content of a polynomial
• content(RingElement) -- the content of a polynomial
• content(RingElement,RingElement) -- 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
• contract'(Matrix,Matrix) -- contract a matrix by a matrix, the dual notion
• contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Matrix,Number) -- contract a matrix by a matrix
• contract(Matrix,RingElement) -- contract a matrix by a matrix
• contract(Matrix,Vector) -- contract a matrix by a matrix
• contract(Number,Matrix) -- contract a matrix by a matrix
• contract(Number,Number) -- contract a matrix by a matrix
• contract(Number,RingElement) -- contract a matrix by a matrix
• contract(Number,Vector) -- contract a matrix by a matrix
• contract(RingElement,Matrix) -- contract a matrix by a matrix
• contract(RingElement,Number) -- contract a matrix by a matrix
• contract(RingElement,RingElement) -- contract a matrix by a matrix
• contract(RingElement,Vector) -- contract a matrix by a matrix
• contract(Vector,Matrix) -- contract a matrix by a matrix
• contract(Vector,Number) -- contract a matrix by a matrix
• contract(Vector,RingElement) -- contract a matrix by a matrix
• contract(Vector,Vector) -- contract a matrix by a matrix
• Contributors -- non-author contributors listed in a documentation node
• conventions for documentation
• copy -- copy an object
• copyDirectory
• copyDirectory(...,Exclude=>...)
• copyDirectory(...,FollowLinks=>...)
• copyDirectory(...,UpdateOnly=>...)
• copyDirectory(...,Verbose=>...)
• copyDirectory(String,String)
• copyFile
• copyFile(...,UpdateOnly=>...)
• copyFile(...,Verbose=>...)
• copyFile(String,String)
• COPYING-GPL-2 -- GNU General Public License, version 2
• COPYING-GPL-3 -- GNU General Public License, version 3
• copyright -- a string containing the copyright notice for Macaulay2
• Copyright and license
• Core -- the core part of Macaulay2
• cos -- compute the cosine
• cos(CC) -- compute the cosine
• cos(RR) -- compute the cosine
• cos(RRi) -- compute the cosine
• cosh -- compute the hyperbolic cosine
• cosh(CC) -- compute the hyperbolic cosine
• cosh(RR) -- compute the hyperbolic cosine
• cosh(RRi) -- compute the hyperbolic cosine
• cot -- cotangent
• cot(CC) -- cotangent
• cot(RR) -- cotangent
• cot(RRi) -- cotangent
• cotangentSheaf -- cotangent sheaf of a projective variety
• cotangentSheaf(...,Minimize=>...) -- cotangent sheaf of a projective variety
• cotangentSheaf(ProjectiveVariety) -- cotangent sheaf of a projective variety
• cotangentSheaf(ZZ,ProjectiveVariety) -- exterior powers of the cotangent sheaf of a projective variety
• coth -- hyperbolic cotangent
• coth(CC) -- hyperbolic cotangent
• coth(RR) -- hyperbolic cotangent
• coth(RRi) -- hyperbolic cotangent
• cover -- get the covering free module
• cover(CoherentSheaf) -- get the covering free module
• cover(GradedModule) -- get the covering free module
• cover(Matrix) -- get the covering free module
• cover(Module) -- get the covering free module
• coverMap -- the surjective map from a free module to a module corresponding to the generators
• 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
• createTask(Function) -- create a task
• createTask(Function,Thing) -- create a task
• creating a package
• creating an ideal
• creating and writing files
• csc -- cosecant
• csc(CC) -- cosecant
• csc(RR) -- cosecant
• csc(RRi) -- cosecant
• csch -- hyperbolic cosecant
• csch(CC) -- hyperbolic cosecant
• csch(RR) -- hyperbolic cosecant
• csch(RRi) -- hyperbolic cosecant
• csdp
• current -- the pseudocode that produced an error
• 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
• currentLayout -- relative locations of Macaulay2 files
• currentPackage -- the current package
• currentPosition -- the current position in the current source file
• currentRowNumber -- current row number of the current input file
• currentString -- evaluate a string
• currentTime -- get the current time
• Daniel R. Grayson
• Database -- the class of all database files
• Database # String -- get value from list, hash table, database, or string
• Database #? String -- check existence of value in a list, hash table, database, or string
• Date -- an optional argument
• David Eisenbud
• dd -- differential in a chain complex
• debug -- open the private dictionary of a package
• debug(Package) -- open the private dictionary of a package
• debugError -- a function to debug
• debugging
• DebuggingMode -- an optional argument
• debuggingMode -- whether to enter the debugger when an error occurs
• debugLevel -- current level debugging
• Decompose -- value of an optional argument
• decompose
• deepSplice -- remove all levels of subsequences from a sequence or list
• deepSplice(BasicList) -- remove all levels of subsequences from a sequence or list
• Default -- value of an optional argument
• default -- default member of a family
• default(InexactFieldFamily) -- default member of a family
• defaultPrecision -- default precision of numbers
• definition of product (block) orders
• Degree -- specify the degree of a map
• degree
• degree(BettiTally) -- the class of all Betti tallies
• degree(Ideal)
• degree(Module)
• degree(ProjectiveHilbertPolynomial)
• degree(ProjectiveVariety)
• degree(Ring)
• degree(RingElement)
• degree(RingElement,RingElement) -- degree with respect to a variable
• degree(Vector)
• DegreeGroup -- an optional argument
• degreeLength -- the length of the degree vector
• degreeLength(Monoid) -- the length of the degree vector
• degreeLength(Ring) -- 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
• degrees(CoherentSheaf) -- degrees of generators
• degrees(FractionField) -- degrees of generators
• degrees(Ideal) -- degrees of generators
• degrees(Matrix) -- degrees of target and source
• degrees(Module) -- degrees of generators
• degrees(Monoid) -- degrees of generators
• degrees(QuotientRing) -- degrees of generators
• degrees(Ring) -- degrees of generators
• degreesMonoid -- the ring or monoid of degrees
• degreesMonoid(List) -- the ring or monoid of degrees
• degreesMonoid(Monoid) -- the ring or monoid of degrees
• degreesMonoid(Ring) -- the ring or monoid of degrees
• degreesMonoid(ZZ) -- the ring or monoid of degrees
• degreesRing -- the ring or monoid of degrees
• degreesRing(List) -- the ring or monoid of degrees
• degreesRing(Monoid) -- the ring or monoid of degrees
• degreesRing(Ring) -- the ring or monoid of degrees
• degreesRing(ZZ) -- the ring or monoid of degrees
• delete -- delete some elements of a list
• delete(Thing,BasicList) -- delete some elements of a list
• demark -- insert a string between elements of a list of strings
• denominator -- denominator of a fraction
• denominator(Divide) -- denominator of a fraction
• Dense -- an optional argument
• Density -- an optional argument
• depth -- depth of a net
• depth(Net) -- depth of a net
• depth(String) -- depth of a net
• Descending -- specify descending order
• Descent
• Describe -- the class of the output of describe
• describe -- real description
• describe(AffineVariety) -- real description
• describe(CoherentSheaf) -- real description
• describe(FractionField) -- real description
• describe(GaloisField) -- real description
• describe(Matrix) -- real description
• describe(Module) -- real description
• describe(Monoid) -- real description
• describe(PolynomialRing) -- real description
• describe(ProjectiveVariety) -- real description
• describe(QuotientRing) -- real description
• describe(RingMap) -- real description
• describe(Thing) -- real description
• determinant -- determinant of a matrix
• determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• determinant(Matrix) -- determinant of a matrix
• determinant(MutableMatrix) -- determinant of a matrix
• determinants and minors
• Developer's Corner
• diagonalMatrix -- make a diagonal matrix
• diagonalMatrix(List) -- make a diagonal matrix from a list
• diagonalMatrix(Matrix) -- make a diagonal matrix from entries of a matrix
• diagonalMatrix(Ring,List) -- make a diagonal matrix from a list
• diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
• diagonalMatrix(RingFamily,List) -- make a diagonal matrix from a list
• diagonalMatrix(RingFamily,ZZ,ZZ,List) -- make a diagonal matrix from a list
• diagonalMatrix(ZZ,ZZ,List) -- make a diagonal matrix from a list
• diameter -- diameter of an interval
• diameter(RRi) -- diameter of an interval
• Dictionary -- the class of all dictionaries
• dictionary -- determine the dictionary to which a symbol belongs
• dictionary(Keyword) -- determine the dictionary to which a symbol belongs
• dictionary(Symbol) -- determine the dictionary to which a symbol belongs
• dictionary(Thing) -- determine the dictionary to which a symbol belongs
• dictionaryPath
• diff -- differentiate or take difference
• diff and contract
• diff' -- differentiate a matrix by a matrix, the dual notion
• diff'(Matrix,Matrix) -- differentiate a matrix by a matrix, the dual notion
• diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• diff(Matrix,RingElement) -- differentiation
• diff(Matrix,Vector) -- differentiate a matrix by a matrix
• diff(ProjectiveHilbertPolynomial)
• diff(ProjectiveHilbertPolynomial,ZZ)
• diff(RingElement,Matrix) -- differentiate each entry of a matrix
• diff(RingElement,RingElement) -- differentiation
• diff(RingElement,Vector) -- differentiate a matrix by a matrix
• diff(Vector,Matrix) -- differentiate a matrix by a matrix
• diff(Vector,RingElement) -- differentiate a matrix by a matrix
• diff(Vector,Vector) -- differentiate a matrix by a matrix
• difference -- difference
• differentiation
• Digamma -- Digamma function
• Digamma(RR) -- Digamma function
• dim -- compute the Krull dimension
• dim(AffineVariety) -- dimension of the affine variety
• dim(FractionField) -- compute the Krull dimension
• dim(GaloisField) -- compute the Krull dimension
• dim(Ideal) -- compute the Krull dimension
• dim(InexactField) -- compute the Krull dimension
• dim(Module) -- compute the Krull dimension
• dim(MonomialIdeal) -- compute the Krull dimension
• dim(PolynomialRing) -- compute the Krull dimension
• dim(ProjectiveHilbertPolynomial) -- the degree of the Hilbert polynomial
• dim(ProjectiveVariety) -- dimension of the projective variety
• dim(QuotientRing) -- compute the Krull dimension
• dim(Ring) -- compute the Krull dimension
• dimension, codimension, and degree
• directSum -- direct sum of modules or maps
• directSum(ChainComplex) -- direct sum of modules or maps
• directSum(GradedModule) -- direct sum of modules or maps
• directSum(List) -- direct sum of modules or maps
• directSum(Matrix) -- direct sum of modules or maps
• directSum(Module) -- direct sum of modules or maps
• directSum(Option) -- direct sum of modules or maps
• directSum(Sequence) -- direct sum of modules or maps
• disassemble -- disassemble pseudocode or a function
• dismiss -- dismiss a package
• dismiss(Package) -- dismiss a package
• dismiss(String) -- dismiss a package
• Dispatch -- make a new method function
• Divide -- the class of all divide expressions
• divideByVariable -- divide all columns by a (power of a) variable
• divideByVariable(Matrix,RingElement) -- divide all columns by a (power of a) variable
• divideByVariable(Matrix,RingElement,ZZ) -- divide all columns by a (power of a) variable
• DivideConquer -- an optional argument
• division in polynomial rings with monomials less than 1
• do -- loop control
• document -- create a documentation node
• document(...,Acknowledgement=>...) -- acknowledgements listed in a documentation node
• document(...,BaseFunction=>...) -- the basename of a function in a documentation node
• document(...,Caveat=>...) -- warnings or limitations listed in a documentation node
• document(...,Consequences=>...) -- side-effects of a function in a documentation node
• document(...,Contributors=>...) -- non-author contributors listed in a documentation node
• document(...,ExampleFiles=>...) -- data files corresponding to a documentation node
• document(...,Headline=>...) -- headline of a documentation node
• document(...,Inputs=>...) -- inputs for a function in a documentation node
• document(...,Key=>...) -- key of a documentation node
• document(...,Outputs=>...) -- outputs for a function in a documentation node
• document(...,References=>...) -- references listed in a documentation node
• document(...,SeeAlso=>...) -- cross-references to other documentation nodes
• document(...,SourceCode=>...) -- sources displayed in a documentation node
• document(...,Subnodes=>...) -- a menu of documentation nodes
• document(...,Usage=>...) -- ways to use a function in a documentation node
• document(List) -- create a documentation node
• documentation keys
• DocumentTag -- the class of all document tags
• Down -- monomial ordering
• drop -- drop some elements from a list or sequence.
• drop(BasicList,List) -- drop some elements from a list or sequence.
• drop(BasicList,ZZ) -- drop some elements from a list or sequence.
• dual -- dual module or map
• dual(BettiTally) -- the class of all Betti tallies
• dual(ChainComplex) -- dual
• dual(ChainComplexMap) -- dual of a chain complex
• dual(CoherentSheaf) -- dual coherent sheaf
• dual(Matrix) -- dual of a map
• dual(Module) -- dual module
• dual(MonomialIdeal) -- the Alexander dual of a monomial ideal
• dual(MonomialIdeal,List) -- the Alexander dual
• dual(MonomialIdeal,List,Strategy=>...)
• dual(MonomialIdeal,RingElement) -- the Alexander dual
• dual(MonomialIdeal,RingElement,Strategy=>...)
• dual(MonomialIdeal,Strategy=>...)
• Dynamic
• eagonNorthcott -- Eagon-Northcott complex of a matrix of linear forms
• eagonNorthcott(Matrix) -- Eagon-Northcott complex of a matrix of linear forms
• echoOff -- turn off echoing
• echoOff(File) -- turn off echoing
• echoOn -- turn on echoing
• echoOn(File) -- turn on echoing
• edit -- edit source code
• editing Macaulay2 code with emacs
• eigenvalues -- find eigenvalues of a matrix
• eigenvalues(...,Hermitian=>...) -- Hermitian=>true means assume the matrix is symmetric or Hermitian
• eigenvalues(Matrix) -- find eigenvalues of a matrix
• eigenvalues(MutableMatrix) -- find eigenvalues of a matrix
• eigenvectors -- find eigenvectors of a matrix over RR or CC
• eigenvectors(...,Hermitian=>...) -- Hermitian=>true means assume the matrix is symmetric or Hermitian
• eigenvectors(Matrix) -- find eigenvectors of a matrix over RR or CC
• eigenvectors(MutableMatrix) -- find eigenvectors of a matrix over RR or CC
• eint -- exponential integral
• eint(RR) -- exponential integral
• elapsedTime -- time a computation using time elapsed
• elapsedTiming -- time a computation using time elapsed
• Elementary uses of Groebner bases I. Math 634 Fall 2005
• elements -- list of elements
• elements(Set) -- list of elements
• elements(Tally) -- list of elements
• Eliminate -- elimination order
• elimination of variables
• else -- condition testing
• Email -- the preamble of a package
• End -- module of endomorphisms
• end -- stop loading a file
• endl -- end an output line
• endPackage -- end a new package
• endPackage(String) -- end a new package
• Engine -- specify whether a ring is handled by the engine
• engine
• engineDebugLevel -- current engine debugging level
• EngineRing -- the class of rings handled by the engine
• entries -- lists the entries of a matrix
• entries(Matrix) -- lists the entries of a matrix
• entries(MutableMatrix) -- lists the entries of a matrix
• entries(Vector) -- lists the entries of a vector
• environment -- the environment variables
• equality and containment
• equality and containment of modules
• Equation -- the class of all equation expressions
• Equation == Equation -- equality
• Equation == Holder -- equality
• erase -- remove a global symbol
• erf -- error function
• erfc -- complementary error function
• error -- deliver error message
• error handling -- signalling and trapping errors
• errorDepth -- set the error printing depth
• euler -- Euler characteristic
• euler(CoherentSheaf) -- Euler characteristic of coherent sheaf
• euler(Ideal) -- Euler characteristic
• euler(Module) -- Euler characteristic
• euler(ProjectiveHilbertPolynomial) -- constant term of the Hilbert polynomial
• euler(ProjectiveVariety) -- topological Euler characteristic of a (smooth) projective variety
• euler(Ring) -- Euler characteristic
• EulerConstant -- the Euler-Mascheroni constant
• eulers -- list the sectional Euler characteristics
• eulers(CoherentSheaf) -- list the sectional Euler characteristics
• eulers(Ideal) -- list the sectional Euler characteristics
• eulers(Module) -- list the sectional Euler characteristics
• eulers(Ring) -- list the sectional Euler characteristics
• evaluation and composition of ring maps
• even -- tell whether an integer is even
• EXAMPLE -- hypertext EXAMPLE item
• EXAMPLE(PRE) -- hypertext EXAMPLE item
• EXAMPLE(String) -- hypertext EXAMPLE item
• EXAMPLE(VisibleList) -- hypertext EXAMPLE item
• ExampleFiles -- data files corresponding to a documentation node
• examples -- list the examples in documentation
• examples of specifying alternate monomial orders
• examples(Thing) -- list the examples in documentation
• Exclude -- an optional argument
• exec -- execute another program
• exit -- exit the program
• exp -- exponential function
• exp(CC) -- exponential function
• exp(RingElement)
• exp(RR) -- exponential function
• exp(RRi) -- exponential function
• expm1 -- exponential minus 1
• expm1(RR) -- exponential minus 1
• expm1(RRi) -- exponential minus 1
• exponents -- the exponents of a polynomial
• exponents(MonoidElement) -- the exponents of a polynomial
• exponents(RingElement) -- the exponents of a polynomial
• export -- export symbols from a package
• export(List) -- export symbols from a package
• export(String) -- export symbols from a package
• exportFrom -- export symbols from a package's private dictionary
• exportFrom(Package,List) -- export symbols from a package's private dictionary
• exportMutable -- export mutable symbols from a package
• exportMutable(List) -- export mutable symbols from a package
• exportMutable(String) -- export mutable symbols from a package
• Expression -- the class of all expressions
• expression -- convert to an expression
• Expression != Expression -- the class of all expressions
• Expression != Holder -- the class of all expressions
• Expression != Thing -- the class of all expressions
• Expression % Expression -- the class of all expressions
• Expression % Holder -- the class of all expressions
• Expression % Thing -- the class of all expressions
• Expression & Expression -- the class of all expressions
• Expression & Holder -- the class of all expressions
• Expression & Thing -- the class of all expressions
• Expression - Expression -- the class of all expressions
• Expression - Holder -- the class of all expressions
• Expression - Thing -- the class of all expressions
• Expression .. Expression -- the class of all expressions
• Expression .. Holder -- the class of all expressions
• Expression .. Thing -- the class of all expressions
• Expression ..< Expression -- the class of all expressions
• Expression ..< Holder -- the class of all expressions
• Expression ..< Thing -- the class of all expressions
• Expression / Expression -- the class of all expressions
• Expression / Holder -- the class of all expressions
• Expression / Thing -- the class of all expressions
• Expression : Expression -- the class of all expressions
• Expression : Holder -- the class of all expressions
• Expression : Thing -- the class of all expressions
• Expression <== Expression -- the class of all expressions
• Expression <== Holder -- the class of all expressions
• Expression <== Thing -- the class of all expressions
• Expression <=== Expression -- the class of all expressions
• Expression <=== Holder -- the class of all expressions
• Expression <=== Thing -- the class of all expressions
• Expression <==> Expression -- the class of all expressions
• Expression <==> Holder -- the class of all expressions
• Expression <==> Thing -- the class of all expressions
• Expression ===> Expression -- the class of all expressions
• Expression ===> Holder -- the class of all expressions
• Expression ===> Thing -- the class of all expressions
• Expression ==> Expression -- the class of all expressions
• Expression ==> Holder -- the class of all expressions
• Expression ==> Thing -- the class of all expressions
• Expression @ Expression -- the class of all expressions
• Expression @ Holder -- the class of all expressions
• Expression @ Thing -- the class of all expressions
