Macaulay2Doc : Index
- ! -- factorial
- != -- inequality
- " -- delineate a string with quotation marks
- # -- length, or access to elements
- # BasicList -- length
- # HashTable -- length
- # Set -- cardinality
- # String -- length
- #? -- check for presence of elements
- % -- a binary operator, usually used for remainder and reduction
- & -- a binary operator
- (*) -- a unary postfix operator, used for indicating a graded object
- * -- a binary operator, usually used for multiplication
- ** -- a binary operator, usually used for tensor product or Cartesian product
- + -- a unary or binary operator, usually used for addition
- + 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
- + 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
- - 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
- ; -- statement 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
- @ -- 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
- ^^ -- a binary operator
- _ -- 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
- abs -- absolute value function
- abs(CC) -- absolute value function
- abs(QQ) -- absolute value function
- abs(RR) -- absolute value function
- abs(ZZ) -- absolute value function
- AbsoluteLinks -- name for an optional argument
- accumulate -- apply binary operator repeatedly
- accumulate(Function,Thing,VisibleList) -- apply binary operator repeatedly
- accumulate(Function,VisibleList) -- apply binary operator repeatedly
- accumulate(VisibleList,Function) -- apply binary operator repeatedly
- accumulate(VisibleList,Thing,Function) -- apply binary operator repeatedly
- Acknowledgements
- acos -- arccosine
- acos(CC) -- arccosine
- acos(QQ) -- arccosine
- acos(RR) -- arccosine
- acos(ZZ) -- arccosine
- acosh -- inverse hyperbolic cosine
- acosh(Number) -- inverse hyperbolic cosine
- acot -- compute the inverse cotangent
- acot(Number) -- compute the inverse cotangent
- 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(HashTable,Thing,Function) -- add a hook function to an object for later processing
- addHook(Symbol,Function) -- add a hook function to an object for later processing
- 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(Matrix,Module,Module) -- an adjoint map
- adjoint1 -- an adjoint map
- adjoint1(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(CC,QQ) -- arithmetic-geometric mean
- agm(CC,RR) -- arithmetic-geometric mean
- agm(CC,ZZ) -- arithmetic-geometric mean
- agm(QQ,CC) -- arithmetic-geometric mean
- agm(QQ,QQ) -- arithmetic-geometric mean
- agm(QQ,RR) -- arithmetic-geometric mean
- agm(QQ,ZZ) -- arithmetic-geometric mean
- agm(RR,CC) -- arithmetic-geometric mean
- agm(RR,QQ) -- arithmetic-geometric mean
- agm(RR,RR) -- arithmetic-geometric mean
- agm(RR,ZZ) -- arithmetic-geometric mean
- agm(ZZ,CC) -- arithmetic-geometric mean
- agm(ZZ,QQ) -- arithmetic-geometric mean
- agm(ZZ,RR) -- arithmetic-geometric mean
- agm(ZZ,ZZ) -- arithmetic-geometric mean
- alarm -- set an alarm
- Algorithm -- name for an optional argument
- Alignment -- name for 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
- annihilator -- the annihilator ideal
- annihilator of a module
- annihilator(..., Strategy => ...) -- the annihilator ideal
- annihilator(CoherentSheaf) -- the annihilator ideal
- annihilator(Ideal) -- the annihilator ideal
- annihilator(Module) -- the annihilator ideal
- annihilator(RingElement) -- the annihilator ideal
- 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 -- append an element to a list
- append(BasicList,Thing) -- append an element to 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(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
- 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 elements of a table
- applyValues -- apply a function to each value
- applyValues(HashTable,Function) -- apply a function to each value
- 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
- ascii -- ASCII character conversion
- ascii(List) -- ASCII character conversion
- ascii(String) -- ASCII character conversion
- asin -- arcsine
- asin(CC) -- arcsine
- asin(QQ) -- arcsine
- asin(RR) -- arcsine
- asin(ZZ) -- arcsine
- asinh -- inverse hyperbolic sine
- asinh(Number) -- inverse hyperbolic sine
- assert -- assert something is true
- assigning values
- associated primes of an ideal
- associatedPrimes -- find the associated primes of an ideal
- associatedPrimes(..., Strategy => ...)
- associative algebras
- AssociativeExpression -- the class of associative expressions
- atan -- compute the arctangent
- atan(CC) -- compute the arctangent of a number
- atan(QQ) -- compute the arctangent of a number
- atan(RR) -- compute the arctangent of a number
- atan(ZZ) -- compute the arctangent of a number
- atan2 -- compute an angle of a certain triangle
- atan2(QQ,QQ) -- compute an angle of a certain triangle
- atan2(QQ,RR) -- compute an angle of a certain triangle
- atan2(QQ,ZZ) -- compute an angle of a certain triangle
- atan2(RR,QQ) -- compute an angle of a certain triangle
- atan2(RR,RR) -- compute an angle of a certain triangle
- atan2(RR,ZZ) -- compute an angle of a certain triangle
- atan2(ZZ,QQ) -- compute an angle of a certain triangle
- atan2(ZZ,RR) -- compute an angle of a certain triangle
- atan2(ZZ,ZZ) -- compute an angle of a certain triangle
- atEndOfFile -- test for end of file
- atEndOfFile(File) -- test for end of file
- Authors -- package item: start a new package
- autoload -- arrange for a function to be loaded automatically
- autoload(Symbol,String) -- arrange for a function to be loaded automatically
- AuxiliaryFiles -- package item: start a new package
- backtrace -- whether a backtrace is displayed following an error message
- backupFileRegexp -- a regular expression for recognizing names of backup files
- Bag -- the class of all bags
- Bag ? Bag -- the class of all bags
- Bareiss
- baseFilename -- the base part of a filename or path
- BaseFunction -- function for a documented feature
- baseName -- the base name of a generator
- 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
- baseRings -- store the list of base rings of a ring
- BaseRow -- name for 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 element from list
- BasicList #? ZZ -- check for element in list
- 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(..., 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,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,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 -- name for an optional argument
- Bayer -- a Strategy option value for saturate
- BeforePrint -- top level method applied before printing results
- beginDocumentation -- package item: start documentation section
- benchmark -- accurate timing of execution
- BesselJ -- Bessel function of the first kind
- BesselJ(ZZ,QQ) -- Bessel function of the first kind
- BesselJ(ZZ,RR) -- Bessel function of the first kind
- BesselJ(ZZ,ZZ) -- Bessel function of the first kind
- BesselY -- Bessel function of the second kind
- BesselY(ZZ,QQ) -- Bessel function of the second kind
- BesselY(ZZ,RR) -- Bessel function of the second kind
- BesselY(ZZ,ZZ) -- Bessel function of the second kind
- betti -- display degrees
- betti(..., Weights => ...)