• Expression @@ Expression -- the class of all expressions
• Expression @@ Holder -- the class of all expressions
• Expression @@ Thing -- the class of all expressions
• Expression ^ Expression -- the class of all expressions
• Expression ^ Holder -- the class of all expressions
• Expression ^ Thing -- the class of all expressions
• Expression ^** Expression -- the class of all expressions
• Expression ^** Holder -- the class of all expressions
• Expression ^** Thing -- the class of all expressions
• Expression ^^ Expression -- the class of all expressions
• Expression ^^ Holder -- the class of all expressions
• Expression ^^ Thing -- the class of all expressions
• Expression _ Expression -- the class of all expressions
• Expression _ Holder -- the class of all expressions
• Expression _ Thing -- the class of all expressions
• Expression | Expression -- the class of all expressions
• Expression | Holder -- the class of all expressions
• Expression | Thing -- the class of all expressions
• Expression |- Expression -- the class of all expressions
• Expression |- Holder -- the class of all expressions
• Expression |- Thing -- the class of all expressions
• Expression || Expression -- the class of all expressions
• Expression || Holder -- the class of all expressions
• Expression || Thing -- the class of all expressions
• Expression and Expression -- the class of all expressions
• Expression and Holder -- the class of all expressions
• Expression and Thing -- the class of all expressions
• Expression Expression -- the class of all expressions
• Expression Holder -- the class of all expressions
• Expression or Expression -- the class of all expressions
• Expression or Holder -- the class of all expressions
• Expression or Thing -- the class of all expressions
• Expression Thing -- the class of all expressions
• Expression xor Expression -- the class of all expressions
• Expression xor Holder -- the class of all expressions
• Expression xor Thing -- the class of all expressions
• Ext -- compute an Ext module
• Ext(Ideal,Ideal) -- total Ext module
• Ext(Ideal,Module) -- total Ext module
• Ext(Ideal,Ring) -- total Ext module
• Ext(Module,Ideal) -- total Ext module
• Ext(Module,Module) -- total Ext module
• Ext(Module,Ring) -- total Ext module
• Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• Ext^ZZ(CoherentSheaf,SheafOfRings) -- global Ext
• Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
• Ext^ZZ(Ideal,Ideal) -- Ext module
• Ext^ZZ(Ideal,Matrix) -- map between Ext modules
• Ext^ZZ(Ideal,Module) -- Ext module
• Ext^ZZ(Ideal,Ring) -- Ext module
• Ext^ZZ(Matrix,Ideal) -- map between Ext modules
• Ext^ZZ(Matrix,Module) -- map between Ext modules
• Ext^ZZ(Matrix,Ring) -- map between Ext modules
• Ext^ZZ(Module,Ideal) -- Ext module
• Ext^ZZ(Module,Matrix) -- map between Ext modules
• Ext^ZZ(Module,Module) -- Ext module
• Ext^ZZ(Module,Ring) -- Ext module
• Ext^ZZ(SheafOfRings,CoherentSheaf) -- global Ext
• Ext^ZZ(SheafOfRings,SheafOfRings) -- global Ext
• Ext^ZZ(SheafOfRings,SumOfTwists) -- global Ext
• extend -- extend a module map to a chain map, if possible
• extend(...,Verify=>...) -- extend a module map to a chain map, if possible
• extend(ChainComplex,ChainComplex,Matrix) -- extend a module map to a chain map, if possible
• exterior algebras
• exterior power of a matrix
• exterior power of a module
• exteriorPower -- exterior power
• exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• exteriorPower(ZZ,CoherentSheaf) -- exterior power
• exteriorPower(ZZ,Matrix) -- exterior power of a matrix
• exteriorPower(ZZ,Module) -- exterior power of a module
• extracting elements
• extracting generators of an ideal
• extracting information about a matrix
• extracting information from chain complexes
• factor -- factor a ring element or a ZZ-module
• factor(Module) -- factor a ZZ-module
• factor(QQ) -- factor a ring element
• factor(RingElement) -- factor a ring element
• factor(ZZ) -- factor a ring element
• factoring polynomials
• false
• Fano -- Fano scheme
• Fano(ZZ,Ideal) -- Fano scheme
• Fano(ZZ,Ideal,Ring) -- Fano scheme
• FastNonminimal -- compute a non-minimal graded free resolution
• fflas-ffpack
• File -- the class of all files
• File << Manipulator -- print to a file
• File << Net -- print to a file
• File << String -- print to a file
• File << Symbol -- print to a file
• File << Thing -- print to a file
• file manipulation -- Unix file manipulation functions
• fileDictionaries -- local dictionaries for loaded files
• fileExecutable
• fileExecutable(String)
• 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
• fileMode(File) -- get file mode
• fileMode(String) -- get file mode
• fileMode(ZZ,File) -- set file mode
• fileMode(ZZ,String) -- set file mode
• FileName -- an optional argument
• FilePosition -- the class of all file positions
• fileReadable
• fileReadable(String)
• fileTime -- get or set file modified time
• fileWritable
• fileWritable(String)
• fillMatrix -- fill a mutable matrix with random numbers
• fillMatrix(...,Density=>...) -- fill a mutable matrix with random numbers
• fillMatrix(...,Height=>...) -- fill a mutable matrix with random numbers
• fillMatrix(...,UpperTriangular=>...) -- fill a mutable matrix with random numbers
• fillMatrix(MutableMatrix) -- fill a mutable matrix with random numbers
• fillMatrix(MutableMatrix,ZZ) -- fill a mutable matrix with random numbers
• findFiles -- find files recursively
• findFiles(...,Exclude=>...) -- find files recursively
• findFiles(...,FollowLinks=>...) -- find files recursively
• findFiles(List) -- find files recursively
• findFiles(String) -- find files recursively
• findHeft -- find a heft vector for a list of degrees
• findHeft(...,DegreeRank=>...) -- find a heft vector for a list of degrees
• findHeft(List) -- find a heft vector for a list of degrees
• finding the Macaulay2 files
• finding your files under cygwin
• FindOne -- find a primitive element
• findProgram -- load external program
• findProgram(...,AdditionalPaths=>...) -- load external program
• findProgram(...,MinimumVersion=>...) -- load external program
• findProgram(...,Prefix=>...) -- load external program
• findProgram(...,RaiseError=>...) -- load external program
• findProgram(...,Verbose=>...) -- load external program
• findProgram(String) -- load external program
• findProgram(String,List) -- load external program
• findProgram(String,String) -- load external program
• findSynonyms -- find synonyms of symbols
• findSynonyms(Symbol) -- find synonyms of symbols
• fine control of a Groebner basis computation
• finite field extensions
• finite fields
• First -- an optional argument
• first -- first element of a list
• firstkey -- get the first key
• fittingIdeal -- Fitting ideal of a module
• fittingIdeal(ZZ,Module) -- Fitting ideal of a module
• flagLookup -- flag a symbol
• FlatMonoid
• flatten -- flatten a nested list or a matrix
• flatten(Matrix) -- flatten a nested list or a matrix
• flatten(VisibleList) -- flatten a nested list or a matrix
• flattenRing -- write a ring as a (quotient of a) polynomial ring
• flattenRing(...,CoefficientRing=>...) -- optionally specify the desired coefficient ring of the flattened ring
• flattenRing(...,Result=>...) -- optionally specify which output(s) to return (see Description for details)
• flattenRing(GaloisField) -- write a ring as a (quotient of a) polynomial ring
• flattenRing(Ideal) -- write a ring as a (quotient of a) polynomial ring
• flattenRing(PolynomialRing) -- write a ring as a (quotient of a) polynomial ring
• flattenRing(QuotientRing) -- write a ring as a (quotient of a) polynomial ring
• flattenRing(Ring) -- write a ring as a (quotient of a) polynomial ring
• Flexible -- a hashtable with information about Macaulay2 operators
• FLINT
• flip -- matrix of commutativity of tensor product
• flip(Module,Module) -- matrix of commutativity of tensor product
• floor -- floor function
• floor(Constant) -- floor function
• floor(Number) -- floor function
• flush -- flush output to file
• fold -- apply a binary operator repeatedly
• fold(Function,Thing) -- apply a binary operator repeatedly
• fold(Function,Thing,Thing) -- apply a binary operator repeatedly
• fold(Function,VisibleList) -- apply a binary operator repeatedly
• fold(VisibleList,Function) -- apply a binary operator repeatedly
• fold(VisibleList,Thing,Function) -- apply a binary operator repeatedly
• FollowLinks -- an optional argument
• for -- for loops
• forceGB -- declare that the columns of a matrix are a Gröbner basis
• forceGB(...,ChangeMatrix=>...) -- inform Macaulay2 about the change of basis matrix from GB to generators
• forceGB(...,MinimalMatrix=>...) -- specify the minimal generator matrix
• forceGB(...,SyzygyMatrix=>...) -- specify the syzygy matrix
• forceGB(Matrix) -- declare that the columns of a matrix are a Gröbner basis
• fork -- fork the process
• format -- format a string or a real number
• format and display of matrices in Macaulay2
• format(CC) -- format a string or a real number
• format(DocumentTag) -- the class of all document tags
• format(RR) -- format a string or a real number
• format(String) -- format a string or a real number
• formation -- recover the methods used to make a module
• formation(ChainComplex) -- recover the methods used to make a module
• formation(ChainComplexMap) -- recover the methods used to make a module
• formation(GradedModule) -- recover the methods used to make a module
• formation(GradedModuleMap) -- recover the methods used to make a module
• formation(Module) -- recover the methods used to make a module
• frac -- construct a fraction field
• frac(EngineRing) -- construct a fraction field
• frac(FractionField) -- construct a fraction field
• frac(Ring) -- construct a fraction field
• fraction
• fraction fields
• fraction(RingElement,RingElement)
• FractionField -- the class of all fraction fields
• frames -- get the frames associated to a closure
• frames(Function) -- get the frames associated to a closure
• frames(Pseudocode) -- get the frames associated to a closure
• frames(Sequence) -- get the frames associated to a closure
• frames(Symbol) -- get the frames associated to a closure
• free modules
• free resolutions of modules
• frobby
• from -- loop control
• Function -- the class of all functions
• Function @@ Function -- composition of functions
• Function \ Ideal -- apply a function to generators of an ideal
• Function \ String -- apply a function to elements of a list
• Function \ VirtualTally -- apply a function to elements of a list
• Function \ VisibleList -- apply a function to elements of a list
• Function \\ Thing -- apply a function
• Function _ Thing -- attach the first argument to a function of two or more arguments
• function documentation template
• function name documentation template
• Function Thing -- function application
• 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
• gb(...,Algorithm=>...) -- compute a Gröbner basis
• gb(...,BasisElementLimit=>...) -- compute a Gröbner basis
• gb(...,ChangeMatrix=>...) -- compute a Gröbner basis
• gb(...,CodimensionLimit=>...) -- compute a Gröbner basis
• gb(...,DegreeLimit=>...) -- compute a Gröbner basis
• gb(...,GBDegrees=>...) -- compute a Gröbner basis
• gb(...,HardDegreeLimit=>...) -- compute a Gröbner basis
• gb(...,Hilbert=>...) -- compute a Gröbner basis
• gb(...,MaxReductionCount=>...) -- compute a Gröbner basis
• gb(...,PairLimit=>...) -- compute a Gröbner basis
• gb(...,StopBeforeComputation=>...) -- compute a Gröbner basis
• gb(...,StopWithMinimalGenerators=>...) -- compute a Gröbner basis
• gb(...,Strategy=>...) -- compute a Gröbner basis
• gb(...,SubringLimit=>...) -- compute a Gröbner basis
• gb(...,Syzygies=>...) -- compute a Gröbner basis
• gb(...,SyzygyLimit=>...) -- compute a Gröbner basis
• gb(...,SyzygyRows=>...) -- compute a Gröbner basis
• gb(Ideal) -- compute a Gröbner basis
• gb(Matrix) -- compute a Gröbner basis
• gb(Module) -- compute a Gröbner basis
• GBDegrees -- an optional argument
• gbRemove -- remove Gröbner basis
• gbRemove(Ideal) -- remove Gröbner basis
• gbRemove(Matrix) -- remove Gröbner basis
• gbRemove(Module) -- remove Gröbner basis
• gbSnapshot -- the Gröbner basis matrix as so far computed
• gbSnapshot(Ideal) -- the Gröbner basis matrix as so far computed
• gbSnapshot(Matrix) -- the Gröbner basis matrix as so far computed
• gbSnapshot(Module) -- the Gröbner basis matrix as so far computed
• gbTrace -- provide tracing output during various computations in the engine.
• GC garbage collector
• gcd -- greatest common divisor
• gcd(List) -- greatest common divisor
• gcd(QQ,QQ) -- greatest common divisor
• gcd(QQ,ZZ) -- greatest common divisor
• gcd(RingElement,RingElement) -- greatest common divisor
• gcd(RingElement,ZZ) -- greatest common divisor
• gcd(Sequence) -- greatest common divisor
• gcd(ZZ,QQ) -- greatest common divisor
• gcd(ZZ,RingElement) -- greatest common divisor
• gcd(ZZ,ZZ) -- greatest common divisor
• gcdCoefficients -- gcd with coefficients
• gcdCoefficients(RingElement,RingElement) -- gcd with coefficients
• gcdCoefficients(ZZ,ZZ) -- gcd with coefficients
• GCstats -- information about the status of the garbage collector
• genera -- list of the successive linear sectional arithmetic genera
• genera(CoherentSheaf) -- list of the successive linear sectional arithmetic genera
• genera(Ideal) -- list of the successive linear sectional arithmetic genera
• genera(Module) -- list of the successive linear sectional arithmetic genera
• genera(ProjectiveVariety) -- list of the successive linear sectional arithmetic genera
• genera(Ring) -- list of the successive linear sectional arithmetic genera
• GeneralOrderedMonoid -- the class of all ordered free commutative monoids
• GenerateAssertions -- trace a function each time it's run
• generateAssertions -- generate assert statements from experimental input
• generateAssertions(String) -- generate assert statements from experimental input
• generator -- provide a single generator
• generator(Ideal) -- provide a single generator
• generator(Module) -- provide a single generator
• generators -- provide matrix or list of generators
• generators of ideals and modules
• generators(...,CoefficientRing=>...) -- the list of generators of a ring
• generators(GroebnerBasis) -- the generator matrix of a Gröbner basis
• generators(Ideal) -- the generator matrix of an ideal
• generators(Module) -- the generator matrix of a module
• generators(Monoid) -- list of generators
• generators(MonomialIdeal) -- the generator matrix of an ideal
• generators(Ring) -- the list of generators of a ring
• Generic -- an optional argument
• genericMatrix -- make a generic matrix of variables
• genericMatrix(Ring,RingElement,ZZ,ZZ) -- make a generic matrix of variables
• genericMatrix(Ring,ZZ,ZZ) -- make a generic matrix of variables
• genericSkewMatrix -- make a generic skew symmetric matrix of variables
• genericSkewMatrix(Ring,RingElement,ZZ) -- make a generic skew symmetric matrix of variables
• genericSkewMatrix(Ring,ZZ) -- make a generic skew symmetric matrix of variables
• genericSymmetricMatrix -- make a generic symmetric matrix
• genericSymmetricMatrix(Ring,RingElement,ZZ) -- make a generic symmetric matrix
• genericSymmetricMatrix(Ring,ZZ) -- make a generic symmetric matrix
• genus -- arithmetic genus
• genus(CoherentSheaf) -- arithmetic genus
• genus(Ideal) -- arithmetic genus
• genus(Module) -- arithmetic genus
• genus(ProjectiveVariety) -- arithmetic genus
• genus(Ring) -- arithmetic genus
• get -- get the contents of a file
• get(File) -- get the contents of a file
• get(String) -- get the contents of a file
• getc -- get a byte
• getc(File) -- get a byte
• getChangeMatrix -- get the change of basis matrix
• getChangeMatrix(GroebnerBasis) -- get the change of basis matrix
• getenv -- get value of environment variable
• getenv(String) -- 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
• getPrimeWithRootOfUnity(...,Range=>...) -- find a prime p with a primitive n-th root of unity r in ZZ/p
• getPrimeWithRootOfUnity(ZZ,ZZ) -- 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
• getting help or reporting bugs
• getting input from the user
• getting started
• getWWW -- get a web page
• getWWW(String) -- get a web page
• getWWW(String,Nothing) -- get a web page
• getWWW(String,String) -- get a web page
• GF -- make a finite field
• GF(...,PrimitiveElement=>...) -- make a finite field
• GF(...,SizeLimit=>...) -- make a finite field
• GF(...,Strategy=>...) -- make a finite field
• GF(...,Variable=>...) -- make a finite field
• GF(Ring) -- make a finite field
• GF(ZZ) -- make a finite field
• GF(ZZ,ZZ) -- make a finite field
• gfan
• givaro
• GLex -- graded lexicographic ordering
• Global -- monomial 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
• GlobalHookStore -- add a hook function to an object for later processing
• globalReleaseFunction -- the standard method for the global variable release hook
• GlobalReleaseHook
• GNU MP
• Gröbner bases
• graded and multigraded polynomial rings
• graded modules
• GradedModule -- the class of all graded modules
• gradedModule -- make a graded module
• GradedModule ** ChainComplex -- tensor product
• GradedModule ** GradedModule -- a binary operator, usually used for tensor product or Cartesian product
• GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product
• GradedModule ++ GradedModule -- direct sum
• GradedModule ++ Module -- direct sum of modules
• GradedModule == GradedModule -- equality
• GradedModule _ ZZ -- component
• GradedModule Array -- degree shift
• gradedModule(ChainComplex) -- make a graded module
• gradedModule(List) -- make a graded module
• gradedModule(Module) -- make a graded module
• gradedModule(Sequence) -- make a graded module
• GradedModuleMap -- the class of all maps between graded modules
• gradedModuleMap -- make a map of graded modules
• GradedModuleMap * GradedModuleMap -- a binary operator, usually used for multiplication
• GradedModuleMap + GradedModuleMap -- a unary or binary operator, usually used for addition
• GradedModuleMap + RingElement -- a unary or binary operator, usually used for addition
• GradedModuleMap ++ GradedModuleMap -- direct sum of maps
• GradedModuleMap - GradedModuleMap -- a unary or binary operator, usually used for negation or subtraction
• GradedModuleMap - RingElement -- a unary or binary operator, usually used for negation or subtraction
• GradedModuleMap == GradedModuleMap -- equality
• GradedModuleMap == RingElement -- equality
• GradedModuleMap == ZZ -- equality
• GradedModuleMap ^ Array -- component of map corresponding to summand of target
• GradedModuleMap ^ ZZ -- iterated composition
• GradedModuleMap _ Array -- component of map corresponding to summand of source
• GradedModuleMap _ ZZ -- component map
• GradedModuleMap | GradedModuleMap -- a binary operator, often used for horizontal concatenation
• GradedModuleMap || GradedModuleMap -- a binary operator, often used for vertical concatenation
• gradedModuleMap(List) -- make a map of graded modules
• gradedModuleMap(Matrix) -- make a map of graded modules
• gradedModuleMap(Sequence) -- make a map of graded modules
• graphIdeal -- the ideal of the graph of the regular map corresponding to a ring map
• graphIdeal(...,MonomialOrder=>...) -- the ideal of the graph of the regular map corresponding to a ring map
• graphIdeal(...,MonomialSize=>...) -- the ideal of the graph of the regular map corresponding to a ring map
• graphIdeal(...,VariableBaseName=>...) -- the ideal of the graph of the regular map corresponding to a ring map
• graphIdeal(RingMap) -- 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
• graphRing(...,MonomialOrder=>...) -- the coordinate ring of the graph of the regular map corresponding to a ring map
• graphRing(...,MonomialSize=>...) -- the coordinate ring of the graph of the regular map corresponding to a ring map
• graphRing(...,VariableBaseName=>...) -- the coordinate ring of the graph of the regular map corresponding to a ring map
• graphRing(RingMap) -- 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
• Grassmannian(...,CoefficientRing=>...) -- the Grassmannian of linear subspaces of a vector space
• Grassmannian(...,Variable=>...) -- the Grassmannian of linear subspaces of a vector space
• Grassmannian(ZZ,ZZ) -- the Grassmannian of linear subspaces of a vector space
• Grassmannian(ZZ,ZZ,PolynomialRing) -- the Grassmannian of linear subspaces of a vector space
• GRevLex -- graded reverse lexicographical monomial order.
• Groebner basis examples and applications
• GroebnerBasis -- the class of all Gröbner bases
• groebnerBasis -- Gröbner basis, as a matrix
• groebnerBasis(...,Strategy=>...) -- Gröbner basis, as a matrix
• groebnerBasis(Ideal) -- Gröbner basis, as a matrix
• groebnerBasis(Matrix) -- Gröbner basis, as a matrix
• groebnerBasis(Module) -- Gröbner basis, as a matrix
• GroebnerBasisOptions
• groupID -- the process group identifier
• GroupLex -- defines a ring where some variables are inverted
• GroupRevLex
• handleInterrupts
• handling hypertext
• HardDegreeLimit -- compute only up to this degree
• hash -- hash code of an object
• hash tables
• hashing
• HashTable -- the class of all hash tables
• hashTable -- make a hash table
• HashTable # Thing -- get value from list, hash table, database, or string
• HashTable #? Thing -- check existence of value in a list, hash table, database, or string
• hashTable(List) -- make a hash table
• HeaderType -- a class of lists with abbreviated constructors
• HeaderType List -- a class of lists with abbreviated constructors
• HeaderType Sequence -- a class of lists with abbreviated constructors
• Heading -- a standardized synopsis for use in documentation nodes
• Headline -- headline of a documentation node
• Heft -- an optional argument
• heft -- heft vector of ring or monoid
• heft vectors
• heft(Monoid) -- heft vector of ring or monoid
• heft(PolynomialRing) -- heft vector of ring or monoid
• heft(QuotientRing) -- heft vector of ring or monoid
• heft(Ring) -- heft vector of ring or monoid
• Height -- an optional argument
• height -- height of a net
• height(File) -- get window height
• height(Net) -- height of a net
• height(String) -- height of a net
• help -- view documentation nodes
• help(Array) -- view documentation nodes
• help(DocumentTag) -- view documentation nodes
• help(List) -- view documentation nodes
• help(Sequence) -- view documentation nodes
• help(String) -- view documentation nodes
• help(Symbol) -- view documentation nodes
• help(Thing) -- view documentation nodes
• help(ZZ) -- search the documentation
• Hermitian -- an optional argument
• HH -- general homology and cohomology functor
• hh -- Hodge numbers of a smooth projective variety
• HH ChainComplex -- homology of a chain complex
• HH ChainComplexMap -- homology of a chain complex map
• hh(Sequence,ProjectiveVariety) -- Hodge numbers of a smooth projective variety
• HH^ZZ ChainComplex -- cohomology of a chain complex
• HH^ZZ ChainComplexMap -- cohomology of a chain complex map
• HH^ZZ CoherentSheaf -- cohomology of a coherent sheaf on a projective variety
• HH^ZZ Module -- local cohomology of a module
• HH^ZZ SheafOfRings -- cohomology of a sheaf of rings on a projective variety
• HH^ZZ SumOfTwists -- coherent sheaf cohomology module
• HH^ZZ(ProjectiveVariety,CoherentSheaf) -- cohomology of a coherent sheaf on a projective variety
• HH_ZZ ChainComplex -- homology of a chain complex
• HH_ZZ ChainComplexMap -- homology of a chain complex map
• Hilbert -- an optional argument
• Hilbert functions and free resolutions -- including degree and betti numbers
• hilbertFunction -- the Hilbert function
• hilbertFunction(List,CoherentSheaf) -- the Hilbert function
• hilbertFunction(List,Ideal) -- the Hilbert function
• hilbertFunction(List,Module) -- the Hilbert function
• hilbertFunction(List,ProjectiveVariety) -- the Hilbert function
• hilbertFunction(List,Ring) -- the Hilbert function
• hilbertFunction(ZZ,CoherentSheaf) -- the Hilbert function
• hilbertFunction(ZZ,Ideal) -- the Hilbert function
• hilbertFunction(ZZ,Module) -- the Hilbert function
• hilbertFunction(ZZ,ProjectiveVariety) -- the Hilbert function
• hilbertFunction(ZZ,Ring) -- the Hilbert function
• hilbertPolynomial -- compute the Hilbert polynomial
• hilbertPolynomial(...,Projective=>...) -- choose how to display the Hilbert polynomial
• hilbertPolynomial(CoherentSheaf) -- compute the Hilbert polynomial of the coherent sheaf
• hilbertPolynomial(Ideal) -- compute the Hilbert polynomial of the quotient of the ambient ring by the ideal
• hilbertPolynomial(Module) -- compute the Hilbert polynomial of the module
• hilbertPolynomial(ProjectiveVariety) -- compute the Hilbert polynomial of the projective variety
• hilbertPolynomial(Ring) -- compute the Hilbert polynomial of the ring
• hilbertPolynomial(ZZ,BettiTally) -- the class of all Betti tallies
• hilbertSeries -- compute the Hilbert series
• hilbertSeries(...,Order=>...) -- display the truncated power series expansion
• hilbertSeries(...,Reduce=>...) -- reduce the Hilbert series
• hilbertSeries(Ideal) -- compute the Hilbert series of the quotient of the ambient ring by the ideal
• hilbertSeries(Module) -- compute the Hilbert series of the module
• hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring
• hilbertSeries(ProjectiveHilbertPolynomial) -- compute the Hilbert series of a projective Hilbert polynomial
• hilbertSeries(ProjectiveVariety) -- compute the Hilbert series of a projective variety
• hilbertSeries(QuotientRing) -- compute the Hilbert series of a ring
• hilbertSeries(ZZ,BettiTally) -- the class of all Betti tallies
• hold -- hold something in a holder expression
• Holder -- the class of all holder expressions
• Holder != Expression -- the class of all expressions
• Holder != Holder -- the class of all expressions
• Holder % Expression -- the class of all expressions
• Holder % Holder -- the class of all expressions
• Holder & Expression -- the class of all expressions
• Holder & Holder -- the class of all expressions
• Holder - Expression -- the class of all expressions
• Holder - Holder -- the class of all expressions
• Holder .. Expression -- the class of all expressions
• Holder .. Holder -- the class of all expressions
• Holder ..< Expression -- the class of all expressions
• Holder ..< Holder -- the class of all expressions
• Holder / Expression -- the class of all expressions
• Holder / Holder -- the class of all expressions
• Holder / OneExpression
• Holder : Expression -- the class of all expressions
• Holder : Holder -- the class of all expressions
• Holder <== Expression -- the class of all expressions
• Holder <== Holder -- the class of all expressions
• Holder <=== Expression -- the class of all expressions
• Holder <=== Holder -- the class of all expressions
• Holder <==> Expression -- the class of all expressions
• Holder <==> Holder -- the class of all expressions
• Holder == Equation -- equality
• Holder ===> Expression -- the class of all expressions
• Holder ===> Holder -- the class of all expressions
• Holder ==> Expression -- the class of all expressions
• Holder ==> Holder -- the class of all expressions
• Holder @ Expression -- the class of all expressions
• Holder @ Holder -- the class of all expressions
• Holder @@ Expression -- the class of all expressions
• Holder @@ Holder -- the class of all expressions
• Holder ^ Expression -- the class of all expressions
• Holder ^ Holder -- the class of all expressions
• Holder ^** Expression -- the class of all expressions
• Holder ^** Holder -- the class of all expressions
• Holder ^^ Expression -- the class of all expressions
• Holder ^^ Holder -- the class of all expressions
• Holder _ Expression -- the class of all expressions
• Holder _ Holder -- the class of all expressions
• Holder | Expression -- the class of all expressions
• Holder | Holder -- the class of all expressions
• Holder |- Expression -- the class of all expressions
• Holder |- Holder -- the class of all expressions
• Holder || Expression -- the class of all expressions
• Holder || Holder -- the class of all expressions
• Holder and Expression -- the class of all expressions
• Holder and Holder -- the class of all expressions
• Holder Expression -- the class of all expressions
• Holder Holder -- the class of all expressions
• Holder or Expression -- the class of all expressions
• Holder or Holder -- the class of all expressions
• Holder xor Expression -- the class of all expressions
• Holder xor Holder -- the class of all expressions
• Hom -- module of homomorphisms
• Hom(ChainComplex,Module)
• Hom(ChainComplexMap,Module) -- induced map on Hom
• Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• Hom(CoherentSheaf,SheafOfRings) -- global Hom
• Hom(Ideal,Ideal) -- module of homomorphisms
• Hom(Ideal,Module) -- module of homomorphisms
• Hom(Ideal,Ring) -- module of homomorphisms
• Hom(Matrix,Matrix) -- induced map on Hom
• Hom(Matrix,Module) -- induced map on Hom
• Hom(Module,ChainComplex)
• Hom(Module,ChainComplexMap) -- induced map on Hom
• Hom(Module,Ideal) -- module of homomorphisms
• Hom(Module,Matrix) -- induced map on Hom
• Hom(Module,Module) -- module of homomorphisms
• Hom(Module,Ring) -- module of homomorphisms
• Hom(Ring,Ideal) -- module of homomorphisms
• Hom(Ring,Module) -- module of homomorphisms
• Hom(SheafOfRings,CoherentSheaf) -- global Hom
• Hom(SheafOfRings,SheafOfRings) -- global Hom
• homeDirectory -- the home directory of the user
• HomePage -- the preamble of a package
• Homogeneous -- a Strategy option value
• Homogeneous2 -- compute a Gröbner basis
• homogenize -- homogenize with respect to a variable
• homogenize(Ideal,RingElement) -- homogenize with respect to a variable
• homogenize(Matrix,RingElement) -- homogenize with respect to a variable
• homogenize(Matrix,RingElement,List) -- homogenize with respect to a variable
• homogenize(Module,RingElement) -- homogenize with respect to a variable
• homogenize(Module,RingElement,List) -- homogenize with respect to a variable
• homogenize(RingElement,RingElement) -- homogenize with respect to a variable
• homogenize(RingElement,RingElement,List) -- homogenize with respect to a variable
• homogenize(Vector,RingElement) -- homogenize with respect to a variable
• homogenize(Vector,RingElement,List) -- homogenize with respect to a variable
• homology -- general homology functor
• homology(Matrix,Matrix) -- homology of a pair of maps
• homomorphism -- get the homomorphism from element of Hom
• homomorphism' -- get the element of Hom from a homomorphism
• homomorphism'(Matrix) -- get the element of Hom from a homomorphism
• homomorphism(Matrix) -- get the homomorphism from element of Hom
• homomorphisms (maps) between modules -- including elements of modules
• hooks -- list hooks attached to a key
• hooks(...,Strategy=>...) -- list hooks attached to a key
• hooks(HashTable) -- list hooks attached to a key
• hooks(List) -- list hooks attached to a key
• hooks(Sequence) -- list hooks attached to a key
• hooks(Symbol) -- list hooks attached to a key
• hooks(Thing) -- list hooks attached to a key
• hooks(ZZ) -- list hooks attached to a key
• horizontalJoin -- join nets or strings horizontally
• horizontalJoin(BasicList) -- join nets or strings horizontally
• HorizontalSpace -- an optional argument
• how Macaulay2 finds its files
• html -- convert to HTML format
• httpHeaders -- prepend http headers to a string
• httpHeaders(String) -- prepend http headers to a string
• hypertext -- prepare hypertext for display
• hypertext list format
• id -- identity map
• id _ ChainComplex -- identity map
• id _ Module -- identity map
• id _ Ring -- identity map
• Ideal -- the class of all ideals
• ideal -- make an ideal
• Ideal * CoherentSheaf -- a binary operator, usually used for multiplication
• Ideal * Ideal -- product of ideals
• Ideal * Module -- a binary operator, usually used for multiplication
• Ideal * MonomialIdeal -- product of ideals
• Ideal * Ring -- a binary operator, usually used for multiplication
• Ideal * Vector -- a binary operator, usually used for multiplication
• Ideal ** Ring -- tensor product
• Ideal + Ideal -- sum of ideals
• Ideal + MonomialIdeal -- sum of ideals
• Ideal + RingElement -- a unary or binary operator, usually used for addition
• Ideal / Function -- apply a function to generators of an ideal
• Ideal / Ideal -- quotient module
• Ideal == Ideal -- equality
• Ideal == Module -- equality
• Ideal == MonomialIdeal -- equality
• Ideal == Ring -- equality
• Ideal == ZZ -- equality
• Ideal ^ Array -- bracket power of an ideal
• Ideal ^ ZZ -- power of an ideal
• Ideal _ List -- map from free module to some generators
• Ideal _ ZZ
• Ideal _* -- get the list of generators of an ideal
• ideal(List) -- make an ideal
• ideal(Matrix) -- make an ideal
• ideal(Module) -- converts a module to an ideal
• ideal(MonomialIdeal) -- converts a monomial ideal to an ideal
• ideal(Number) -- make an ideal
• ideal(QuotientRing) -- returns the defining ideal
• ideal(Ring) -- returns the defining ideal
• ideal(RingElement) -- make an ideal
• ideal(Sequence) -- make an ideal
• ideal(Variety) -- returns the defining ideal
• ideals
• ideals to and from matrices
• ideals to and from modules
• identity -- the identity function
• if -- condition testing
• IgnoreExampleErrors -- an optional argument
• ii -- the square root of -1
• image -- image of a map
• image(ChainComplexMap) -- image of a map
• image(GradedModuleMap) -- image of a map
• image(Matrix) -- image of a map
• image(RingElement) -- image of a map
• imaginaryPart -- imaginary part
• imaginaryPart(Number) -- imaginary part
• ImmutableType -- the class of immutable types
• importFrom -- import symbols to the current private dictionary
• importFrom(Package,List) -- import symbols to the current private dictionary
• importFrom(String,List) -- import symbols to the current private dictionary
• importing and exporting matrices
• in -- a keyword used in for-loops
• incomparable -- a result indicating incomparability
• independentSets -- some size-maximal independent subsets of variables modulo an ideal
• independentSets(...,Limit=>...) -- some size-maximal independent subsets of variables modulo an ideal
• independentSets(Ideal) -- some size-maximal independent subsets of variables modulo an ideal
• independentSets(MonomialIdeal) -- some size-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
• index(RingElement) -- numeric index of a ring variable
• indexComponents -- specify keys for components of a direct sum
• IndexedVariable -- the class of all indexed variables
• IndexedVariable .. IndexedVariable -- sequences of consecutive indexed variables
• IndexedVariable ..< IndexedVariable -- sequences of consecutive indexed variables
• IndexedVariable <- Thing -- assignment with left side evaluated
• IndexedVariable ? IndexedVariable -- comparison operator
• IndexedVariable _ Ring -- get a ring variable by name
• IndexedVariableTable
• IndexedVariableTable _ Thing
• IndexedVariableTable _ Thing = Thing
• indices -- indices of a polynomial; also components for a direct sum
• indices(Matrix) -- indices of variables occurring in a polynomial
• indices(RingElement) -- indices of variables occurring in a polynomial
• inducedMap -- compute an induced map
• inducedMap(...,Degree=>...) -- specify the degree of a map
• inducedMap(...,Verify=>...) -- verify that a map is well-defined
• inducedMap(ChainComplex,ChainComplex) -- compute the map induced by the identity
• inducedMap(Module,Module) -- compute the map induced by the identity
• inducedMap(Module,Module,Matrix) -- compute the induced map
• inducedMap(Module,Nothing,Matrix) -- compute the induced map
• inducedMap(Nothing,Module,Matrix) -- compute the induced map
• inducedMap(Nothing,Nothing,Matrix) -- compute the induced map
• inducesWellDefinedMap -- whether a map is well defined
• inducesWellDefinedMap(Module,Module,Matrix) -- whether a map is well defined
• inducesWellDefinedMap(Module,Nothing,Matrix) -- whether a map is well defined
• inducesWellDefinedMap(Nothing,Module,Matrix) -- whether a map is well defined
• inducesWellDefinedMap(Nothing,Nothing,Matrix) -- whether a map is well defined
• InexactField -- the class of inexact fields
• InexactFieldFamily -- the class of all families of inexact fields
• InexactFieldFamily Array -- the standard way to make a polynomial ring
• InexactFieldFamily List -- make a local polynomial ring
• InexactFieldFamily Monoid -- make a polynomial ring
• InexactNumber
• InexactNumber * Constant -- a binary operator, usually used for multiplication
• InexactNumber + Constant -- a unary or binary operator, usually used for addition
• InexactNumber - Constant -- a unary or binary operator, usually used for negation or subtraction
• InexactNumber / Constant
• InexactNumber == Constant
• InexactNumber ^ Constant
• InexactNumber'
• InfiniteNumber -- the class of all infinite numbers
• InfiniteNumber + InfiniteNumber -- a unary or binary operator, usually used for addition
• InfiniteNumber + Number -- a unary or binary operator, usually used for addition
• InfiniteNumber - InfiniteNumber -- a unary or binary operator, usually used for negation or subtraction
• InfiniteNumber - Number -- a unary or binary operator, usually used for negation or subtraction
• InfiniteNumber // QQ -- a binary operator, usually used for quotient
• InfiniteNumber // RR -- a binary operator, usually used for quotient
• InfiniteNumber // ZZ -- a binary operator, usually used for quotient
• InfiniteNumber == InfiniteNumber -- equality
• InfiniteNumber == Number -- equality
• infinity -- infinity
• info -- convert hypertext to info format
• InfoDirSection -- an optional argument
• infoHelp -- view documentation in Info format
• infoHelp(DocumentTag) -- view documentation in Info format
• infoHelp(Thing) -- view documentation in Info format
• infoHelp(ZZ) -- search the documentation
• information about a map of modules
• informing others about your package
• inheritance
• Inhomogeneous -- a Strategy option value
• initial help
• initialization file
• input -- read Macaulay2 commands and echo
• Inputs -- inputs for a function in a documentation node
• inputting a matrix
• insert -- copy a list, inserting an element
• insert(ZZ,Thing,VisibleList) -- copy a list, inserting an element
• installAssignmentMethod -- install methods assignment to the value of an operator
• installAssignmentMethod(Symbol,HashTable,Function) -- install methods assignment to the value of an operator
• installAssignmentMethod(Symbol,HashTable,HashTable,Function) -- install methods assignment to the value of an operator
• installAssignmentMethod(Symbol,HashTable,HashTable,Option) -- install methods assignment to the value of an operator
• installAssignmentMethod(Symbol,HashTable,Option) -- install methods assignment to the value of an operator
• installedPackages
• installHilbertFunction -- assemble degrees of a ring, module, or ideal into a polynomial
• installing methods
• installMethod -- install methods
• installPackage -- load and install a package and its documentation
• installPackage(...,CacheExampleOutput=>...) -- load and install a package and its documentation
• installPackage(...,CheckDocumentation=>...) -- load and install a package and its documentation
• installPackage(...,DebuggingMode=>...) -- load and install a package and its documentation
• installPackage(...,FileName=>...) -- load and install a package and its documentation
• installPackage(...,IgnoreExampleErrors=>...) -- load and install a package and its documentation
• installPackage(...,InstallPrefix=>...) -- load and install a package and its documentation
• installPackage(...,MakeDocumentation=>...) -- load and install a package and its documentation
• installPackage(...,MakeHTML=>...) -- load and install a package and its documentation
• installPackage(...,MakeInfo=>...) -- load and install a package and its documentation
• installPackage(...,MakeLinks=>...) -- load and install a package and its documentation
• installPackage(...,MakePDF=>...) -- load and install a package and its documentation
• installPackage(...,RemakeAllDocumentation=>...) -- load and install a package and its documentation
• installPackage(...,RerunExamples=>...) -- load and install a package and its documentation
• installPackage(...,RunExamples=>...) -- load and install a package and its documentation
• installPackage(...,SeparateExec=>...) -- load and install a package and its documentation
• installPackage(...,UserMode=>...) -- load and install a package and its documentation
• installPackage(...,Verbose=>...) -- load and install a package and its documentation
• installPackage(Package) -- load and install a package and its documentation
• installPackage(String) -- load and install a package and its documentation
• InstallPrefix -- an optional argument
• instance -- whether something has a certain type
• instance(Thing,Type) -- whether something has a certain type
• instances
• instances(Type)
• integers modulo a prime
• integrate -- numerical integration
• integrate(Function,Constant,Constant) -- numerical integration
• integrate(Function,Constant,InfiniteNumber) -- numerical integration
• integrate(Function,Constant,Number) -- numerical integration
• integrate(Function,InfiniteNumber,Constant) -- numerical integration
• integrate(Function,InfiniteNumber,InfiniteNumber) -- numerical integration
• integrate(Function,InfiniteNumber,Number) -- numerical integration
• integrate(Function,Number,Constant) -- numerical integration
• integrate(Function,Number,InfiniteNumber) -- numerical integration
• integrate(Function,Number,Number) -- numerical integration
• interpreterDepth -- nesting depth of the interpreter
• intersect -- compute an intersection
• intersect(Ideal) -- compute an intersection of a sequence of ideals or modules
• intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
• intersect(Ideal,Ideal,MinimalGenerators=>...) -- compute an intersection of a sequence of ideals or modules
• intersect(Ideal,Ideal,Strategy=>...) -- compute an intersection of a sequence of ideals or modules
• intersect(List) -- compute an intersection
• intersect(Module) -- compute an intersection of a sequence of ideals or modules
• intersect(Module,Module) -- compute an intersection of a sequence of ideals or modules
• intersect(Module,Module,MinimalGenerators=>...) -- compute an intersection of a sequence of ideals or modules
• intersect(Module,Module,Strategy=>...) -- compute an intersection of a sequence of ideals or modules
• intersect(RRi) -- computes intersection of input intervals
• intersect(RRi,Precision=>...) -- computes intersection of input intervals
• intersect(Sequence) -- compute an intersection
• Intersection -- value of an optional argument
• intersection -- compute an intersection
• intersection of ideals
• intersection(RRi,RRi) -- computes intersection of input intervals
• intersection(RRi,RRi,Precision=>...) -- computes intersection of input intervals
• interval -- construct an interval
• interval(...,Precision=>...) -- construct an interval
• interval(Array) -- construct an interval
• interval(QQ) -- construct an interval
• interval(QQ,QQ) -- construct an interval
• interval(QQ,RR) -- construct an interval
• interval(QQ,ZZ) -- construct an interval
• interval(RR) -- construct an interval
• interval(RR,QQ) -- construct an interval
• interval(RR,RR) -- construct an interval
• interval(RR,ZZ) -- construct an interval
• interval(ZZ) -- construct an interval
• interval(ZZ,QQ) -- construct an interval
• interval(ZZ,RR) -- construct an interval
• interval(ZZ,ZZ) -- construct an interval
• inverse -- compute the inverse
• inverse(Matrix) -- compute the inverse
• inverse(MutableMatrix) -- compute the inverse
• inverse(RingMap) -- 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
• Invertible -- an optional argument
• Invoking the program
• irreducibleCharacteristicSeries -- irreducible characteristic series of an ideal
• irreducibleCharacteristicSeries(Ideal) -- irreducible characteristic series of an ideal
• isAffineRing -- whether something is an affine ring
• isAffineRing(PolynomialRing) -- whether something is an affine ring
• isAffineRing(QuotientRing) -- whether something is an affine ring
• isAffineRing(Ring) -- whether something is an affine ring
• isANumber -- whether a number is not not-a-number
• isANumber(Number) -- whether a number is not not-a-number
• isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
• isBorel(MonomialIdeal) -- whether an ideal is fixed by upper triangular changes of coordinates
• isCanceled -- whether a task has been canceled
• isCanceled(Task) -- whether a task has been canceled
• isCommutative -- whether a ring is commutative
• isCommutative(Ring) -- whether a ring is commutative
• isConstant -- whether a ring element is constant
• isConstant(RingElement) -- whether a ring element is constant
• isDirectory -- whether a file is a directory
• isDirectSum -- whether something is a direct sum
• isDirectSum(ChainComplex) -- whether something is a direct sum
• isDirectSum(GradedModule) -- whether something is a direct sum
• isDirectSum(Module) -- whether something is a direct sum
• isEmpty
• isEmpty(RRi) -- empty test for an interval
• isField -- whether something is a field
• isField(EngineRing) -- whether something is a field
• isField(Ring) -- whether something is a field
• isFinite -- whether a number is finite
• isFinite(Number) -- whether a number is finite
• isFinitePrimeField -- whether a ring is a finite prime field
• isFreeModule -- whether something is a free module
• isFreeModule(Module) -- whether something is a free module
• isFreeModule(Thing) -- whether something is a free module
• isGlobalSymbol -- whether a global symbol with a given name exists
• isHomogeneous -- whether something is homogeneous (graded)
• isHomogeneous(ChainComplex) -- whether something is homogeneous (graded)
• isHomogeneous(ChainComplexMap) -- whether something is homogeneous (graded)
• isHomogeneous(Ideal) -- whether something is homogeneous (graded)
• isHomogeneous(Matrix) -- whether something is homogeneous (graded)
• isHomogeneous(Module) -- whether something is homogeneous (graded)
• isHomogeneous(Ring) -- whether something is homogeneous (graded)
• isHomogeneous(RingElement) -- whether something is homogeneous (graded)
• isHomogeneous(RingMap) -- whether something is homogeneous (graded)
• isHomogeneous(Vector) -- whether something is homogeneous (graded)
• isIdeal -- whether something is an ideal
• isIdeal(Ideal) -- whether something is an ideal
• isIdeal(Module) -- whether something is an ideal
• isIdeal(MonomialIdeal) -- whether something is an ideal
• isIdeal(Thing) -- whether something is an ideal
• isInfinite -- whether a number is infinite
• isInfinite(Constant) -- whether a number is infinite
• isInfinite(InfiniteNumber) -- whether a number is infinite
• isInfinite(Number) -- whether a number is infinite
• isInjective -- whether a map is injective
• isInjective(Matrix) -- whether a map is injective
• isInjective(RingMap) -- whether a map is injective
• isInputFile -- whether a file is open for input
• isInputFile(File) -- whether a file is open for input
• isIsomorphism -- whether a map is an isomorphism
• isIsomorphism(Matrix) -- whether a map is an isomorphism
• isListener -- whether a file is open for listening
• isListener(File) -- whether a file is open for listening
• isMember -- test membership in a list or set
• isMember(QQ,RRi) -- membership test in an interval
• isMember(RR,RRi) -- membership test in an interval
• isMember(Thing,Set) -- test membership in a list or set
• isMember(Thing,VisibleList) -- test membership in a list or set
• isMember(ZZ,RRi) -- membership test in an interval
• isModule -- whether something is a module
• isModule(Module) -- whether something is a module
• isModule(Thing) -- whether something is a module
• isMonomialIdeal -- whether something is a monomial ideal
• isMonomialIdeal(Ideal) -- whether something is a monomial ideal
• isMonomialIdeal(MonomialIdeal) -- whether something is a monomial ideal
• isMonomialIdeal(Thing) -- whether something is a monomial ideal
• isMutable -- whether something may be modified
• isMutable(Thing) -- whether something may be modified
• isOpen -- whether a file or database is open
• isOpen(Database) -- whether a file or database is open
• isOpen(File) -- whether a file or database is open
• isOutputFile -- whether a file is open for output
• isOutputFile(File) -- whether a file is open for output
• isPolynomialRing -- whether something is a polynomial ring
• isPolynomialRing(PolynomialRing) -- whether something is a polynomial ring
• isPolynomialRing(Thing) -- whether something is a polynomial ring
• isPrime -- whether a integer or polynomial is prime
• isPrime(ZZ) -- whether a integer or polynomial is prime
• isPrimitive -- whether an element is a primitive element of a finite field
• isPseudoprime -- whether an integer is probably prime
• isPseudoprime(ZZ) -- whether an integer is probably prime
• isQuotientModule -- whether something is evidently a quotient of a free module
• isQuotientModule(Module) -- whether something is evidently a quotient of a free module
• isQuotientModule(Thing) -- whether something is evidently a quotient of a free module
• isQuotientOf -- whether one thing is a quotient of another
• isQuotientOf(Ring,QuotientRing) -- whether one ring is a quotient of another
• isQuotientOf(Ring,Ring) -- whether one ring is a quotient of another
• isQuotientOf(Type,QuotientRing) -- whether one ring is a quotient of a ring of a given type
• isQuotientOf(Type,Ring) -- whether one ring is a quotient of a ring of a given type
• isQuotientRing -- whether something is a quotient ring
• isQuotientRing(QuotientRing) -- whether something is a quotient ring
• isQuotientRing(Ring) -- whether something is a quotient ring
• isReady -- whether a file has data available for reading
• isReady(File) -- whether a file has data available for reading
• isReady(Task) -- whether a task is finished
• isReal -- whether a number is real
• isReal(CC) -- whether a number is real
• isReal(Constant) -- whether a number is real
• isReal(InfiniteNumber) -- whether a number is real
• isReal(QQ) -- whether a number is real
• isReal(RR) -- whether a number is real
• isReal(RRi) -- whether a number is real
• isReal(ZZ) -- whether a number is real
• isRegularFile -- whether a file is a regular file
• isRing -- whether something is a ring
• isRing(Ring) -- whether something is a ring
• isRing(Thing) -- whether something is a ring
• isSkewCommutative -- whether a ring has skew commuting variables
• isSkewCommutative(PolynomialRing) -- whether a ring has skew commuting variables
• isSkewCommutative(QuotientRing) -- whether a ring has skew commuting variables
• isSkewCommutative(Ring) -- whether a ring has skew commuting variables
• isSorted -- whether a list is sorted
• isSorted(VisibleList) -- whether a list is sorted
• isSquareFree -- whether something is square free monomial ideal
• isSquareFree(MonomialIdeal) -- whether something is square free monomial ideal
• isSubmodule -- whether a module is evidently a submodule of a free module
• isSubmodule(Module) -- whether a module is evidently a submodule of a free module
• isSubmodule(Thing) -- whether a module is evidently a submodule of a free module
• isSubquotient -- check whether a module is a subquotient of another
• isSubquotient(Module,Module) -- check whether a module is a subquotient of another
• isSubset -- whether one object is a subset of another
• isSubset(Ideal,Ideal) -- whether one object is a subset of another
• isSubset(Ideal,Module) -- whether one object is a subset of another
• isSubset(Module,Ideal) -- whether one object is a subset of another
• isSubset(Module,Module) -- whether one object is a subset of another
• isSubset(RRi,RRi) -- subset test for intervals
• isSubset(Set,Set) -- whether one object is a subset of another
• isSubset(Set,VisibleList) -- whether one object is a subset of another
• isSubset(VisibleList,Set) -- whether one object is a subset of another
• isSubset(VisibleList,VisibleList) -- whether one object is a subset of another
• isSurjective -- whether a map is surjective
• isSurjective(Matrix) -- whether a map is surjective
• isTable -- whether something is a list of lists of equal length
• isUnit -- whether a ring element is a unit
• isUnit(Number) -- whether a ring element is a unit
• isUnit(RingElement) -- whether a ring element is a unit
• isUnit(ZZ) -- whether a ring element is a unit
• isWellDefined -- whether a map is well defined
• isWellDefined(Matrix) -- whether a map is well defined
• isWellDefined(RingMap) -- whether a map is well defined
• isWeylAlgebra
• Iterate -- value of an optional argument
• Iterator -- class for iterators
• iterator -- get an iterator
• iterator(Iterator) -- get an iterator
• iterator(String) -- get an iterator
• iterator(VisibleList) -- get an iterator
• Jacobian
• jacobian -- the Jacobian matrix of partial derivatives
• jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal
• jacobian(Matrix) -- the matrix of partial derivatives of polynomials in a matrix
• jacobian(MonomialIdeal) -- the Jacobian matrix of the generators of an ideal
• jacobian(Ring) -- the Jacobian matrix of the polynomials defining a quotient ring
• Join -- an optional argument
• join -- join lists, sequences, and iterable objects
• Jupyter -- top level printing method used in the Jupyter kernel
• KeepFiles -- whether to keep temporary files
• KeepZeroes -- an optional argument
• kernel -- kernel of a ringmap, matrix, or chain complex
• kernel and coimage of a ring map
• kernel(...,SubringLimit=>...)
• kernel(ChainComplexMap) -- kernel of a chain complex map
• kernel(GradedModuleMap) -- kernel of a chain complex map
• kernel(Matrix) -- kernel of a matrix
• kernel(RingElement) -- kernel of a matrix
• kernel(RingMap) -- kernel of a ringmap
• Key -- key of a documentation node
• keys -- keys used in a hash table, dictionary, or database
• keys(Database) -- keys used in a hash table, dictionary, or database
• keys(Dictionary) -- keys used in a hash table, dictionary, or database
• keys(HashTable) -- keys used in a hash table, dictionary, or database
• Keyword -- the class of all keywords
• Keywords -- an optional argument
• kill -- kill a process
• kill(File) -- kill a process
• kill(ZZ) -- kill a process
• koszul -- Koszul complex or specific matrix in the Koszul complex
• koszul(Matrix) -- the Koszul complex
• koszul(ZZ,Matrix) -- a differential in a Koszul complex
• LAPACK
• last -- last element of a list
• lastMatch -- regular expression matching
• Layout -- relative locations of Macaulay2 files
• lcm -- least common multiple
• lcm(List) -- least common multiple
• lcm(MonomialIdeal) -- least common multiple of all minimal generators
• lcm(QQ,QQ) -- least common multiple
• lcm(QQ,ZZ) -- least common multiple
• lcm(RingElement,RingElement) -- least common multiple
• lcm(RingElement,ZZ) -- least common multiple
• lcm(Sequence) -- least common multiple
• lcm(ZZ,QQ) -- least common multiple
• lcm(ZZ,RingElement) -- least common multiple
• lcm(ZZ,ZZ) -- least common multiple
• leadCoefficient -- the coefficient of the leading term
• leadCoefficient(RingElement) -- the coefficient of the leading term
• leadComponent -- the leading component(s) of a vector or matrix
• leadComponent(Matrix) -- the leading component(s) of a vector or matrix
• leadComponent(Vector) -- the leading component(s) of a vector or matrix
• leadMonomial -- the leading monomial of a ring element
• leadMonomial(RingElement) -- the leading monomial of a ring element
• leadTerm -- get the greatest term
• leadTerm(GroebnerBasis) -- get the greatest term of each column
• leadTerm(Ideal) -- get the ideal of greatest terms
• leadTerm(Matrix) -- get the greatest term of each column
• leadTerm(RingElement) -- get the greatest term
• leadTerm(Vector) -- get the greatest term of each column
• leadTerm(ZZ,Ideal) -- get the ideal of lead polynomials
• leadTerm(ZZ,Matrix) -- get the matrix of lead polynomials of each column
• leadTerm(ZZ,RingElement) -- get the lead polynomials using part of the monomial order
• Left -- value of an optional argument
• left -- left endpoint of an interval
• left shift
• length -- length of an object
• length(ChainComplex) -- length of a chain complex or graded module
• length(Dictionary) -- length of a dictionary
• length(GradedModule) -- length of a graded module
• length(Module) -- Computes the length of a module
• length(String) -- length of a string
• length(VisibleList) -- length of a visible list
• LengthLimit -- stop when the resolution reaches this length
• Lex -- lexicographical monomial order.
• lift -- lift to another ring
• lift(...,Verify=>...) -- lift to another ring
• lift(BettiTally,type of ZZ) -- the class of all Betti tallies
• lift(CC,type of QQ) -- lift to another ring
• lift(CC,type of RR_*) -- lift to another ring
• lift(CC,type of ZZ) -- lift to another ring
• lift(Ideal,type of QQ) -- lift to another ring
• lift(Ideal,type of RingElement) -- lift to another ring
• lift(Ideal,type of ZZ) -- lift to another ring
• lift(Matrix,type of CC_*,type of QQ) -- lift to another ring
• lift(Matrix,type of CC_*,type of RR_*) -- lift to another ring
• lift(Matrix,type of CC_*,type of ZZ) -- lift to another ring
• lift(Matrix,type of Number) -- lift to another ring
• lift(Matrix,type of QQ,type of QQ) -- lift to another ring
• lift(Matrix,type of QQ,type of ZZ) -- lift to another ring
• lift(Matrix,type of RingElement) -- lift to another ring
• lift(Matrix,type of RR_*,type of QQ) -- lift to another ring
• lift(Matrix,type of RR_*,type of ZZ) -- lift to another ring
• lift(Matrix,type of RRi_*,type of QQ) -- lift to another ring
• lift(Matrix,type of RRi_*,type of RR_*) -- lift to another ring
• lift(Matrix,type of RRi_*,type of ZZ) -- lift to another ring
• lift(Matrix,type of ZZ,type of ZZ) -- lift to another ring
• lift(QQ,type of QQ) -- lift to another ring
• lift(QQ,type of ZZ) -- lift to another ring
• lift(RR,type of QQ) -- lift to another ring
• lift(RR,type of ZZ) -- lift to another ring
• lift(RRi,type of QQ) -- lift to another ring
• lift(RRi,type of RR_*) -- lift to another ring
• lift(RRi,type of ZZ) -- lift to another ring
• lift(ZZ,type of ZZ) -- lift to another ring
• liftable -- whether lifting to another ring is possible
• Limit -- an optional argument
• limitFiles
• limitProcesses
• Linear -- value of an optional argument
• LinearAlgebra -- compute a Gröbner basis
• lineNumber -- current line number
• lines -- split a string into lines
• lines(String) -- split a string into lines
• lines(String,String) -- split a string into lines
• linkFile -- make a new link to a file
• linkFile(String,String) -- make a new link to a file
• List -- the class of all lists -- {...}
• list -- loop control
• List ** List -- Cartesian product of two lists
• List + List -- sum of two vectors
• List - List -- difference of two vectors
• List - Set -- set difference
• List .. List -- rectangular sequences of consecutive lists and sequences
• List ..< List -- rectangular sequences of consecutive lists and sequences
• List / Command -- apply a function to elements of a list
• List / Function -- apply a function to elements of a list
• List / RingMap -- apply a function to elements of a list
• List / Thing -- vector division
• List << List -- component-wise comparison of lists
• List >> Function -- attaching options to a function
• List ? List -- comparison operator
• List | List -- join lists, sequences or arrays
• list of obsolete functions
• listForm -- convert to list form
• listForm(MonoidElement) -- convert to list form
• listForm(RingElement) -- convert to list form
• listLocalSymbols -- display of local symbols and their values
• lists and sequences -- a detailed overview of lists and sequences in Macaulay2
• listSymbols -- compact display of symbols and their values
• listSymbols(Dictionary) -- compact display of symbols and their values
• listSymbols(List) -- compact display of symbols and their values
• listUserSymbols -- display the user's symbols
• lngamma -- logarithm of the Gamma function
• lngamma(Constant) -- logarithm of the Gamma function
• lngamma(QQ) -- logarithm of the Gamma function
• lngamma(RR) -- logarithm of the Gamma function
• lngamma(ZZ) -- logarithm of the Gamma function
• load -- read Macaulay2 commands
• loadDepth -- the load depth
• LoadDocumentation -- an optional argument
• loadedFiles
• loadedPackages -- the list of loaded packages
• loadPackage -- load a package
• loadPackage(...,Configuration=>...) -- load a package
• loadPackage(...,DebuggingMode=>...) -- load a package
• loadPackage(...,FileName=>...) -- load a package
• loadPackage(...,LoadDocumentation=>...) -- load a package
• loadPackage(...,Reload=>...) -- load a package
• loadPackage(Package) -- load a package
• loadPackage(String) -- load a package
• Local -- an optional argument
• local -- get a local symbol
• local variables in a file
• local variables in a function
• localDictionaries -- get local dictionaries
• localDictionaries(Dictionary) -- get local dictionaries
• localDictionaries(Function) -- get local dictionaries
• localDictionaries(Pseudocode) -- get local dictionaries
• localDictionaries(Symbol) -- get local dictionaries
• LocalDictionary -- the class of all local dictionaries
• locate -- locate source code
• locate(DocumentTag) -- the class of all document tags
• locate(Function) -- locate source code
• locate(FunctionBody) -- locate source code
• locate(List) -- locate source code
• locate(Nothing) -- locate source code
• locate(Pseudocode) -- locate source code
• locate(Sequence) -- locate source code
• locate(Symbol) -- locate source code
• locate(TestInput) -- locate a package's tests
• locate(ZZ) -- locate source code
• log -- logarithm function
• log(CC) -- logarithm function
• log(RR) -- logarithm function
• log(RR,RR) -- logarithm function
• log(RRi) -- logarithm function
• log(RRi,RRi) -- logarithm function
• log1p -- logarithm of 1+x
• log1p(RR) -- logarithm of 1+x
• log1p(RRi) -- 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
• lrslib
• LUdecomposition -- LU decomposition
• LUdecomposition(Matrix) -- LU decomposition
• LUdecomposition(MutableMatrix) -- LU decomposition
• M2SingularBook -- Macaulay2 examples for the Singular book
• Macaulay2 -- Macaulay2 documentation
• Macaulay2Doc -- Macaulay2 documentation
• makeDirectory -- make a directory
• makeDirectory(String) -- make a directory
• MakeDocumentation -- an optional argument
• makeDocumentTag -- the class of all document tags
• makeDocumentTag(DocumentTag) -- the class of all document tags
• makeDocumentTag(List) -- the class of all document tags
• makeDocumentTag(String) -- the class of all document tags
• makeDocumentTag(Thing) -- the class of all document tags
• MakeHTML -- an optional argument
• MakeInfo -- an optional argument
• MakeLinks -- an optional argument
• makePackageIndex -- create an index of installed packages
• makePackageIndex(List) -- create an index of installed packages
• makePackageIndex(Sequence) -- create an index of installed packages
• MakePDF -- an optional argument
• making a new method function
• making chain complexes by hand
• making functions
• making functions with a variable number of arguments
• making functions with multiple return values
• making modules from matrices
• making new classes
• making new functions with optional arguments
• manipulating chain complexes
• manipulating modules
• manipulating polynomials
• Manipulator -- the class of all file manipulators
• Manipulator Database -- the class of all file manipulators
• Manipulator File -- the class of all file manipulators
• Manipulator NetFile -- the class of all net files
• Manipulator Nothing -- the class of all file manipulators
• map -- make a map
• map(...,Degree=>...) -- specify the degree of a map
• map(...,DegreeLift=>...) -- make a ring map
• map(...,DegreeMap=>...) -- make a ring map
• map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
• map(GradedModule,GradedModule,Function) -- make a map of chain complexes
• map(Matrix) -- make a matrix with a different degree
• map(Module) -- identity map
• map(Module,Module,Function) -- create a matrix by specifying a function that gives each entry
• map(Module,Module,List) -- create a matrix by giving a sparse or dense list of entries
• map(Module,Module,Matrix) -- create the matrix induced on generators by a given matrix
• map(Module,Module,Number) -- construct the map induced by multiplication by a ring element on the generators
• map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
• map(Module,Module,RingMap,List) -- homomorphism of modules over different rings
• map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
• map(Module,Module,ZZ) -- construct the map induced by multiplication by a ring element on the generators
• map(Module,Nothing,List) -- create a matrix by giving a doubly nested list of ring elements
• map(Module,Nothing,Matrix) -- recast a matrix to have a new target, and a free module as source
• map(Module,Nothing,RingMap,List) -- homomorphism of modules over different rings
• map(Module,Nothing,RingMap,Matrix) -- homomorphism of modules over different rings
• map(Module,RingMap) -- homomorphism of modules over different rings
• map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry
• map(Module,ZZ,List) -- create a matrix by giving a sparse or dense list of entries
• map(Module,ZZ,ZZ) -- construct the map induced by multiplication by a ring element on the generators
• map(Ring,Matrix) -- make a ring map
• map(Ring,Ring) -- make a ring map, using the names of the variables
• map(Ring,Ring,List) -- make a ring map
• map(Ring,Ring,Matrix) -- make a ring map
• map(Ring,Ring,RingMap) -- make a ring map
• MapExpression -- the class of map expressions
• mapping over hash tables -- apply a function to each element of a hash table
• maps between chain complexes
• maps between modules
• markedGB -- make a marked Gröbner basis
• markedGB(...,ChangeMatrix=>...) -- make a marked Gröbner basis
• markedGB(...,MinimalMatrix=>...) -- make a marked Gröbner basis
• markedGB(...,SyzygyMatrix=>...) -- make a marked Gröbner basis
• markedGB(Matrix,Matrix) -- make a marked Gröbner basis
• match -- regular expression matching
• match(...,POSIX=>...) -- regular expression matching
• match(...,Strategy=>...) -- regular expression matching
• match(List,String) -- regular expression matching
• match(String,String) -- regular expression matching
• mathematical examples
• mathML -- convert to MathML format
• matrices
• matrices to and from modules -- including kernel, cokernel and image
• Matrix -- the class of all matrices
• matrix -- make a matrix
• Matrix % GroebnerBasis -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis
• Matrix % Ideal -- normal form of ring elements and matrices
• Matrix % Matrix -- normal form of ring elements and matrices
• Matrix % Module -- normal form of ring elements and matrices
• Matrix % MonomialIdeal -- normal form of ring elements and matrices
• Matrix % RingElement -- normal form of ring elements and matrices
• Matrix * Matrix -- matrix multiplication
• Matrix * Number -- a binary operator, usually used for multiplication
• Matrix * RingElement -- a binary operator, usually used for multiplication
• Matrix * Vector -- a binary operator, usually used for multiplication
• Matrix ** Matrix -- tensor product
• Matrix ** Module -- tensor product
• Matrix ** Ring -- tensor product
• Matrix ** RingElement -- a binary operator, usually used for tensor product or Cartesian product
• Matrix + Matrix -- a unary or binary operator, usually used for addition
• Matrix + Number -- a unary or binary operator, usually used for addition
• Matrix + RingElement -- a unary or binary operator, usually used for addition
• Matrix ++ Matrix -- direct sum of maps
• Matrix ++ RingElement -- direct sum of maps
• Matrix - Matrix -- a unary or binary operator, usually used for negation or subtraction
• Matrix - Number -- a unary or binary operator, usually used for negation or subtraction
• Matrix - RingElement -- a unary or binary operator, usually used for negation or subtraction
• Matrix // GroebnerBasis -- factor a map through another
• Matrix // Matrix -- factor a map through another
• Matrix // MonomialIdeal -- factor a map through another
• Matrix // Number -- a binary operator, usually used for quotient
• Matrix // RingElement -- factor a map through another
• Matrix == Matrix -- equality
• Matrix == Number -- equality
• Matrix == RingElement -- equality
• Matrix == ZZ -- equality
• Matrix \\ Matrix -- factor a map through another
• Matrix \\ RingElement -- factor a map through another
• Matrix ^ Array -- component of map corresponding to summand of target
• Matrix ^ List -- select rows
• Matrix ^ ZZ -- power
• Matrix _ Array -- component of map corresponding to summand of source
• Matrix _ List -- select columns
• Matrix _ Sequence -- get entry of matrix
• Matrix _ ZZ
• Matrix | Matrix -- join matrices horizontally
• Matrix | Number -- join matrices horizontally
• Matrix | RingElement -- join matrices horizontally
• Matrix || Matrix -- join matrices vertically
• Matrix || Number -- join matrices vertically
• Matrix || RingElement -- join matrices vertically
• matrix(...,Degree=>...) -- create a matrix from a doubly-nested list of ring elements or matrices
• matrix(List) -- create a matrix from a doubly-nested list of ring elements or matrices
• matrix(Matrix) -- the matrix between generators
• matrix(MutableMatrix) -- make a matrix from a mutable one
• matrix(Number) -- make a matrix from a ring element
• matrix(Ring,List) -- create a matrix from a doubly nested list of ring elements or matrices
• matrix(RingElement) -- make a matrix from a ring element
• matrix(RingFamily,List) -- create a matrix from a doubly nested list of ring elements or matrices
• matrix(RingMap) -- the matrix associated to a ring map
• matrix(Vector) -- make a matrix
• MatrixExpression -- the class of all matrix expressions
• max -- yields the maximum element in a list or sequence
• max(GradedModule)
• max(VisibleList) -- 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
• maxPosition(BasicList) -- position of the largest element
• MaxReductionCount -- an optional argument
• memoize -- record results of function evaluation for future use
• memoize(Function) -- record results of function evaluation for future use
• memoize(Function,List) -- record results of function evaluation for future use
• memoizeClear -- record results of function evaluation for future use
• memoizeValues -- record results of function evaluation for future use
• merge -- merge two hash tables
• merge(HashTable,HashTable,Function) -- merge two hash tables
• mergePairs -- merge sorted lists of pairs
• mergePairs(BasicList,BasicList,Function) -- merge sorted lists of pairs
• method -- make a new method function
• method(...,Binary=>...) -- make a new method function
• method(...,Dispatch=>...) -- make a new method function
• method(...,Options=>...) -- make a new method function
• method(...,TypicalValue=>...) -- 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 -- recover the options used when a method function was created
• methodOptions(Command) -- recover the options used when a method function was created
• methodOptions(Function) -- recover the options used when a method function was created
• methodOptions(ScriptedFunctor) -- recover the options used when a method function was created
• methods -- list methods
• methods for normal forms and remainder -- normal form of ring elements and matrices
• methods(Command) -- list methods
• methods(Manipulator) -- list methods
• methods(Package) -- list methods
• methods(ScriptedFunctor) -- list methods
• methods(Sequence) -- list methods
• methods(Symbol) -- list methods
• methods(Thing) -- list methods
• methods(Type) -- list methods
• Michael E. Stillman
• midpoint -- midpoint of an interval
• min -- yields the minimum element in a list or sequence
• min(GradedModule)
• min(VisibleList) -- yields the minimum element in a list or sequence
• minExponent
• mingens -- minimal generator matrix
• mingens(...,Strategy=>...) -- a Strategy option value
• mingens(GroebnerBasis) -- (partially constructed) minimal generator matrix
• mingens(Ideal) -- minimal generator matrix
• mingens(Module) -- minimal generator matrix
• mingle -- mingle elements of several lists
• mingle(BasicList) -- mingle elements of several lists
• minimal presentations and generators
• minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• minimalBetti(...,DegreeLimit=>...) -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• minimalBetti(...,LengthLimit=>...) -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• minimalBetti(...,Weights=>...) -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• minimalBetti(Ideal) -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• minimalBetti(Module) -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• minimalBetti(MonomialIdeal) -- 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
• minimalPresentation(...,Exclude=>...) -- compute a minimal presentation of a quotient ring
• minimalPresentation(ChainComplex) -- minimal presentation of a module
• minimalPresentation(ChainComplexMap) -- minimal presentation of a module
• minimalPresentation(CoherentSheaf) -- minimal presentation of a module
• minimalPresentation(GradedModule) -- minimal presentation of a module
• minimalPresentation(GradedModuleMap) -- minimal presentation of a module
• minimalPresentation(Ideal) -- compute a minimal presentation of the quotient ring defined by an ideal
• minimalPresentation(Matrix) -- minimally present source and target of a matrix
• minimalPresentation(Module) -- minimal presentation of a module
• minimalPresentation(Ring) -- compute a minimal presentation of a quotient ring
• minimalPresentationMap -- compute a minimal presentation of a quotient ring
• minimalPresentationMapInv -- compute a minimal presentation of a quotient ring
• Minimize -- an optional argument
• minimizeFilename -- minimize a file name
• MinimumVersion -- the minimum required version of a program
• minors -- ideal generated by minors
• minors(...,First=>...) -- ideal generated by minors
• minors(...,Limit=>...) -- ideal generated by minors
• minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• minors(ZZ,Matrix) -- ideal generated by minors
• minPosition -- position of the smallest element
• minPosition(BasicList) -- 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
• Module ** ChainComplex -- tensor product
• Module ** ChainComplexMap -- tensor product
• Module ** GradedModule -- a binary operator, usually used for tensor product or Cartesian product
• Module ** Matrix -- tensor product
• Module ** Module -- tensor product
• Module ** Ring -- tensor product
• Module + Module -- sum of submodules
• Module ++ GradedModule -- direct sum of modules
• Module ++ Module -- direct sum of modules
• Module / Ideal -- quotient module
• Module / List -- quotient module
• Module / Module -- quotient module
• Module / RingElement -- quotient module
• Module / Sequence -- quotient module
• Module / Vector -- quotient module
• Module == Ideal -- equality
• Module == Module -- equality
• Module == ZZ -- equality
• Module ^ Array -- projection onto summand
• Module ^ List -- projection onto summand
• Module ^ ZZ -- direct sum
• Module ^** ZZ -- tensor power
• Module _ Array -- inclusion from summand
• Module _ List -- map from free module to some generators
• Module _ ZZ
• Module ~ -- make a coherent sheaf
• Module Array -- make a chain complex from a module
• module homomorphisms
• module(CoherentSheaf) -- get the module defining a coherent sheaf
• module(Ring) -- make or get a module
• module(SheafOfRings) -- make or get a module
• module(Vector) -- the module of a vector
• modules
• modules in Macaulay2
• modulo -- find the pre-image (pullback) of image of a map (low level version)
• modulo(Matrix,Matrix) -- find the pre-image (pullback) of image of a map (low level version)
• modulo(Matrix,Nothing) -- find the pre-image (pullback) of image of a map (low level version)
• modulo(Nothing,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
• Monoid ** Monoid -- tensor product of monoids
• Monoid ^** ZZ -- tensor product of monoids
• monoid(...,DegreeLift=>...) -- specify maps between degree groups
• monoid(...,DegreeMap=>...) -- specify maps between degree groups
• monoid(...,DegreeRank=>...) -- specify the degrees of the variables
• monoid(...,Degrees=>...) -- specify the degrees of the variables
• monoid(...,Global=>...) -- specify local or global monomial order
• monoid(...,Heft=>...) -- specify a heft vector
• monoid(...,Inverses=>...) -- allow negative exponents in monomials
• monoid(...,Join=>...) -- specify how to handle degrees in the coefficient ring
• monoid(...,Local=>...) -- specify local or global monomial order
• monoid(...,MonomialOrder=>...) -- specify the monomial ordering
• monoid(...,MonomialSize=>...) -- specify the bit-length of monomial exponents in the ring
• monoid(...,SkewCommutative=>...) -- specify Skew commuting variables in the ring
• monoid(...,VariableBaseName=>...) -- specify the names of the indeterminates
• monoid(...,Variables=>...) -- specify the names of the indeterminates
• monoid(...,Weights=>...) -- specify weights of the variables
• monoid(...,WeylAlgebra=>...) -- specify differential operators in the ring
• monoid(Array) -- make or retrieve a monoid
• monoid(List) -- make or retrieve a monoid
• monoid(Ring) -- make or retrieve a monoid
• MonoidElement -- the class of all monoid elements
• MonoidElement == MonoidElement -- equality
• Monomial -- value of an optional argument
• monomial orderings
• monomial orders for free modules
• monomialCurveIdeal -- make the ideal of a monomial curve
• MonomialIdeal -- the class of all monomial ideals handled by the engine
• monomialIdeal -- make a monomial ideal
• MonomialIdeal * Ideal -- product of ideals
• MonomialIdeal * Module -- a binary operator, usually used for multiplication
• MonomialIdeal * MonomialIdeal -- a binary operator, usually used for multiplication
• MonomialIdeal * Ring -- a binary operator, usually used for multiplication
• MonomialIdeal + Ideal -- sum of ideals
• MonomialIdeal + MonomialIdeal -- a unary or binary operator, usually used for addition
• MonomialIdeal - MonomialIdeal -- monomial ideal difference
• MonomialIdeal == Ideal -- equality
• MonomialIdeal == MonomialIdeal -- equality
• MonomialIdeal == Ring -- equality
• MonomialIdeal == ZZ -- equality
• MonomialIdeal ^ Array -- bracket power of an ideal
• MonomialIdeal ^ ZZ -- power of an ideal
• MonomialIdeal _ ZZ
• monomialIdeal(Ideal) -- monomial ideal of lead monomials of a Gröbner basis
• monomialIdeal(List) -- monomial ideal of lead monomials
• monomialIdeal(Matrix) -- monomial ideal of lead monomials
• monomialIdeal(Module) -- monomial ideal of lead monomials of a Gröbner basis
• monomialIdeal(MonomialIdeal) -- monomial ideal of lead monomials of a Gröbner basis
• monomialIdeal(RingElement) -- monomial ideal of lead monomials
• monomialIdeal(Sequence) -- monomial ideal of lead monomials
• MonomialOrder -- monomial ordering
• Monomials -- whether to display the number of monomial
• monomials -- matrix of monomials in a ring element or matrix
• monomials(...,Variables=>...) -- specify variables
• monomials(Matrix) -- matrix of monomials in a ring element or matrix
• monomials(RingElement) -- matrix of monomials in a ring element or matrix
• MonomialSize -- an optional argument
• monomialSubideal -- find the largest monomial ideal in an ideal
• monomialSubideal(Ideal) -- find the largest monomial ideal in an ideal
• moveFile
• moveFile(...,Verbose=>...)
• moveFile(String)
• moveFile(String,String)
• moving or copying the Macaulay2 files
• MPFI
• MPFR
• MPIR
• MPSolve -- a library for finding roots of univariate polynomials
• multidegree -- multidegree
• multidegree(Ideal) -- multidegree
• multidegree(Module) -- multidegree
• multidegree(Ring) -- multidegree
• multigraded -- convert a Betti tally into a multigraded Betti tally
• multigraded(BettiTally) -- convert a Betti tally into a multigraded Betti tally
• MultigradedBettiTally -- the class of all multigraded Betti tallies
• MultigradedBettiTally Sequence -- the class of all multigraded Betti tallies
• mutable matrices
• MutableHashTable -- the class of all mutable hash tables
• mutableIdentity -- make a mutable identity matrix
• mutableIdentity(...,Dense=>...) -- make a mutable identity matrix
• mutableIdentity(Ring,ZZ) -- make a mutable identity matrix
• mutableIdentity(RingFamily,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
• MutableMatrix * MutableMatrix -- a binary operator, usually used for multiplication
• MutableMatrix + MutableMatrix -- a unary or binary operator, usually used for addition
• MutableMatrix - MutableMatrix -- a unary or binary operator, usually used for negation or subtraction
• MutableMatrix == MutableMatrix -- equality
• MutableMatrix == ZZ -- equality
• MutableMatrix _ Sequence -- get entry of matrix
• MutableMatrix _ Sequence = Thing -- assignment to an element of a mutable matrix
• mutableMatrix(...,Dense=>...) -- make a mutable matrix
• mutableMatrix(List) -- make a mutable matrix
• mutableMatrix(Matrix) -- make a mutable matrix
• mutableMatrix(MutableMatrix) -- make a mutable matrix
• mutableMatrix(Ring,ZZ,ZZ) -- make a mutable matrix filled with zeroes
• mutableMatrix(RingFamily,ZZ,ZZ) -- make a mutable matrix filled with zeroes
• Name -- the preamble of a package
• nanosleep -- sleep for a given number of nanoseconds
• nauty
• NCLex -- Non-commutative lexicographical order.
• needs -- read Macaulay2 commands if necessary
• needsPackage -- load a package if not already loaded
• needsPackage(...,Configuration=>...) -- load a package if not already loaded
• needsPackage(...,DebuggingMode=>...) -- load a package if not already loaded
• needsPackage(...,FileName=>...) -- load a package if not already loaded
• needsPackage(...,LoadDocumentation=>...) -- load a package if not already loaded
• needsPackage(...,Reload=>...) -- load a package if not already loaded
• needsPackage(String) -- load a package if not already loaded
• Net -- the class of all nets and strings
• net -- format for printing, as a net
• Net == Net -- equality
• Net == String -- equality
• Net ^ ZZ -- raise a net or string
• Net | Net -- join strings or nets
• Net || Net -- join nets or strings vertically
• net(String) -- convert a string to a net
• net(Thing) -- format for printing, as a net
• NetFile -- the class of all net files
• NetFile << Manipulator -- the class of all net files
• NetFile << Net -- the class of all net files
• NetFile << String -- the class of all net files
• netList -- a table of boxes
• netList(...,Alignment=>...) -- a table of boxes
• netList(...,BaseRow=>...) -- a table of boxes
• netList(...,Boxes=>...) -- a table of boxes
• netList(...,HorizontalSpace=>...) -- a table of boxes
• netList(...,VerticalSpace=>...) -- a table of boxes
• netList(VisibleList) -- a table of boxes
• new -- new objects and new types
• new ChainComplex -- make a new chain complex from scratch
• new HashTable from List -- make a hash table from a list
• new Manipulator from Function -- the class of all file manipulators
• new URL from String -- a type representing a URL
• newClass -- set the class and parent of an object
• newCoordinateSystem -- change variables
• newCoordinateSystem(PolynomialRing,Matrix) -- change variables
• NewFromMethod
• newline -- the new line character sequence
• NewMethod
• newNetFile -- create a new net file
• NewOfFromMethod
• NewOfMethod
• newPackage -- the preamble of a package
• newPackage(...,Authors=>...) -- the preamble of a package
• newPackage(...,AuxiliaryFiles=>...) -- the preamble of a package
• newPackage(...,CacheExampleOutput=>...) -- the preamble of a package
• newPackage(...,Certification=>...) -- the preamble of a package
• newPackage(...,Configuration=>...) -- the preamble of a package
• newPackage(...,Date=>...) -- the preamble of a package
• newPackage(...,DebuggingMode=>...) -- the preamble of a package
• newPackage(...,Headline=>...) -- the preamble of a package
• newPackage(...,HomePage=>...) -- the preamble of a package
• newPackage(...,InfoDirSection=>...) -- the preamble of a package
• newPackage(...,Keywords=>...) -- the preamble of a package
• newPackage(...,OptionalComponentsPresent=>...) -- the preamble of a package
• newPackage(...,PackageExports=>...) -- the preamble of a package
• newPackage(...,PackageImports=>...) -- the preamble of a package
• newPackage(...,Reload=>...) -- the preamble of a package
• newPackage(...,UseCachedExampleOutput=>...) -- the preamble of a package
• newPackage(...,Version=>...) -- the preamble of a package
• newPackage(String) -- the preamble of a package
• newRing -- make a copy of a ring, with some features changed
• newRing(...,DegreeLift=>...) -- make a copy of a ring, with some features changed
• newRing(...,DegreeMap=>...) -- make a copy of a ring, with some features changed
• newRing(...,DegreeRank=>...) -- make a copy of a ring, with some features changed
• newRing(...,Degrees=>...) -- make a copy of a ring, with some features changed
• newRing(...,Global=>...) -- make a copy of a ring, with some features changed
• newRing(...,Heft=>...) -- make a copy of a ring, with some features changed
• newRing(...,Inverses=>...) -- make a copy of a ring, with some features changed
• newRing(...,Join=>...) -- make a copy of a ring, with some features changed
• newRing(...,Local=>...) -- make a copy of a ring, with some features changed
• newRing(...,MonomialOrder=>...) -- make a copy of a ring, with some features changed
• newRing(...,MonomialSize=>...) -- make a copy of a ring, with some features changed
• newRing(...,SkewCommutative=>...) -- make a copy of a ring, with some features changed
• newRing(...,VariableBaseName=>...) -- make a copy of a ring, with some features changed
• newRing(...,Variables=>...) -- make a copy of a ring, with some features changed
• newRing(...,Weights=>...) -- make a copy of a ring, with some features changed
• newRing(...,WeylAlgebra=>...) -- make a copy of a ring, with some features changed
• newRing(PolynomialRing) -- make a copy of a ring, with some features changed
• newRing(QuotientRing) -- make a copy of a ring, with some features changed
• next -- get the next object from an iterator
• next(Iterator) -- 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
• nextPrime(Number) -- compute the smallest prime greater than or equal to a given number
• NoPrint -- top level method for non-printing results
• norm
• norm(InexactField,MutableMatrix)
• norm(InfiniteNumber,Matrix)
• norm(InfiniteNumber,Number)
• norm(InfiniteNumber,RingElement)
• norm(List)
• norm(Matrix)
• norm(MutableMatrix)
• norm(Number)
• norm(RingElement)
• norm(RR,Matrix)
• norm(RR,MutableMatrix)
• norm(RR,Number)
• norm(RR,RingElement)
• norm(Vector)
• normal forms
• normaliz
• not -- negation
• not documented yet
• Nothing -- the empty class
• Nothing << Manipulator -- print to a file
• Nothing << Thing -- print to a file
• Nothing == Nothing -- equality
• notify -- whether to notify the user when a file is loaded
• notImplemented -- print an 'not implemented' error message
• NTL library
• null -- the unique member of the empty class
• nullaryMethods
• nullhomotopy -- make a null homotopy
• nullhomotopy(ChainComplexMap) -- make a null homotopy
• nullSpace -- find the null space of a mutable matrix
• nullSpace(MutableMatrix) -- 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
• Number % GroebnerBasis -- a binary operator, usually used for remainder and reduction
• Number % Ideal -- a binary operator, usually used for remainder and reduction
• Number % RingElement -- a binary operator, usually used for remainder and reduction
• Number * Constant -- a binary operator, usually used for multiplication
• Number * Matrix -- a binary operator, usually used for multiplication
• Number + Constant -- a unary or binary operator, usually used for addition
• Number + InfiniteNumber -- a unary or binary operator, usually used for addition
• Number + Matrix -- a unary or binary operator, usually used for addition
• Number - Constant -- a unary or binary operator, usually used for negation or subtraction
• Number - InfiniteNumber -- a unary or binary operator, usually used for negation or subtraction
• Number - Matrix -- a unary or binary operator, usually used for negation or subtraction
• Number / Constant
• Number // InfiniteNumber -- a binary operator, usually used for quotient
• Number // Matrix -- a binary operator, usually used for quotient
• Number // RingElement -- a binary operator, usually used for quotient
• Number == InfiniteNumber -- equality
• Number == Matrix -- equality
• Number == RingElement -- equality
• Number ^ Constant
• Number ^ Ring -- lift to another ring
• Number ^ RingFamily -- lift to another ring
• Number _ Ring -- promote to another ring
• Number | Matrix -- join matrices horizontally
• Number || Matrix -- join matrices vertically
• numbered variables
• NumberedVerticalList -- a type of visible self-initializing list that prints vertically
• numColumns -- number of columns in a matrix or mutable matrix
• numColumns(Matrix) -- number of columns in a matrix or mutable matrix
• numColumns(MutableMatrix) -- number of columns in a matrix or mutable matrix
• numerator -- numerator of a fraction
• numerator(Divide) -- numerator of a fraction
• numeric -- convert to floating point
• numeric types
• numeric(CC) -- convert to floating point
• numeric(Constant) -- convert to floating point
• numeric(InfiniteNumber) -- convert to floating point
• numeric(Matrix) -- convert to floating point
• numeric(Number) -- convert to floating point
• numeric(RR) -- convert to floating point
• numeric(RRi) -- convert to floating point
• numeric(Vector) -- convert to floating point
• numeric(VisibleList) -- convert to floating point
• numeric(ZZ,CC) -- convert to floating point
• numeric(ZZ,Constant) -- convert to floating point
• numeric(ZZ,InfiniteNumber) -- convert to floating point
• numeric(ZZ,Matrix) -- convert to floating point
• numeric(ZZ,Number) -- convert to floating point
• numeric(ZZ,RRi) -- convert to floating point
• numeric(ZZ,Vector) -- convert to floating point
• numeric(ZZ,VisibleList) -- convert to floating point
• numericInterval -- converts to an interval
• numericInterval(Constant) -- converts to an interval
• numericInterval(ZZ,Constant) -- converts to an interval
• numgens -- the number of generators
• numgens(CoherentSheaf) -- the number of generators of the underlying module
• numgens(EngineRing) -- number of generators of a polynomial ring
• numgens(FractionField) -- number of generators of a polynomial ring
• numgens(Ideal) -- number of generators of an ideal
• numgens(Module) -- number of generators of a module
• numgens(Monoid) -- number of generators of a monoid
• numgens(MonomialIdeal) -- number of generators of a polynomial ring
• numgens(PolynomialRing) -- number of generators of a polynomial ring
• numgens(QuotientRing) -- number of generators of a polynomial ring
• numgens(Ring) -- number of generators of a polynomial ring
• numRows -- number of rows in a matrix or mutable matrix
• numRows(Matrix) -- number of rows in a matrix or mutable matrix
• numRows(MutableMatrix) -- number of rows in a matrix or mutable matrix
• obtaining the monomial order of a ring
• odd -- tell whether an integer is odd
• of -- a keyword
• ofClass -- English phrases for types
• ofClass(ImmutableType) -- English phrases for types
• ofClass(List) -- English phrases for types
• ofClass(Type) -- English phrases for types
• on -- trace a function each time it's run
• on(...,CallLimit=>...) -- trace a function each time it's run
• on(...,GenerateAssertions=>...) -- trace a function each time it's run
• on(...,Name=>...) -- trace a function each time it's run
• OneExpression -- the class all one expressions
• OO -- the structure sheaf
• oo -- the last output value
• OO _ Variety -- the structure sheaf
• ooo -- the next to the last output value
• oooo -- the third to the last output value
• openDatabase -- open a database file
• openDatabase(String) -- open a database file
• openDatabaseOut -- open a database file for writing
• openDatabaseOut(String) -- open a database file for writing
• openFiles -- list the open files
• openIn -- open an input file
• openIn(String) -- open an input file
• openInOut -- open an input output file
• openInOut(File) -- open an input output file
• openInOut(String) -- open an input output file
• openListener -- open a port for listening
• openListener(String) -- open a port for listening
• openOut -- open an output file
• openOut(String) -- open an output file
• openOutAppend -- open an output file for appending
• openOutAppend(String) -- open an output file for appending
• operatorAttributes -- a hashtable with information about Macaulay2 operators
• operators
• Option -- the class of all key-value pairs K => V
• Option ++ Option -- direct sum of modules or maps
• optional argument documentation template
• optional argument name documentation template
• OptionalComponentsPresent -- an optional argument
• Options -- an optional argument
• options -- get options
• options(Command) -- get optional arguments and default values of functions and methods
• options(Function) -- get optional arguments and default values of functions and methods
• options(Monoid) -- get values used for optional arguments
• options(Package)
• options(PolynomialRing) -- get values used for optional arguments
• options(QuotientRing) -- get values used for optional arguments
• options(Ring) -- get values used for optional arguments
• options(Sequence) -- get optional arguments and default values of functions and methods
• options(ZZ) -- get optional arguments and default values of functions and methods
• OptionTable -- the class of hash tables for optional arguments
• OptionTable ++ List -- a binary operator, usually used for direct sum
• OptionTable ++ OptionTable -- a binary operator, usually used for direct sum
• OptionTable >> Function -- attaching options to a function
• or -- disjunction
• Order -- specify the order of a Hilbert series required
• order -- a key used internally
• OrderedMonoid -- the class of all ordered monoids
• Other sources of information about Macaulay2
• OutputDictionary -- the dictionary for output values
• Outputs -- outputs for a function in a documentation node
• override -- override default values for optional arguments
• overview documentation template
• pack -- pack elements of a list or string into several shorter lists or strings
• pack(BasicList,ZZ) -- pack elements of a list or string into several shorter lists or strings
• pack(String,ZZ) -- pack elements of a list or string into several shorter lists or strings
• pack(ZZ,BasicList) -- pack elements of a list or string into several shorter lists or strings
• pack(ZZ,String) -- pack elements of a list or string into several shorter lists or strings
• Package -- the class of all packages
• package -- get containing package
• package documentation template
• package(Array) -- get containing package
• package(Dictionary) -- get containing package
• package(DocumentTag) -- get containing package
• package(Function) -- get containing package
• package(HashTable) -- get containing package
• package(Nothing) -- get containing package
• package(Option) -- get containing package
• package(Package) -- get containing package
• package(Sequence) -- get containing package
• package(String) -- get containing package
• package(Symbol) -- get containing package
• package(Thing) -- get containing package
• PackageDictionary -- the dictionary for names of packages
• PackageExports -- an optional argument
• PackageImports -- an optional argument
• packages -- Macaulay2 packages
• packages provided with Macaulay2
• packing monomials for efficiency
• pad -- pad a string or net with spaces
• pad(Net,ZZ) -- pad a string or net with spaces
• pad(String,ZZ) -- pad a string or net with spaces
• pad(ZZ,Net) -- pad a string or net with spaces
• pad(ZZ,String) -- 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
• pairs(BasicList) -- list the pairs in a hash table, dictionary, or basic list
• pairs(Dictionary) -- list the pairs in a hash table, dictionary, or basic list
• pairs(HashTable) -- list the pairs in a hash table, dictionary, or basic list
• PairsRemaining -- whether to display the number of S-pairs remaining
• parallel programming with threads and tasks
• parent -- parent type of an object
• Parenthesize
• parsing precedence, in detail
• part -- select terms of a polynomial by degree(s) or weight(s)
• part(InfiniteNumber,InfiniteNumber,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(InfiniteNumber,InfiniteNumber,VisibleList,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(InfiniteNumber,ZZ,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(InfiniteNumber,ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(List,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(Nothing,Nothing,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(Nothing,Nothing,VisibleList,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(Nothing,ZZ,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(Nothing,ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,InfiniteNumber,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,InfiniteNumber,VisibleList,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,Nothing,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,Nothing,VisibleList,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,ZZ,RingElement) -- select terms of a polynomial by degree(s) or weight(s)
• part(ZZ,ZZ,VisibleList,RingElement) -- 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
• Partition _ ZZ -- get element
• partition(Function,VirtualTally) -- partition a set or list by values of a function
• partition(Function,VirtualTally,VisibleList) -- partition a set or list by values of a function
• partition(Function,VisibleList) -- partition a set or list by values of a function
• partition(Function,VisibleList,VisibleList) -- partition a set or list by values of a function
• partitions -- list the partitions of an integer
• partitions(ZZ) -- list the partitions of an integer
• partitions(ZZ,ZZ) -- list the partitions of an integer
• parts -- display terms of a polynomial degree by degree
• parts(RingElement) -- display terms of a polynomial degree by degree
• path -- list of directories to look in
• pdim -- calculate the projective dimension
• pdim(BettiTally) -- the class of all Betti tallies
• pdim(CoherentSheaf) -- calculate the projective dimension
• pdim(Module) -- calculate the projective dimension of a module
• peek -- examine contents of an object
• peek' -- examine contents of an object
• peek'(ZZ,Thing) -- examine contents of an object
• permanents -- ideal generated by square permanents of a matrix
• permanents(ZZ,Matrix) -- ideal generated by square permanents of a matrix
• permutations -- produce all permutations of a list
• permutations(VisibleList) -- produce all permutations of a list
• permutations(ZZ) -- produce all permutations of a list
• Pfaffians
• pfaffians -- ideal generated by Pfaffians
• pfaffians(ZZ,Matrix) -- ideal generated by Pfaffians
• pi
• pivots -- list of pivot locations of a matrix
• pivots(Matrix) -- list of pivot locations of a matrix
• plus -- addition
• poincare -- assemble degrees of a ring, module, or ideal into a polynomial
• poincare(BettiTally) -- the class of all Betti tallies
• poincare(ChainComplex) -- assemble degrees of a chain complex into a polynomial
• poincare(Ideal) -- assemble degrees of a ring, module, or ideal into a polynomial
• poincare(Module) -- assemble degrees of a ring, module, or ideal into a polynomial
• poincare(MonomialIdeal) -- assemble degrees of a ring, module, or ideal into a polynomial
• poincare(Ring) -- assemble degrees of a ring, module, or ideal into a polynomial
• poincareN -- assemble degrees into polynomial
• poincareN(ChainComplex) -- assemble degrees into polynomial
• polarize -- given a monomial ideal, computes the squarefree monomial ideal obtained via polarization
• polarize(...,VariableBaseName=>...) -- given a monomial ideal, computes the squarefree monomial ideal obtained via polarization
• polarize(MonomialIdeal) -- given a monomial ideal, computes the squarefree monomial ideal obtained via polarization
• polynomial rings
• PolynomialRing -- the class of all ordered monoid rings
• Position -- monomial ordering
• position -- the first element of a list satisfying a condition
• position(...,Reverse=>...) -- the first element of a list satisfying a condition
• position(VisibleList,Function) -- the first element of a list satisfying a condition
• position(VisibleList,VisibleList,Function) -- the first element of a list satisfying a condition
• positions -- which elements of a list satisfy a condition
• positions(MutableList,Function) -- which elements of a list satisfy a condition
• positions(VisibleList,Function) -- which elements of a list satisfy a condition
• POSIX -- evaluate a regular expression search
• Postfix -- a hashtable with information about Macaulay2 operators
• Power -- the class of all power expressions
• power -- power
• powermod -- powers of integers mod N
• powermod(ZZ,ZZ,ZZ) -- powers of integers mod N
• powers
• precedence of operators
• Precision -- name of an optional argument.
• precision
• precision(FractionField)
• precision(GaloisField)
• precision(InexactField)
• precision(InexactNumber)
• precision(Matrix)
• precision(MutableMatrix)
• precision(Number)
• precision(PolynomialRing)
• precision(QuotientRing)
• precision(Ring)
• precision(RingElement)
• Prefix -- a hashtable with information about Macaulay2 operators
• prefixDirectory -- the prefix directory
• prefixPath -- absolute locations of Macaulay2 files
• preimage -- preimage of a map
• preimage(Matrix,Module) -- preimage of a map
• preimage(RingMap,Ideal) -- preimage of a map
• prepend -- add an element to the beginning of a list
• prepend(Thing,BasicList) -- add an element to the beginning of a list
• presentation -- presentation of a module or ring
• presentation(Module) -- presentation of a module
• presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring
• presentation(QuotientRing) -- presentation of a quotient ring
• pretty -- a pretty printer
• PrimitiveElement -- specify a primitive element
• Print -- top level method for printing results
• print -- print something
• printerr -- print something to stderr
• printing and formatting for new classes
• printing to the screen
• printingAccuracy -- current accuracy for printing numbers
• printingLeadLimit -- maximum number of leading zeroes to use when printing real numbers
• printingPrecision -- current precision for printing numbers
• printingSeparator -- string used to separate mantissa from exponent when printing real numbers
• printingTimeLimit
• printingTrailLimit -- maximum number of additional trailing digits to use when printing real numbers
• printString -- lowlevel function to print a string, net, or symbol
• printWidth
• processID -- the process identifier
• Product -- the class of all product expressions
• product
• product(List) -- product of elements
• product(Set) -- product of elements
• product(VirtualTally) -- product of elements
• product(VisibleList,Function) -- product of values of a function
• product(VisibleList,VisibleList,Function) -- product of results of applying a function pairwise
• product(ZZ,Function) -- product of consecutive values of a function
• ProductOrder -- product ordering
• profile -- profile a function
• profile(Function) -- profile a function
• profile(String,Function) -- profile a function
• profileSummary -- display profiling data
• Program -- external program object
• Program << Thing -- run program with input redirection
• programPaths -- user-defined external program paths
• ProgramRun -- result of running an external program
• Proj -- make a projective variety
• Proj(Ring) -- make a projective variety
• projections, inclusions, and permutations
• Projective -- whether to produce a projective Hilbert polynomial
• ProjectiveHilbertPolynomial -- the class of all Hilbert polynomials
• projectiveHilbertPolynomial -- Hilbert polynomial of projective space
• ProjectiveHilbertPolynomial * ZZ -- a binary operator, usually used for multiplication
• ProjectiveHilbertPolynomial + ProjectiveHilbertPolynomial -- a unary or binary operator, usually used for addition
• ProjectiveHilbertPolynomial + ZZ -- a unary or binary operator, usually used for addition
• ProjectiveHilbertPolynomial - ProjectiveHilbertPolynomial -- a unary or binary operator, usually used for negation or subtraction
• ProjectiveHilbertPolynomial - ZZ -- a unary or binary operator, usually used for negation or subtraction
• ProjectiveHilbertPolynomial == ProjectiveHilbertPolynomial -- equality
• ProjectiveHilbertPolynomial == ZZ -- equality
• ProjectiveHilbertPolynomial ZZ -- value of polynomial
• projectiveHilbertPolynomial(ZZ) -- Hilbert polynomial of projective space
• projectiveHilbertPolynomial(ZZ,ZZ) -- Hilbert polynomial of projective space
• ProjectiveVariety -- the class of all projective varieties
• promote -- promote to another ring
• promote(RR,type of QQ) -- promote to another ring
• protect -- protect a symbol
• Prune -- value of an optional argument
• prune -- prune, e.g., compute a minimal presentation
• prune(...,Exclude=>...) -- compute a minimal presentation of a quotient ring
• prune(ChainComplex) -- minimal presentation of a module
• prune(ChainComplexMap) -- minimal presentation of a module
• prune(CoherentSheaf) -- minimal presentation of a module
• prune(GradedModule) -- minimal presentation of a module
• prune(GradedModuleMap) -- minimal presentation of a module
• prune(Ideal) -- compute a minimal presentation of the quotient ring defined by an ideal
• prune(Matrix) -- minimally present source and target of a matrix
• prune(Module) -- minimal presentation of a module
• prune(Ring) -- compute a minimal presentation of a quotient ring
• pruningMap
• Pseudocode -- the class of pseudocodes
• pseudocode -- produce the pseudocode for a function
• pseudoRemainder -- compute the pseudo-remainder
• pseudoRemainder(RingElement,RingElement) -- compute the pseudo-remainder
• pushForward
• pushForward(...,DegreeLimit=>...)
• pushForward(...,MonomialOrder=>...)
• pushForward(...,PairLimit=>...)
• pushForward(...,StopBeforeComputation=>...)
• pushForward(...,UseHilbertFunction=>...)
• pushForward(RingMap,Module)
• QQ -- the class of all rational numbers
• QQ ! -- factorial
• QQ % QQ -- a binary operator, usually used for remainder and reduction
• QQ % ZZ -- a binary operator, usually used for remainder and reduction
• QQ * BettiTally -- the class of all Betti tallies
• QQ * CC -- a binary operator, usually used for multiplication
• QQ * QQ -- a binary operator, usually used for multiplication
• QQ * RR -- a binary operator, usually used for multiplication
• QQ * RRi -- a binary operator, usually used for multiplication
• QQ * ZZ -- a binary operator, usually used for multiplication
• QQ + CC -- a unary or binary operator, usually used for addition
• QQ + QQ -- a unary or binary operator, usually used for addition
• QQ + RR -- a unary or binary operator, usually used for addition
• QQ + RRi -- a unary or binary operator, usually used for addition
• QQ + ZZ -- a unary or binary operator, usually used for addition
• QQ - CC -- a unary or binary operator, usually used for negation or subtraction
• QQ - QQ -- a unary or binary operator, usually used for negation or subtraction
• QQ - RR -- a unary or binary operator, usually used for negation or subtraction
• QQ - RRi -- a unary or binary operator, usually used for negation or subtraction
• QQ - ZZ -- a unary or binary operator, usually used for negation or subtraction
• QQ / CC -- a binary operator, usually used for division
• QQ / QQ -- a binary operator, usually used for division
• QQ / RR -- a binary operator, usually used for division
• QQ / RRi -- a binary operator, usually used for division
• QQ / ZZ -- a binary operator, usually used for division
• QQ // QQ -- a binary operator, usually used for quotient
• QQ // ZZ -- a binary operator, usually used for quotient
• QQ == CC -- equality
• QQ == QQ -- equality
• QQ == RR -- equality
• QQ == RRi -- equality
• QQ == ZZ -- equality
• QRDecomposition -- compute a QR decomposition of a real matrix
• QRDecomposition(Matrix) -- compute a QR decomposition of a real matrix
• QRDecomposition(MutableMatrix) -- compute a QR decomposition of a real matrix
• quit -- quit the program
• Quotient -- value of an optional argument
• quotient -- quotient or division
• quotient rings
• quotient' -- matrix quotient (opposite)
• quotient'(Matrix,Matrix) -- matrix quotient (opposite)
• quotient(Ideal) -- submodule to quotient module
• quotient(Matrix,GroebnerBasis) -- matrix quotient
• quotient(Matrix,Matrix) -- matrix quotient
• quotient(Module) -- submodule to quotient module
• quotientRemainder -- matrix quotient and remainder
• quotientRemainder' -- matrix quotient and remainder (opposite)
• quotientRemainder'(Matrix,Matrix) -- matrix quotient and remainder (opposite)
• quotientRemainder(InexactNumber,RingElement) -- quotient and remainder
• quotientRemainder(Matrix,GroebnerBasis) -- matrix quotient and remainder
• quotientRemainder(Matrix,Matrix) -- matrix quotient and remainder
• quotientRemainder(Number,RingElement) -- quotient and remainder
• quotientRemainder(RingElement,InexactNumber) -- quotient and remainder
• quotientRemainder(RingElement,Number) -- quotient and remainder
• quotientRemainder(RingElement,RingElement) -- quotient and remainder
• quotientRemainder(ZZ,ZZ) -- quotient and remainder
• QuotientRing -- the class of all quotient rings
• RaiseError -- whether to raise an error
• random -- get a random object
• random and generic matrices
• random(...,Density=>...) -- make a random module map
• random(...,Height=>...) -- get a random homogeneous element from a graded ring
• random(...,MaximalRank=>...) -- make a random module map
• random(...,UpperTriangular=>...) -- make a random module map
• random(List) -- shuffle a list randomly
• random(List,Ideal) -- get a random homogeneous element from a graded ideal
• random(List,Ring) -- get a random homogeneous element from a graded ring
• random(Module,Module) -- make a random module map
• random(RR) -- get a random integer or real number
• random(RR,RR) -- get a random integer or real number
• random(Type) -- get a random object of a type
• random(ZZ) -- get a random integer or real number
• random(ZZ,Ideal) -- get a random homogeneous element from a graded ideal
• random(ZZ,Ring) -- get a random homogeneous element from a graded ring
• random(ZZ,ZZ) -- get a random integer or real number
• randomKRationalPoint -- Pick a random K rational point on the scheme X defined by I
• randomKRationalPoint(Ideal) -- Pick a random K rational point on the scheme X defined by I
• randomMutableMatrix -- a random mutable matrix of integers
• randomMutableMatrix(...,Dense=>...) -- a random mutable matrix of integers
• randomMutableMatrix(ZZ,ZZ,RR,ZZ) -- a random mutable matrix of integers
• Range -- can be assigned a integral interval
• rank -- compute the rank
• rank of a matrix
• rank(CoherentSheaf) -- compute the rank
• rank(GradedModule) -- compute the rank
• rank(Matrix) -- compute the rank
• rank(Module) -- compute the rank
• rank(MutableMatrix) -- compute the rank
• read -- read from a file
• read(File) -- read from a file
• read(File,ZZ) -- read from a file
• read(Sequence) -- read from a file
• read(String) -- read from a file
• readDirectory -- read the contents of a directory
• reading files
• reading the documentation
• readlink -- readlink fn
• readPackage -- read the package preamble
• readPackage(...,FileName=>...) -- read the package preamble
• readPackage(Package) -- read the package preamble
• readPackage(String) -- read the package preamble
• RealField -- the class of all real fields
• realPart -- real part
• realPart(Number) -- real part
• realpath -- convert a filename to one passing through no symbolic links
• recursionDepth -- the current recursion depth
• recursionLimit -- set the limit on recursion
• Reduce -- an optional argument
• reducedRowEchelonForm -- compute the reduced row echelon form of a matrix or mutable matrix over a field
• reducedRowEchelonForm(Matrix) -- compute the reduced row echelon form of a matrix or mutable matrix over a field
• reducedRowEchelonForm(MutableMatrix) -- compute the reduced row echelon form of a matrix or mutable matrix over a field
• reduceHilbert -- reduce a Hilbert series expression
• reduceHilbert(Divide) -- reduce a Hilbert series expression
• References -- references listed in a documentation node
• regex -- evaluate a regular expression search
• regex(...,POSIX=>...) -- evaluate a regular expression search
• regex(String,String) -- evaluate a regular expression search
• regex(String,ZZ,String) -- evaluate a regular expression search
• regex(String,ZZ,ZZ,String) -- evaluate a regular expression search
• regexQuote -- escape special characters in regular expressions
• regexQuote(String) -- escape special characters in regular expressions
• registerFinalizer -- register a string that will be displayed when an object is garbage collected
• regular expressions -- syntax for regular expressions
• regularity -- compute the Castelnuovo-Mumford regularity
• regularity(...,Weights=>...) -- compute the Castelnuovo-Mumford regularity
• regularity(BettiTally) -- the class of all Betti tallies
• regularity(ChainComplex) -- compute the Castelnuovo-Mumford regularity
• regularity(Ideal) -- compute the Castelnuovo-Mumford regularity
• regularity(Module) -- compute the Castelnuovo-Mumford regularity
• regularizedBeta -- regularized beta function
• regularizedGamma -- upper regularized gamma function
• relations -- the defining relations
• relations(Module) -- the defining relations
• relativizeFilename -- relativize a file name
• Reload -- an optional argument
• remainder -- matrix remainder
• remainder' -- matrix quotient and remainder (opposite)
• remainder'(Matrix,Matrix) -- matrix quotient and remainder (opposite)
• remainder(Matrix,GroebnerBasis) -- matrix remainder
• remainder(Matrix,Matrix) -- matrix remainder
• RemakeAllDocumentation -- an optional argument
• remove -- remove an entry from a mutable hash table, list, or database
• remove(Database,String) -- remove an entry from a mutable hash table, list, or database
• remove(HashTable,Thing) -- remove an entry from a mutable hash table, list, or database
• remove(MutableList,ZZ) -- remove an entry from a mutable hash table, list, or database
• removeDirectory -- remove a directory
• removeFile -- remove a file
• reorganize -- reorganize a database file
• replace -- replacement in strings and lists
• replace(String,String,String) -- replace substrings matching a regular expression
• replace(String,String,String,POSIX=>...) -- replace substrings matching a regular expression
• replace(ZZ,Thing,VisibleList) -- copy a list, replacing an element
• replacements for commands and scripts from Macaulay
• RerunExamples -- an optional argument
• reshape -- reshape a matrix
• reshape(Module,Module,Matrix) -- reshape a matrix
• Resolution -- the class of all resolution computations
• resolution -- projective resolution
• resolution(...,DegreeLimit=>...) -- compute only up to this degree
• resolution(...,FastNonminimal=>...) -- compute a non-minimal graded free resolution
• resolution(...,HardDegreeLimit=>...)
• resolution(...,LengthLimit=>...) -- stop when the resolution reaches this length
• resolution(...,PairLimit=>...) -- stop when this number of pairs has been handled
• resolution(...,SortStrategy=>...)
• resolution(...,StopBeforeComputation=>...) -- whether to stop the computation immediately
• resolution(...,Strategy=>...)
• resolution(...,SyzygyLimit=>...) -- stop when this number of syzygies is reached
• resolution(Ideal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal
• resolution(Matrix) -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target
• resolution(Module) -- compute a free resolution of a module
• resolution(MonomialIdeal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal
• restart -- restart Macaulay2
• Result -- an optional argument
• return -- return from a function
• returnCode
• Reverse -- an optional argument
• reverse -- reverse a list, sequence, or string
• reverse(BasicList) -- reverse a list, sequence, or string
• reverse(String) -- reverse a list, sequence, or string
• RevLex -- reverse lexicographic ordering
• Right -- value of an optional argument
• right -- right endpoint of an interval
• right modules or left modules?
• right shift
• Ring -- the class of all rings
• ring -- get the associated ring of an object
• Ring * Ideal -- a binary operator, usually used for multiplication
• Ring * MonomialIdeal -- a binary operator, usually used for multiplication
• Ring * RingElement -- a binary operator, usually used for multiplication
• Ring * Vector -- a binary operator, usually used for multiplication
• Ring ** Ideal -- tensor product
• Ring ** Matrix -- tensor product
• Ring ** Module -- tensor product
• Ring ** Ring -- tensor product of monoids
• Ring / Ideal -- make a quotient ring
• Ring / List -- make a quotient ring
• Ring / Module -- make a quotient ring
• Ring / MonomialIdeal -- make a quotient ring
• Ring / RingElement -- make a quotient ring
• Ring / Sequence -- make a quotient ring
• Ring / ZZ -- make a quotient ring
• Ring == Ideal -- equality
• Ring == MonomialIdeal -- equality
• Ring == ZZ -- equality
• Ring ^ BettiTally -- the class of all Betti tallies
• Ring ^ List -- make a free module
• Ring ^ ZZ -- make a free module
• Ring ^** ZZ -- tensor product of monoids
• Ring _ List -- make a monomial from a list of exponents
• Ring _ ZZ -- get a ring variable by index
• Ring ~ -- make a coherent sheaf of rings
• Ring Array -- the standard way to make a polynomial ring
• Ring List -- make a local polynomial ring
• Ring Monoid -- make a polynomial ring
• ring(CC) -- get the associated ring of an object
• ring(ChainComplex) -- get the associated ring of an object
• ring(ChainComplexMap) -- get the associated ring of an object
• ring(CoherentSheaf) -- get the associated ring of an object
• ring(GradedModule) -- get the associated ring of an object
• ring(GradedModuleMap) -- get the associated ring of an object
• ring(GroebnerBasis) -- get the associated ring of an object
• ring(Ideal) -- get the associated ring of an object
• ring(Matrix) -- get the associated ring of an object
• ring(Module) -- get the associated ring of an object
• ring(MonomialIdeal) -- get the associated ring of an object
• ring(MutableMatrix) -- get the associated ring of an object
• ring(Number) -- get the associated ring of an object
• ring(Resolution) -- get the associated ring of an object
• ring(RingElement) -- get the associated ring of an object
• ring(RR) -- get the associated ring of an object
• ring(RRi) -- get the associated ring of an object
• ring(SheafOfRings) -- get the associated ring of an object
• ring(Variety) -- get the associated ring of an object
• ring(Vector) -- get the associated ring of an object
• RingElement -- the class of all ring elements handled by the engine
• RingElement % GroebnerBasis -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis
• RingElement % Ideal -- normal form of ring elements and matrices
• RingElement % Matrix -- normal form of ring elements and matrices
• RingElement % MonomialIdeal -- normal form of ring elements and matrices
• RingElement % Number -- a binary operator, usually used for remainder and reduction
• RingElement % RingElement -- normal form of ring elements and matrices
• RingElement * ChainComplexMap -- a binary operator, usually used for multiplication
• RingElement * Constant
• RingElement * GradedModuleMap -- a binary operator, usually used for multiplication
• RingElement * Ideal -- a binary operator, usually used for multiplication
• RingElement * Matrix -- a binary operator, usually used for multiplication
• RingElement * Module -- a binary operator, usually used for multiplication
• RingElement * MonomialIdeal -- a binary operator, usually used for multiplication
• RingElement * MutableMatrix -- a binary operator, usually used for multiplication
• RingElement * RingElement -- a binary operator, usually used for multiplication
• RingElement * Vector -- a binary operator, usually used for multiplication
• RingElement + ChainComplexMap -- a unary or binary operator, usually used for addition
• RingElement + Constant
• RingElement + GradedModuleMap -- a unary or binary operator, usually used for addition
• RingElement + Matrix -- a unary or binary operator, usually used for addition
• RingElement + RingElement -- a unary or binary operator, usually used for addition
• RingElement ++ Matrix -- direct sum of maps
• RingElement ++ RingElement -- direct sum of maps
• RingElement - ChainComplexMap -- a unary or binary operator, usually used for negation or subtraction
• RingElement - Constant
• RingElement - GradedModuleMap -- a unary or binary operator, usually used for negation or subtraction
• RingElement - Matrix -- a unary or binary operator, usually used for negation or subtraction
• RingElement - RingElement -- a unary or binary operator, usually used for negation or subtraction
• RingElement .. RingElement -- a sequence of consecutive generators of a polynomial ring
• RingElement ..< RingElement -- a sequence of consecutive generators of a polynomial ring
• RingElement / Constant
• RingElement / RingElement -- fraction
• RingElement // GroebnerBasis -- factor a map through another
• RingElement // Matrix -- factor a map through another
• RingElement // MonomialIdeal -- factor a map through another
• RingElement // Number -- a binary operator, usually used for quotient
• RingElement // RingElement -- factor a map through another
• RingElement == ChainComplexMap -- equality
• RingElement == GradedModuleMap -- equality
• RingElement == Matrix -- equality
• RingElement == Number -- equality
• RingElement == RingElement -- equality
• RingElement == ZZ -- equality
• RingElement \\ Matrix -- factor a map through another
• RingElement ^ ZZ -- power
• RingElement _ Ring -- promote to another ring
• RingElement | Matrix -- join matrices horizontally
• RingElement | RingElement -- join matrices horizontally
• RingElement || Matrix -- join matrices vertically
• RingElement || RingElement -- join matrices vertically
• RingElement Array -- substitution of variables
• RingFamily
• RingFamily ^ List -- make a free module
• RingFamily ^ ZZ -- make a free module
• RingFamily _* -- a unary postfix operator, used for indicating pushforward maps
• RingMap -- the class of all ring maps
• RingMap * RingMap -- a binary operator, usually used for multiplication
• RingMap ** Matrix -- tensor product via a ring map
• RingMap ** Module -- tensor product via a ring map
• RingMap == ZZ -- equality
• RingMap \ List -- apply a function to elements of a list
• RingMap ^ ZZ
• RingMap ChainComplex -- apply a ring map
• RingMap Ideal -- apply a ring map
• RingMap Matrix -- apply a ring map
• RingMap Module -- apply a ring map
• RingMap RingElement -- apply a ring map
• RingMap Vector -- apply a ring map
• rings
• rootPath
• roots -- compute the roots of a polynomial
• roots(RingElement) -- compute the roots of a polynomial
• roots(RingElement,Precision=>...) -- compute the roots of a polynomial
• roots(RingElement,Unique=>...) -- compute the roots of a polynomial
• rootURI
• rotate -- rotate a list
• rotate(ZZ,VisibleList) -- rotate a list
• round -- round a number
• round(CC) -- round a number
• round(QQ) -- round a number
• round(RR) -- round a number
• round(ZZ) -- round a number
• round(ZZ,RR) -- round a number
• row and column operations
• rowAdd -- add a multiple of one row to another
• rowAdd(MutableMatrix,ZZ,Number,ZZ) -- add a multiple of one row to another
• rowAdd(MutableMatrix,ZZ,RingElement,ZZ) -- add a multiple of one row to another
• RowExpression -- the class of all matrix expressions
• rowMult -- multiply a row by a ring element
• rowMult(MutableMatrix,ZZ,Number) -- multiply a row by a ring element
• rowMult(MutableMatrix,ZZ,RingElement) -- multiply a row by a ring element
• rowPermute -- permute some rows
• rowPermute(MutableMatrix,ZZ,List) -- permute some rows
• rowRankProfile -- find the row rank profile of a mutable matrix
• rowRankProfile(MutableMatrix) -- find the row rank profile of a mutable matrix
• rowSwap -- interchange rows
• rowSwap(MutableMatrix,ZZ,ZZ) -- interchange rows
• RR -- the class of all real numbers
• RR ! -- factorial
• RR % QQ -- a binary operator, usually used for remainder and reduction
• RR % RR -- a binary operator, usually used for remainder and reduction
• RR % ZZ -- a binary operator, usually used for remainder and reduction
• RR * CC -- a binary operator, usually used for multiplication
• RR * QQ -- a binary operator, usually used for multiplication
• RR * RR -- a binary operator, usually used for multiplication
• RR * RRi -- a binary operator, usually used for multiplication
• RR * ZZ -- a binary operator, usually used for multiplication
• RR + CC -- a unary or binary operator, usually used for addition
• RR + QQ -- a unary or binary operator, usually used for addition
• RR + RR -- a unary or binary operator, usually used for addition
• RR + RRi -- a unary or binary operator, usually used for addition
• RR + ZZ -- a unary or binary operator, usually used for addition
• RR - CC -- a unary or binary operator, usually used for negation or subtraction
• RR - QQ -- a unary or binary operator, usually used for negation or subtraction
• RR - RR -- a unary or binary operator, usually used for negation or subtraction
• RR - RRi -- a unary or binary operator, usually used for negation or subtraction
• RR - ZZ -- a unary or binary operator, usually used for negation or subtraction
• RR / CC -- a binary operator, usually used for division
• RR / QQ -- a binary operator, usually used for division
• RR / RR -- a binary operator, usually used for division
• RR / RRi -- a binary operator, usually used for division
• RR / ZZ -- a binary operator, usually used for division
• RR // QQ -- a binary operator, usually used for quotient
• RR // RR -- a binary operator, usually used for quotient
• RR // ZZ -- a binary operator, usually used for quotient
• RR << ZZ
• RR == CC -- equality
• RR == QQ -- equality
• RR == RR -- equality
• RR == RRi -- equality
• RR == ZZ -- equality
• RR >> ZZ
• RR' -- the parent class of all rings of real numbers
• RRi -- the class of all real intervals
• RRi * QQ -- a binary operator, usually used for multiplication
• RRi * RR -- a binary operator, usually used for multiplication
• RRi * RRi -- a binary operator, usually used for multiplication
• RRi * ZZ -- a binary operator, usually used for multiplication
• RRi + QQ -- a unary or binary operator, usually used for addition
• RRi + RR -- a unary or binary operator, usually used for addition
• RRi + RRi -- a unary or binary operator, usually used for addition
• RRi + ZZ -- a unary or binary operator, usually used for addition
• RRi - QQ -- a unary or binary operator, usually used for negation or subtraction
• RRi - RR -- a unary or binary operator, usually used for negation or subtraction
• RRi - RRi -- a unary or binary operator, usually used for negation or subtraction
• RRi - ZZ -- a unary or binary operator, usually used for negation or subtraction
• RRi / QQ -- a binary operator, usually used for division
• RRi / RR -- a binary operator, usually used for division
• RRi / RRi -- a binary operator, usually used for division
• RRi / ZZ -- a binary operator, usually used for division
• RRi << ZZ
• RRi == QQ -- equality
• RRi == RR -- equality
• RRi == RRi -- equality
• RRi == ZZ -- equality
• RRi >> ZZ
• rsort -- sort a list or matrix in reverse order
• rsort(...,DegreeOrder=>...) -- specify Ascending, Descending, or null
• rsort(...,MonomialOrder=>...) -- specify Ascending or Descending monomial order
• rsort(List) -- sort a list or matrix in reverse order
• rsort(Matrix) -- 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
• runHooks(MutableHashTable,Thing,Thing) -- run the hook functions stored in an object
• runHooks(Sequence,Thing) -- run the hook functions stored in an object
• runHooks(Symbol,Thing) -- run the hook functions stored in an object
• runLengthEncode -- run length encoding
• runLengthEncode(VisibleList) -- run length encoding
• running Macaulay2 in a terminal window
• running Macaulay2 in emacs
• runProgram -- run an external program
• runProgram(...,KeepFiles=>...) -- run an external program
• runProgram(...,RaiseError=>...) -- run an external program
• runProgram(...,RunDirectory=>...) -- run an external program
• runProgram(...,Verbose=>...) -- run an external program
• runProgram(Program,String) -- run an external program
• runProgram(Program,String,String) -- run an external program
• runProgram(String,String) -- run an external program
• same -- whether everything in a list is the same
• saving polynomials and matrices in files
• scan -- apply a function to each element in a list or sequence
• scan(BasicList,BasicList,Function) -- apply a function to each element in a list or sequence
• scan(BasicList,Function) -- apply a function to each element in a list or sequence
• scan(Thing,Function) -- apply a function to each element in a list or sequence
• scan(ZZ,Function) -- apply a function to each element in a list or sequence
• scanKeys -- apply a function to each key in a hash table or database
• scanKeys(Database,Function) -- apply a function to each key in a hash table or database
• scanKeys(HashTable,Function) -- apply a function to each key in a hash table or database
• scanLines -- apply a function to each line of a file
• scanLines(Function,List) -- apply a function to each line of a file
• scanLines(Function,String) -- apply a function to each line of a file
• scanPairs -- apply a function to the pairs in a hash table
• scanPairs(HashTable,Function) -- apply a function to the pairs in a hash table
• scanValues -- apply a function to each value in a hash table or database
• scanValues(HashTable,Function) -- apply a function to each value in a hash table or database
• schedule -- schedule a task for execution
• schedule(Function) -- schedule a task for execution
• schedule(Function,Thing) -- schedule a task for execution
• schedule(Task) -- schedule a task for execution
• Schreyer orders -- induced monomial order on a free module
• schreyerOrder -- create or obtain free modules with Schreyer monomial orders
• schreyerOrder(Matrix) -- create a matrix with the same entries whose source free module has a Schreyer monomial order
• schreyerOrder(Module) -- obtain Schreyer order information
• Schubert -- find the Plücker ideal of a Schubert variety
• Schubert(...,CoefficientRing=>...) -- find the Plücker ideal of a Schubert variety
• Schubert(...,Variable=>...) -- find the Plücker ideal of a Schubert variety
• Schubert(ZZ,ZZ,VisibleList) -- find the Plücker ideal of a Schubert variety
• scriptCommandLine -- the command line arguments to be used when running a script
• ScriptedFunctor -- the class of all scripted functors
• ScriptedFunctor ^ Thing -- the class of all scripted functors
• ScriptedFunctor _ Thing -- the class of all scripted functors
• ScriptedFunctor Thing -- the class of all scripted functors
• searchPath -- search a path for a file
• searchPath(List,String) -- search a path for a file
• searchPath(String) -- search a path for a file
• sec -- secant
• sec(CC) -- secant
• sec(RR) -- secant
• sec(RRi) -- secant
• sech -- hyperbolic secant
• sech(CC) -- hyperbolic secant
• sech(RR) -- hyperbolic secant
• sech(RRi) -- 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
• select(BasicList,Function) -- select elements from a list
• select(BasicList,Type) -- select elements of a given type in a list
• select(HashTable,Function) -- select part of a hash table
• select(String,String) -- select and reformat substrings matching a regular expression
• select(String,String,POSIX=>...) -- select and reformat substrings matching a regular expression
• select(String,String,String) -- select and reformat substrings matching a regular expression
• select(String,String,String,POSIX=>...) -- select and reformat substrings matching a regular expression
• select(Thing,Function) -- select elements from an object with an iterator
• select(ZZ,BasicList,Function) -- select a limited number of elements from a list
• select(ZZ,Function) -- select integers
• select(ZZ,HashTable,Function) -- select a limited number of pairs from a hash table
• selectInSubring -- select columns in a subring
• selectInSubring(ZZ,Matrix) -- select columns in a subring
• selectVariables -- make a subring of a polynomial ring generated by selected variables
• selectVariables(List,PolynomialRing) -- make a subring of a polynomial ring generated by selected variables
• SelfInitializingType -- the class of all self initializing types
• SelfInitializingType \ VisibleList -- apply a function to elements of a list
• SelfInitializingType \\ Thing -- apply a function
• SelfInitializingType Thing -- the class of all self initializing types
• separate -- split a string into substrings using a regular expression
• separate(...,POSIX=>...) -- split a string into substrings using a regular expression
• separate(String) -- split a string into substrings using a regular expression
• separate(String,String) -- split a string into substrings using a regular expression
• separate(String,ZZ,String) -- split a string into substrings using a regular expression
• SeparateExec -- an optional argument
• separateRegexp -- split a string into substrings using a regular expression
• Sequence -- the class of all sequences -- (...)
• sequence -- make a sequence
• Sequence .. Sequence -- rectangular sequences of consecutive lists and sequences
• Sequence ..< Sequence -- rectangular sequences of consecutive lists and sequences
• Sequence <- Thing -- assignment with left side evaluated
• Sequence == Sequence -- equality
• Sequence | Sequence -- join lists, sequences or arrays
• serialNumber -- serial number of a dictionary, task, symbol, mutable hash table, or mutable list,
• Set -- the class of all sets
• set -- make a set
• Set #? Thing -- test set membership
• Set * Set -- intersection of sets
• Set ** Set -- Cartesian product
• Set + Set -- set union
• Set - List -- set difference
• Set - Set -- set difference
• set(VisibleList) -- 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
• setRandomSeed(Sequence) -- set starting point for random number generator
• setRandomSeed(String) -- set starting point for random number generator
• setRandomSeed(ZZ) -- set starting point for random number generator
• setting up the Macaulay2 emacs interface
• setup
• setup()
• setupEmacs
• setupEmacs()
• sheaf -- make a coherent sheaf
• sheaf(Module) -- make a coherent sheaf
• sheaf(Ring) -- make a coherent sheaf of rings
• sheaf(Variety) -- make a coherent sheaf
• sheaf(Variety,Module) -- make a coherent sheaf
• sheaf(Variety,Ring) -- make a coherent sheaf of rings
• SheafExpression -- the class of sheaf expressions
• sheafExt -- sheaf Ext of coherent sheaves
• sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves
• sheafExt^ZZ(CoherentSheaf,SheafOfRings) -- sheaf Ext of coherent sheaves
• sheafExt^ZZ(SheafOfRings,CoherentSheaf) -- sheaf Ext of coherent sheaves
• sheafExt^ZZ(SheafOfRings,SheafOfRings) -- sheaf Ext of coherent sheaves
• sheafHom -- sheaf Hom
• sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• sheafHom(CoherentSheaf,SheafOfRings) -- sheaf Hom
• sheafHom(SheafOfRings,CoherentSheaf) -- sheaf Hom
• sheafHom(SheafOfRings,SheafOfRings) -- sheaf Hom
• SheafOfRings -- the class of sheaves of rings
• SheafOfRings (*) -- sum of twists
• SheafOfRings ^ List -- make a graded free coherent sheaf
• SheafOfRings ^ ZZ -- direct sum
• SheafOfRings LowerBound -- the class of lower bound objects
• SheafOfRings ZZ -- canonical twist of a coherent sheaf
• shield -- shield evaluation from interrupts
• show -- display various objects in an external viewer
• show(URL) -- display various objects in an external viewer
• showClassStructure -- display class structure
• showHtml -- display various objects in an external viewer
• showStructure -- display parent structure
• showTex -- display various objects in an external viewer
• showUserStructure -- show parent structure for those types defined by user
• simple Groebner basis computations over various rings
• sin -- compute the sine
• sin(CC) -- compute the sine
• sin(RR) -- compute the sine
• sin(RRi) -- compute the sine
• Singular Book 1.1.8 -- computation in fields
• Singular Book 1.1.9 -- computation in polynomial rings
• Singular Book 1.1.10 -- methods for creating ring maps
• Singular Book 1.2.3 -- leading data
• Singular Book 1.2.13 -- monomial orderings
• Singular Book 1.3.3 -- properties of ring maps
• Singular Book 1.3.13 -- computation in quotient rings
• Singular Book 1.3.15 -- computing with radicals
• Singular Book 1.4.9 -- global versus local rings
• Singular Book 1.5.10 -- realization of rings
• Singular Book 1.6.13 -- normal form
• Singular Book 1.7.10 -- standard bases
• Singular Book 1.7.12 -- highest corner
• Singular Book 1.8.1 -- ideal membership
• Singular Book 1.8.2 -- linear combination of ideal members
• Singular Book 1.8.4 -- elimination of variables
• Singular Book 1.8.6 -- Zariski closure of the image
• Singular Book 1.8.7 -- solving equations
• Singular Book 1.8.9 -- radical membership
• Singular Book 1.8.11 -- intersection of ideals
• Singular Book 1.8.13 -- quotient of ideals
• Singular Book 1.8.15 -- saturation
• Singular Book 1.8.18 -- kernel of a ring map
• Singular Book 1.8.19 -- algebraic dependence
• Singular Book 1.8.20 -- subalgebra membership
• Singular Book 2.1.6 -- matrix operations
• Singular Book 2.1.7 -- maps induced by Hom
• Singular Book 2.1.10 -- Submodules of A^n
• Singular Book 2.1.13 -- kernel, image and cokernel of a module homomorphism
• Singular Book 2.1.20 -- sum, intersection, module quotient
• Singular Book 2.1.24 -- submodules, presentation of a module
• Singular Book 2.1.26 -- computation of Hom
• Singular Book 2.1.34 -- minimal presentations, prune
• Singular Book 2.2.15 -- graded rings and modules
• Singular Book 2.3.10 -- normal form
• Singular Book 2.3.12 -- standard bases
• Singular Book 2.4.12 -- resolution and Betti numbers
• Singular Book 2.4.15 -- homogeneous resolution and graded Betti numbers
• Singular Book 2.5.5 -- syzygies
• Singular Book 2.5.18 -- Schreyer resolution
• Singular Book 2.6.3 -- diagonal form
• Singular Book 2.6.11 -- cyclic decomposition
• Singular Book 2.6.15 -- Jordan normal form
• Singular Book 2.7.5 -- tensor product of maps
• Singular Book 2.7.9 -- tensor product of modules
• Singular Book 2.7.14 -- tensor product of rings
• Singular Book 2.8.1 -- module membership
• Singular Book 2.8.3 -- elimination of module components
• Singular Book 2.8.5 -- intersection of modules
• Singular Book 2.8.6 -- quotient of modules
• Singular Book 2.8.7 -- radical, zerodivisors of modules
• Singular Book 2.8.8 -- annihilator and Fitting ideal
• Singular Book 2.8.9 -- kernel of a module homomorphism
• Singular Book 2.8.10 -- solving linear equations
• Singular-Factory
• singularLocus -- singular locus
• singularLocus(AffineVariety) -- singular locus
• singularLocus(Ideal) -- singular locus
• singularLocus(ProjectiveVariety) -- singular locus
• singularLocus(Ring) -- singular locus
• sinh -- compute the hyperbolic sine
• sinh(CC) -- compute the hyperbolic sine
• sinh(RR) -- compute the hyperbolic sine
• sinh(RRi) -- compute the hyperbolic sine
• size -- the size of an object
• size(RingElement) -- the size of an object
• size2 -- number of binary digits to the left of the point
• size2(CC) -- number of binary digits to the left of the point
• size2(RR) -- number of binary digits to the left of the point
• size2(RRi) -- number of binary digits to the left of the point
• size2(ZZ) -- number of binary digits to the left of the point
• SizeLimit -- an optional argument
• SkewCommutative -- an optional argument
• sleep -- sleep for a while
• smithNormalForm -- smith normal form for a matrix over ZZ or a PID
• smithNormalForm(...,ChangeMatrix=>...) -- smith normal form for a matrix over ZZ or a PID
• smithNormalForm(...,KeepZeroes=>...) -- smith normal form for a matrix over ZZ or a PID
• smithNormalForm(Matrix) -- smith normal form for a matrix over ZZ or a PID
• solve -- solve linear equation(s)
• solve(...,ClosestFit=>...) -- solve linear equation(s)
• solve(...,MaximalRank=>...) -- solve linear equation(s)
• solve(...,Precision=>...) -- solve linear equation(s)
• solve(Matrix,Matrix) -- solve linear equation(s)
• solve(MutableMatrix,MutableMatrix) -- solve linear equation(s)
• someTerms -- select some terms of a polynomial
• someTerms(RingElement,ZZ,ZZ) -- select some terms of a polynomial
• Sort -- a Strategy option value
• sort -- sort a list or columns of a matrix
• sort(...,DegreeOrder=>...) -- specify Ascending, Descending, or null
• sort(...,MonomialOrder=>...) -- specify Ascending or Descending monomial order
• sort(List) -- sort a list
• sort(Matrix) -- sort the columns of a matrix
• sortColumns -- permutation giving sort order
• sortColumns(...,DegreeOrder=>...) -- specify Ascending, Descending, or null
• sortColumns(...,MonomialOrder=>...) -- specify Ascending or Descending monomial order
• sortColumns(Matrix) -- permutation giving sort order
• SortStrategy -- specify a strategy for sorting S-pairs
• source -- source of a map
• source(ChainComplexMap) -- find the source of a map of chain complexes
• source(GradedModuleMap) -- find the source of a map of graded modules
• source(Matrix) -- find the source module of matrix
• source(RingMap) -- find the source ring for a map of rings
• 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
• span(List) -- construct smallest interval
• span(List,Precision=>...) -- construct smallest interval
• span(Sequence) -- construct smallest interval
• span(Sequence,Precision=>...) -- 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
• Spec(Ring) -- make an affine variety
• specifying typical values
• splice -- remove subsequences from a sequence or list
• splice(BasicList) -- remove subsequences from a sequence or list
• splitWWW -- separate an http response into header and body
• splitWWW(String) -- separate an http response into header and body
• sqrt -- square root function
• sqrt(CC) -- square root function
• sqrt(RR) -- square root function
• sqrt(RRi) -- square root function
• stack -- join nets or string vertically
• stack(BasicList) -- join nets or string vertically
• Standard -- the standard top level printing method
• standardForm -- convert to standard form
• standardForm(MonoidElement) -- convert to standard form
• standardForm(RingElement) -- convert to standard form
• standardPairs -- find the standard pairs of a monomial ideal
• standardPairs(MonomialIdeal) -- find the standard pairs of a monomial ideal
• standardPairs(MonomialIdeal,List) -- find the standard pairs of a monomial ideal
• stashValue -- stash values of functions in their arguments
• status -- status of a resolution computation
• status(...,Monomials=>...) -- status of a resolution computation
• status(...,PairsRemaining=>...) -- status of a resolution computation
• status(...,TotalPairs=>...) -- status of a resolution computation
• status(ChainComplex) -- status of a resolution computation
• status(GroebnerBasis) -- status of a resolution computation
• status(ProgramRun) -- get the return status of a program run
• status(Resolution) -- 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
• stopIfError -- whether to stop the program when an error occurs
• StopIteration -- stop iteration
• StopWithMinimalGenerators -- an optional argument
• Strategy -- an optional argument
• String -- the class of all strings
• String # ZZ -- get value from list, hash table, database, or string
• String #? ZZ -- check existence of value in a list, hash table, database, or string
• String .. String -- a sequence of consecutive strings
• String ..< String -- a sequence of consecutive strings, not including the endpoint
• String / Command -- apply a function to elements of a list
• String / Function -- apply a function to elements of a list
• String << Thing -- print to a file
• String == Net -- equality
• String == String -- equality
• String ^ Sequence -- vertically stacked copies of a string
• String ^ ZZ -- raise a net or string
• String _ Ring -- get a ring variable by name
• String _ Sequence -- substring
• String _ ZZ -- get element from string
• String | String -- join strings or nets
• String | ZZ -- join strings or nets
• strings and nets -- an overview of strings and nets in Macaulay2
• sublists -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function) -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Function) -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Function,Function) -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Function,Nothing) -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Nothing) -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Nothing,Function) -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Nothing,Nothing) -- process interspersed subsequences of a visible list
• submatrix
• submatrix' -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,Nothing,Nothing) -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,Nothing,VisibleList) -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,VisibleList) -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,VisibleList,Nothing) -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,VisibleList,VisibleList) -- exclude rows and/or columns of a matrix
• submatrix(Matrix,VisibleList) -- select columns
• submatrix(Matrix,VisibleList,VisibleList) -- select part of a matrix
• submatrix(MutableMatrix,VisibleList) -- select columns
• submatrix(MutableMatrix,VisibleList,VisibleList) -- select part of a matrix
• submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
• submatrixByDegrees(Matrix,List,List) -- submatrix consisting of rows and columns in an interval or box of degrees
• submatrixByDegrees(Matrix,Sequence,Sequence) -- submatrix consisting of rows and columns in an interval or box of degrees
• submatrixByDegrees(Matrix,ZZ,ZZ) -- submatrix consisting of rows and columns in an interval or box of degrees
• submodules and quotients
• Subnodes -- a menu of documentation nodes
• subquotient -- make a subquotient module
• subquotient modules -- the way Macaulay2 represents modules
• subquotient(Matrix,Matrix) -- make a subquotient module
• subquotient(Matrix,Nothing) -- make a subquotient module
• subquotient(Module,Matrix,Matrix) -- make a subquotient module
• subquotient(Module,Matrix,Nothing) -- make a subquotient module
• subquotient(Module,Nothing,Matrix) -- make a subquotient module
• subquotient(Module,Nothing,Nothing) -- make a subquotient module
• subquotient(Nothing,Matrix) -- 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
• subscripted variables
• subsets -- produce the subsets of a set or list
• subsets(List) -- produce the subsets of a set or list
• subsets(List,ZZ) -- produce the subsets of a set or list
• subsets(Sequence,ZZ) -- produce the subsets of a set or list
• subsets(Set) -- produce the subsets of a set or list
• subsets(Set,ZZ) -- produce the subsets of a set or list
• subsets(ZZ) -- produce the subsets of a set or list
• subsets(ZZ,ZZ) -- produce the subsets of a set or list
• substitute -- substituting values for variables
• substitute(Divide,Thing) -- substituting values for variables
• substitute(Ideal,List) -- substituting values for variables
• substitute(Ideal,Matrix) -- substituting values for variables
• substitute(Ideal,Option) -- substituting values for variables
• substitute(Ideal,Ring) -- substituting values for variables
• substitute(Ideal,RingFamily) -- substituting values for variables
• substitute(Matrix,List) -- substituting values for variables
• substitute(Matrix,Matrix) -- substituting values for variables
• substitute(Matrix,Option) -- substituting values for variables
• substitute(Matrix,Ring) -- substituting values for variables
• substitute(Matrix,RingFamily) -- substituting values for variables
• substitute(Matrix,ZZ) -- substituting values for variables
• substitute(Module,List) -- substituting values for variables
• substitute(Module,Matrix) -- substituting values for variables
• substitute(Module,Option) -- substituting values for variables
• substitute(Module,Ring) -- substituting values for variables
• substitute(Module,RingFamily) -- substituting values for variables
• substitute(Number,Ring) -- substituting values for variables
• substitute(Number,RingFamily) -- substituting values for variables
• substitute(Power,Thing) -- substituting values for variables
• substitute(Product,Thing) -- substituting values for variables
• substitute(RingElement,List) -- substituting values for variables
• substitute(RingElement,Matrix) -- substituting values for variables
• substitute(RingElement,Option) -- substituting values for variables
• substitute(RingElement,Ring) -- substituting values for variables
• substitute(RingElement,RingFamily) -- substituting values for variables
• substitute(Sum,Thing) -- substituting values for variables
• substitute(Vector,List) -- substituting values for variables
• substitute(Vector,Matrix) -- substituting values for variables
• substitute(Vector,Option) -- substituting values for variables
• substitute(Vector,Ring) -- substituting values for variables
• substitute(Vector,RingFamily) -- substituting values for variables
• substituting values for variables
• substitution and maps between rings
• substring -- extract part of a string
• substring(Sequence,String) -- extract part of a string
• substring(String,ZZ) -- extract part of a string
• substring(String,ZZ,ZZ) -- extract part of a string
• substring(ZZ,String) -- extract part of a string
• substring(ZZ,ZZ,String) -- extract part of a string
• subtable -- extract a subtable from a table
• Sugarless -- compute a Gröbner basis
• Sum -- the class of all sum expressions
• sum -- compute the sum
• sum(ChainComplex) -- direct sum of the components of a chain complex
• sum(ChainComplexMap) -- direct sum of the components of a chain map
• sum(List) -- sum the elements of a list
• sum(Set) -- sum of elements
• sum(VirtualTally) -- sum of elements
• sum(VisibleList,Function) -- sum results of applying a function
• sum(VisibleList,VisibleList,Function) -- sum results of applying a function pairwise
• sum(ZZ,Function) -- sum consecutive values of a function
• SumOfTwists -- the class of all sums of twists
• sums, products, and powers of ideals
• super -- get the ambient module
• super(CoherentSheaf) -- get the ambient module
• super(GradedModule) -- get the ambient module
• super(Matrix) -- get the ambient module
• super(Module) -- get the ambient module
• super(Vector) -- 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
• support(Ideal) -- list of variables occurring in the generators of an ideal
• support(Matrix) -- list of variables occurring in a polynomial or matrix
• support(RingElement) -- list of variables occurring in a polynomial or matrix
• SVD -- singular value decomposition of a matrix
• SVD(...,DivideConquer=>...) -- Use the lapack divide and conquer SVD algorithm
• SVD(Matrix) -- singular value decomposition of a matrix
• SVD(MutableMatrix) -- singular value decomposition of a matrix
• switch -- copy a list, switching two elements
• switch(ZZ,ZZ,VisibleList) -- copy a list, switching two elements
• Symbol -- the class of all symbols
• symbol -- get a symbol
• Symbol .. Symbol -- sequences of consecutive symbols
• Symbol ..< Symbol -- sequences of consecutive symbols
• Symbol == Symbol -- equality
• Symbol ? IndexedVariable -- comparison operator
• Symbol _ Ring -- get a ring variable by name
• Symbol _ Thing -- index variable
• Symbol _ Thing = Thing -- assignment to an indexed variable
• SymbolBody -- symbol bodies
• symbolBody -- symbol bodies
• symbols used as the name or value of an optional argument
• symlinkDirectory -- make symbolic links for all files in a directory tree
• symlinkDirectory(...,Exclude=>...) -- make symbolic links for all files in a directory tree
• symlinkDirectory(...,FollowLinks=>...) -- make symbolic links for all files in a directory tree
• symlinkDirectory(...,Undo=>...) -- make symbolic links for all files in a directory tree
• symlinkDirectory(...,Verbose=>...) -- make symbolic links for all files in a directory tree
• symlinkDirectory(String,String) -- make symbolic links for all files in a directory tree
• symlinkFile -- make a symbolic link to a file
• symmetric algebras
• symmetricAlgebra -- the symmetric algebra of a module
• symmetricAlgebra(...,DegreeLift=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,DegreeMap=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,DegreeRank=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Degrees=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Global=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Heft=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Inverses=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Join=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Local=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,MonomialOrder=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,MonomialSize=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,SkewCommutative=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,VariableBaseName=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Variables=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,Weights=>...) -- the symmetric algebra of a module
• symmetricAlgebra(...,WeylAlgebra=>...) -- the symmetric algebra of a module
• symmetricAlgebra(Matrix) -- the symmetric algebra of a module
• symmetricAlgebra(Module) -- the symmetric algebra of a module
• symmetricAlgebra(Nothing,Nothing,Matrix) -- the symmetric algebra of a module
• symmetricAlgebra(Nothing,Ring,Matrix) -- the symmetric algebra of a module
• symmetricAlgebra(Ring,Nothing,Matrix) -- the symmetric algebra of a module
• symmetricAlgebra(Ring,Ring,Matrix) -- the symmetric algebra of a module
• symmetricPower -- symmetric power
• symmetricPower(ZZ,Matrix) -- symmetric power
• symmetricPower(ZZ,Module) -- symmetric power
• synonym -- synonym for members of a class
• SYNOPSIS -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(...,BaseFunction=>...) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(...,Consequences=>...) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(...,Heading=>...) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(...,Inputs=>...) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(...,Outputs=>...) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(...,Usage=>...) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(List) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(Sequence) -- a standardized synopsis for use in documentation nodes
• SYNOPSIS(Thing) -- a standardized synopsis for use in documentation nodes
• system facilities
• syz -- the syzygy matrix
• syz(...,Algorithm=>...) -- compute the syzygy matrix
• syz(...,BasisElementLimit=>...) -- compute the syzygy matrix
• syz(...,DegreeLimit=>...) -- compute the syzygy matrix
• syz(...,GBDegrees=>...) -- compute the syzygy matrix
• syz(...,HardDegreeLimit=>...) -- compute the syzygy matrix
• syz(...,MaxReductionCount=>...) -- compute the syzygy matrix
• syz(...,PairLimit=>...) -- compute the syzygy matrix
• syz(...,StopBeforeComputation=>...) -- compute the syzygy matrix
• syz(...,Strategy=>...) -- compute the syzygy matrix
• syz(...,SyzygyLimit=>...) -- compute the syzygy matrix
• syz(...,SyzygyRows=>...) -- compute the syzygy matrix
• syz(GroebnerBasis) -- retrieve the syzygy matrix
• syz(Matrix) -- compute 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.
• take(BasicList,List) -- Take some elements from a list or sequence.
• take(BasicList,ZZ) -- Take some elements from a list or sequence.
• take(Thing,ZZ) -- 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
• Tally + Tally -- union of tallies
• Tally - Tally -- difference of tallies
• tally(String) -- tally the elements of a list, sequence, array, or string
• tally(VisibleList) -- tally the elements of a list, sequence, array, or string
• tan -- compute the tangent
• tan(CC) -- compute the tangent
• tan(RR) -- compute the tangent
• tan(RRi) -- compute the tangent
• tangentSheaf -- tangent sheaf of a projective variety
• tangentSheaf(...,Minimize=>...) -- tangent sheaf of a projective variety
• tangentSheaf(ProjectiveVariety) -- tangent sheaf of a projective variety
• tanh -- compute the hyperbolic tangent
• tanh(CC) -- compute the hyperbolic tangent
• tanh(RR) -- compute the hyperbolic tangent
• tanh(RRi) -- compute the hyperbolic tangent
• target -- target of a map
• target(ChainComplexMap) -- find the target of a map of chain complexes
• target(GradedModuleMap) -- find the target of a map of graded modules
• target(GroebnerBasis) -- find target of a Gröbner basis
• target(Matrix) -- find the target module of matrix
• target(RingMap) -- find the target ring for a map of rings
• Task -- the class of all tasks
• taskResult -- retrieve the value returned by a task
• taskResult(Task) -- retrieve the value returned by a task
• teaching emacs how to find M2
• teaching emacs how to find M2-init.el
• teaching M2 how to find its shared libraries
• teaching your shell how to find M2
• temporaryFileName -- make a temporary file name
• tensor -- tensor product
• tensor products of rings
• tensor(List) -- tensor product
• tensor(Monoid,Monoid) -- tensor product of monoids
• tensor(Monoid,Monoid,DegreeLift=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,DegreeMap=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,DegreeRank=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Degrees=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Global=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Heft=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Inverses=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Join=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Local=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,MonomialOrder=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,MonomialSize=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,SkewCommutative=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,VariableBaseName=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Variables=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,Weights=>...) -- tensor product of monoids
• tensor(Monoid,Monoid,WeylAlgebra=>...) -- tensor product of monoids
• tensor(Ring,Ring) -- tensor product of monoids
• tensor(Ring,Ring,DegreeLift=>...) -- tensor product of monoids
• tensor(Ring,Ring,DegreeMap=>...) -- tensor product of monoids
• tensor(Ring,Ring,DegreeRank=>...) -- tensor product of monoids
• tensor(Ring,Ring,Degrees=>...) -- tensor product of monoids
• tensor(Ring,Ring,Global=>...) -- tensor product of monoids
• tensor(Ring,Ring,Heft=>...) -- tensor product of monoids
• tensor(Ring,Ring,Inverses=>...) -- tensor product of monoids
• tensor(Ring,Ring,Join=>...) -- tensor product of monoids
• tensor(Ring,Ring,Local=>...) -- tensor product of monoids
• tensor(Ring,Ring,MonomialOrder=>...) -- tensor product of monoids
• tensor(Ring,Ring,MonomialSize=>...) -- tensor product of monoids
• tensor(Ring,Ring,SkewCommutative=>...) -- tensor product of monoids
• tensor(Ring,Ring,VariableBaseName=>...) -- tensor product of monoids
• tensor(Ring,Ring,Variables=>...) -- tensor product of monoids
• tensor(Ring,Ring,Weights=>...) -- tensor product of monoids
• tensor(Ring,Ring,WeylAlgebra=>...) -- tensor product of monoids
• tensor(RingMap,Matrix) -- tensor product via a ring map
• tensor(RingMap,Module) -- tensor product via a ring map
• tensor(Sequence) -- tensor product
• tensorAssociativity -- associativity isomorphisms for tensor products
• tensorAssociativity(ChainComplex,ChainComplex,ChainComplex) -- associativity isomorphisms for tensor products
• tensorAssociativity(GradedModule,GradedModule,GradedModule) -- associativity isomorphisms for tensor products
• tensorAssociativity(Module,Module,Module) -- associativity isomorphisms for tensor products
• terms -- provide a list of terms of a polynomial
• terms(Ring,RingElement) -- provide a list of terms of a polynomial
• terms(RingElement) -- provide a list of terms of a polynomial
• TEST -- add a test for a package
• Test -- value of an optional argument
• TEST(...,FileName=>...) -- add a test for a package
• TEST(List) -- add a test for a package
• TEST(String) -- add a test for a package
• TestInput -- locate a package's tests
• tests -- locate a package's tests
• tests(Package) -- locate a package's tests
• tests(String) -- locate a package's tests
• tests(ZZ,Package) -- locate a package's tests
• tests(ZZ,String) -- locate a package's tests
• tex -- convert to $\TeX$ format
• TeXmacs -- the TeXmacs top level printing method
• texMath -- convert to TeX math format
• The authors
• the debugger
• The Macaulay2 language
• then -- condition testing
• Thing -- the class of all things
• Thing != Expression -- the class of all expressions
• Thing % Expression -- the class of all expressions
• Thing & Expression -- the class of all expressions
• Thing * List -- a binary operator, usually used for multiplication
• Thing - Expression -- the class of all expressions
• Thing .. Expression -- the class of all expressions
• Thing ..< Expression -- the class of all expressions
• Thing / Expression -- the class of all expressions
• Thing // Command -- apply a function
• Thing // Function -- apply a function
• Thing // SelfInitializingType -- apply a function
• Thing : Expression -- the class of all expressions
• Thing <== Expression -- the class of all expressions
• Thing <=== Expression -- the class of all expressions
• Thing <==> Expression -- the class of all expressions
• Thing =!= Thing -- strict inequality
• Thing === Thing -- strict equality
• Thing ===> Expression -- the class of all expressions
• Thing ==> Expression -- the class of all expressions
• Thing => Thing -- produce an Option
• Thing @ Expression -- the class of all expressions
• Thing @@ Expression -- the class of all expressions
• Thing ^ Expression -- the class of all expressions
• Thing ^** Expression -- the class of all expressions
• Thing ^^ Expression -- the class of all expressions
• Thing _ Expression -- the class of all expressions
• Thing | Expression -- the class of all expressions
• Thing |- Expression -- the class of all expressions
• Thing || Expression -- the class of all expressions
• Thing and Expression -- the class of all expressions
• Thing Expression -- the class of all expressions
• Thing or Expression -- the class of all expressions
• Thing xor Expression -- the class of all expressions
• threadVariable -- create a symbol whose value in one thread is not shared with others
• 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
• toCC(CC) -- convert to high-precision complex number
• toCC(QQ) -- convert to high-precision complex number
• toCC(RR) -- convert to high-precision complex number
• toCC(RR,RR) -- convert to high-precision complex number
• toCC(ZZ) -- convert to high-precision complex number
• toCC(ZZ,CC) -- convert to high-precision complex number
• toCC(ZZ,QQ) -- convert to high-precision complex number
• toCC(ZZ,QQ,QQ) -- convert to high-precision complex number
• toCC(ZZ,QQ,RR) -- convert to high-precision complex number
• toCC(ZZ,QQ,ZZ) -- convert to high-precision complex number
• toCC(ZZ,RR) -- convert to high-precision complex number
• toCC(ZZ,RR,QQ) -- convert to high-precision complex number
• toCC(ZZ,RR,RR) -- convert to high-precision complex number
• toCC(ZZ,RR,ZZ) -- convert to high-precision complex number
• toCC(ZZ,ZZ) -- convert to high-precision complex number
• toCC(ZZ,ZZ,QQ) -- convert to high-precision complex number
• toCC(ZZ,ZZ,RR) -- convert to high-precision complex number
• toCC(ZZ,ZZ,ZZ) -- convert to high-precision complex number
• toExternalString -- convert to a readable string
• toField -- declare that a ring is a field
• toField(Ring) -- declare that a ring is a field
• toList -- create a list
• toList(BasicList) -- create a list
• toList(Set) -- create a list
• toList(String) -- create a list
• toList(Thing) -- create a list
• toLower -- convert to lower case
• top level loop
• topCoefficients -- first variable and its coefficient of a polynomial or matrix
• topCoefficients(Matrix) -- first variable and its coefficient of a polynomial or matrix
• topCoefficients(RingElement) -- first variable and its coefficient of a polynomial or matrix
• topcom
• topLevelMode -- the current top level mode
• Tor -- Tor module
• Tor_ZZ(Ideal,Ideal) -- compute a Tor module
• Tor_ZZ(Ideal,Module) -- compute a Tor module
• Tor_ZZ(Ideal,Ring) -- compute a Tor module
• Tor_ZZ(Module,Ideal) -- compute a Tor module
• Tor_ZZ(Module,Module) -- compute a Tor module
• Tor_ZZ(Module,Ring) -- compute a Tor module
• Toric -- compute a Gröbner basis
• toRR -- convert to high-precision real number
• toRRi -- construct an interval
• Torsion -- value of an optional argument
• toSequence -- convert to sequence
• toSequence(BasicList) -- convert to sequence
• toSequence(String) -- convert to sequence
• toSequence(Thing) -- convert to sequence
• toString -- convert to a string
• TotalPairs -- whether to display the total number of S-pairs
• toUpper -- convert to upper case
• trace -- trace of a matrix
• trace(Matrix) -- trace of a matrix
• transpose -- transpose a table or a matrix
• transpose(ChainComplexMap) -- transpose a map of chain complexes
• transpose(List) -- transposes a table
• transpose(Matrix) -- transpose a matrix
• transpose(MutableMatrix) -- transpose a matrix
• trim -- minimize generators and relations
• trim(...,Strategy=>...) -- a Strategy option value
• trim(Ideal) -- minimize generators and relations
• trim(Module) -- minimize generators and relations
• trim(MonomialIdeal) -- minimize generators and relations
• trim(QuotientRing) -- minimize generators and relations
• trim(Ring) -- minimize generators and relations
• true
• Truncate -- an optional argument
• truncate
• truncate(Constant) -- round a number toward zero
• truncate(Number) -- round a number toward zero
• truncateOutput
• truncateOutput(InfiniteNumber)
• truncateOutput(ZZ)
• try -- catch an error
• tutorial -- convert documentation from tutorial format
• Tutorial: Canonical Embeddings of Plane Curves and Gonality
• Tutorial: Divisors
• Tutorial: Elementary uses of Groebner bases
• Tutorial: Fano varieties
• two dimensional formatting
• Type -- the class of all types
• TypicalValue -- make a new method function
• typicalValues -- types of values returned by functions
• ultimate -- ultimate value for an iteration
• ultimate(Function,Thing) -- ultimate value for an iteration
• unbag
• unbag(Bag)
• uncurry -- uncurry a function
• Undo -- an optional argument
• undocumented -- declare that something need not be documented
• undocumented(List) -- declare that something need not be documented
• undocumented(Thing) -- 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
• uninstallPackage(...,InstallPrefix=>...) -- uninstall a package and remove its documentation
• uninstallPackage(Package) -- uninstall a package and remove its documentation
• uninstallPackage(String) -- uninstall a package and remove its documentation
• Unique -- do not return repeated polynomial roots
• unique -- eliminate duplicates from a list
• unique(Sequence) -- eliminate duplicates from a list
• unique(VisibleList) -- eliminate duplicates from a list
• uniquePermutations -- produce all unique permutations of a list
• uniquePermutations(VisibleList) -- produce all unique permutations of a list
• uniquePermutations(ZZ) -- 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
• unstack(Net) -- list the rows of a net
• Up -- monomial ordering
• UpdateOnly -- only copies of newer files should replace files
• UpperTriangular -- an optional argument
• URL -- a type representing a URL
• urlEncode -- URL encoding
• urlEncode(Nothing) -- URL encoding
• urlEncode(String) -- URL encoding
• Usage -- ways to use a function in a documentation node
• use -- install or activate object
• use(Monoid) -- install ring variables and ring operations
• use(Package) -- activate a previously dismissed package
• use(Ring) -- install ring variables and ring operations
• UseCachedExampleOutput -- an optional argument
• UseHilbertFunction -- an optional argument
• UserMode -- an optional argument
• userSymbols -- a list of the user's symbols
• UseSyzygies -- compute a Gröbner basis
• using functions
• using functions with optional inputs
• using hooks
• using Macaulay2 with emacs
• using Macaulay2 with emacs after it has been set up
• using Macaulay2 with TeXmacs
• using packages -- Macaulay2 packages
• using sockets
• utf8 -- encode and decode unicode utf-8-encoded strings
• utf8check -- encode and decode unicode utf-8-encoded strings
• utf8substring -- extract part of a utf8 string
• valid names
• value -- evaluate
• value(Expression) -- the class of all expressions
• value(IndexedVariable) -- retrieve the value of an indexed variable
• value(Pseudocode) -- execute pseudocode
• value(String) -- evaluate a string
• value(Symbol) -- retrieve the value of a symbol
• values -- values in a hash table
• values(HashTable) -- values in a hash table
• Variable -- specify a name for a variable
• VariableBaseName -- an optional argument
• Variables -- an optional argument
• variables
• varieties
• Variety -- the class of all algebraic varieties
• variety -- get the variety
• variety(CoherentSheaf)
• variety(Ideal) -- the closed projective subvariety defined by an ideal
• variety(Ring) -- the variety previously associated to a given ring
• variety(RingElement) -- the variety previously associated to a given ring
• variety(SheafOfRings) -- get the variety
• vars -- variables
• vars(List) -- a sequence of variables
• vars(Monoid) -- list of variables in a monoid
• vars(Ring) -- row matrix of the variables
• vars(Sequence) -- a sequence of variables
• vars(ZZ) -- a sequence of variables
• Vector -- the class of all elements of free modules that are handled by the engine
• vector -- make a vector
• Vector ** Vector -- tensor product
• Vector + Vector -- a unary or binary operator, usually used for addition
• Vector - Vector -- a unary or binary operator, usually used for negation or subtraction
• Vector == Vector -- equality
• Vector || Vector -- join Vectors
• vector(List) -- make a vector
• vector(Matrix) -- make a vector
• VectorExpression -- the class of all vector expressions
• Verbose -- request verbose feedback
• Verbosity -- an optional argument
• Verify -- an optional argument
• 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
• viewHelp(DocumentTag) -- view online documentation in a web browser
• viewHelp(String) -- view online documentation in a web browser
• viewHelp(Thing) -- view online documentation in a web browser
• viewHelp(ZZ) -- search the documentation
• viewing the symbols defined so far
• VirtualTally
• VirtualTally ** VirtualTally -- Cartesian product of tallies
• VirtualTally + VirtualTally -- union of tallies
• VirtualTally - VirtualTally
• VirtualTally / Command -- apply a function to elements of a list
• VirtualTally / Function -- apply a function to elements of a list
• VirtualTally ? VirtualTally -- comparison operator
• VirtualTally ^** ZZ -- Cartesian power of sets and tallies
• VirtualTally _ Thing -- get a count from a tally
• VisibleList -- the class of all visible lists
• VisibleList / Command -- apply a function to elements of a list
• VisibleList / Function -- apply a function to elements of a list
• VisibleList / SelfInitializingType -- apply a function to elements of a list
• VisibleList == VisibleList -- equality
• VisibleList _ List -- get some entries of a list
• VisibleList _ ZZ -- get element from list
• w3
• wait -- wait for child process
• WebApp -- the web app top level printing method
• wedgeProduct -- the exterior multiplication map
• wedgeProduct(ZZ,ZZ,Module) -- the exterior multiplication map
• weightRange -- the pair of lowest and highest weights of the monomials
• weightRange(List,RingElement) -- the pair of lowest and highest weights of the monomials
• weightRange(RingElement) -- the pair of lowest and highest weights of the monomials
• Weights -- assigning weights to the variables
• Weyl algebras
• WeylAlgebra -- specify differential operators in the ring
• what a class is
• what is a Groebner basis?
• when -- a keyword
• while -- while loops
• width -- width of a file or net
• width(File) -- get window width
• width(Net) -- width of a net
• width(String) -- width of a net
• working with multiple rings
• Wrap -- a key for methods for wrapping printed output
• wrap
• WrapperType -- a class of lists with abbreviated constructors
• WrapperType List -- a class of lists with abbreviated constructors
• WrapperType Sequence -- a class of lists with abbreviated constructors
• WrapperType Thing -- a class of lists with abbreviated constructors
• writing documentation
• 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
• zeta(RR) -- Riemann zeta function
• ZZ -- the class of all integers
• ZZ ! -- factorial
• ZZ % MonomialIdeal -- a binary operator, usually used for remainder and reduction
• ZZ % ZZ -- a binary operator, usually used for remainder and reduction
• ZZ & ZZ -- logical and
• ZZ * BettiTally -- the class of all Betti tallies
• ZZ * CC -- a binary operator, usually used for multiplication
• ZZ * ProjectiveHilbertPolynomial -- a binary operator, usually used for multiplication
• ZZ * QQ -- a binary operator, usually used for multiplication
• ZZ * RR -- a binary operator, usually used for multiplication
• ZZ * RRi -- a binary operator, usually used for multiplication
• ZZ * ZZ -- a binary operator, usually used for multiplication
• ZZ + CC -- a unary or binary operator, usually used for addition
• ZZ + ChainComplexMap -- a unary or binary operator, usually used for addition
• ZZ + ProjectiveHilbertPolynomial -- a unary or binary operator, usually used for addition
• ZZ + QQ -- a unary or binary operator, usually used for addition
• ZZ + RR -- a unary or binary operator, usually used for addition
• ZZ + RRi -- a unary or binary operator, usually used for addition
• ZZ + ZZ -- a unary or binary operator, usually used for addition
• ZZ - CC -- a unary or binary operator, usually used for negation or subtraction
• ZZ - ProjectiveHilbertPolynomial -- a unary or binary operator, usually used for negation or subtraction
• ZZ - QQ -- a unary or binary operator, usually used for negation or subtraction
• ZZ - RR -- a unary or binary operator, usually used for negation or subtraction
• ZZ - RRi -- a unary or binary operator, usually used for negation or subtraction
• ZZ - ZZ -- a unary or binary operator, usually used for negation or subtraction
• ZZ .. ZZ -- sequences of consecutive integers
• ZZ ..< ZZ -- sequences of consecutive integers
• ZZ / CC -- a binary operator, usually used for division
• ZZ / QQ -- a binary operator, usually used for division
• ZZ / RR -- a binary operator, usually used for division
• ZZ / RRi -- a binary operator, usually used for division
• ZZ / ZZ -- a binary operator, usually used for division
• ZZ // MonomialIdeal -- a binary operator, usually used for quotient
• ZZ // ZZ -- a binary operator, usually used for quotient
• ZZ : Thing -- repeat an item
• ZZ << ZZ
• ZZ == CC -- equality
• ZZ == ChainComplex -- equality
• ZZ == ChainComplexMap -- equality
• ZZ == GradedModuleMap -- equality
• ZZ == Ideal -- equality
• ZZ == Module -- equality
• ZZ == MonomialIdeal -- equality
• ZZ == MutableMatrix -- equality
• ZZ == ProjectiveHilbertPolynomial -- equality
• ZZ == QQ -- equality
• ZZ == Ring -- equality
• ZZ == RingElement -- equality
• ZZ == RingMap -- equality
• ZZ == RR -- equality
• ZZ == RRi -- equality
• ZZ == ZZ -- equality
• ZZ >> ZZ
• ZZ ^^ ZZ -- logical exclusive-or
• ZZ _ Module -- integers or zero element
• ZZ | String -- join strings or nets
• ZZ | ZZ -- logical or
• ZZ ~ -- logical not