- betti(BettiTally) -- view and set the weights of a betti display
- betti(CoherentSheaf) -- show the degrees of the generators and relations of a module or a coherent sheaf
- betti(GradedModule) -- display of degrees in a graded module
- betti(GroebnerBasis) -- diagram of the degrees of a groebner basis
- betti(Ideal) -- gives the degrees of generators.
- betti(Matrix) -- display of the degrees of a map
- betti(Module) -- show the degrees of the generators and relations of a module or a coherent sheaf
- betti(MonomialIdeal) -- gives the degrees of generators.
- 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
- binary methods
- BinaryOperation -- the class of all binary operation expressions
- Binomial -- name for an optional argument
- binomial -- binomial coefficient
- binomial(ZZ,ZZ) -- binomial coefficient
- BLAS
- Boolean -- the class of Boolean values
- Boolean == Boolean -- equality
- Boolean >> Function -- attaching options to a function
- borel -- make a Borel fixed submodule
- borel(Matrix) -- make a Borel fixed submodule
- borel(MonomialIdeal) -- make a Borel fixed submodule
- Boxes -- name for an optional argument
- break -- break from a loop
- cache -- a key under which to store cache tables
- CacheExampleOutput -- name for 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 (under development)
- capture(String) -- evaluate Macaulay2 code and capture the output (under development)
- catch -- catch a thrown exception
- Caveat -- warnings
- 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 ^ ZZ -- a binary operator, usually used for powers
- cdd+
- ceiling -- ceiling function
- Center -- value for an optional argument
- centerString -- center a string or net
- Certification -- name for 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
- ChangeMatrix -- name for an optional argument
- 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
- 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
- characters(String) -- get characters from a string
- check -- perform tests of a package
- check(..., UserMode => ...) -- 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 -- name for an optional argument
- checking your Macaulay2 installation -- and bookmarking the Macaulay2 documentation
- 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 -- name for an optional argument
- code -- 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 -- name for an optional argument
- coefficient -- coefficient of a monomial
- CoefficientRing -- name for 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
- 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
- columnSwap -- interchange columns
- columnSwap(MutableMatrix,ZZ,ZZ) -- interchange columns
- combinatorial functions
- combine -- combine hash tables
- Command -- the class of all commands
- Command \ Tally -- 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
- 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 -- name for an optional argument
- ComplexField -- the class of all complex fields
- component example
- components -- list the components of a direct sum
- components(ChainComplex) -- list the components of a direct sum
- 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
- compositions -- compositions of an integer
- compositions(ZZ,ZZ) -- 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 -- package item: start a new package
- 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
- 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
- constructing maps between modules
- content -- the content of a polynomial
- content(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
- 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(QQ) -- compute the cosine
- cos(RR) -- compute the cosine
- cos(ZZ) -- compute the cosine
- cosh -- compute the hyperbolic cosine
- cosh(CC) -- compute the hyperbolic cosine
- cosh(QQ) -- compute the hyperbolic cosine
- cosh(RR) -- compute the hyperbolic cosine
- cosh(ZZ) -- compute the hyperbolic cosine
- cot -- cotangent
- cot(CC) -- cotangent
- cot(QQ) -- cotangent
- cot(RR) -- cotangent
- cot(ZZ) -- 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(QQ) -- hyperbolic cotangent
- coth(RR) -- hyperbolic cotangent
- coth(ZZ) -- 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(QQ) -- cosecant
- csc(RR) -- cosecant
- csc(ZZ) -- cosecant
- csch -- hyperbolic cosecant
- csch(CC) -- hyperbolic cosecant
- csch(QQ) -- hyperbolic cosecant
- csch(RR) -- hyperbolic cosecant
- csch(ZZ) -- hyperbolic cosecant
- current -- the pseudocode that produced an error
- currentDirectory -- current working directory
- currentFileDirectory -- the directory containing the current input file
- currentFileName -- the current source file
- currentLayout -- relative locations of Macaulay2 files
- currentLineNumber -- current line number of the current input file
- currentPackage -- the current package
- currentString -- evaluate a string
- currentTime -- get the current time
- CurrentVersion -- download a package from the repository
- Daniel R. Grayson
- Database -- the class of all database files
- Database # String -- get value from database
- Database #? String -- check for value in database
- Date -- package item: start a new package
- David Eisenbud
- dd -- differential in a chain complex
- debug -- open private dictionary of a package
- debug(Package) -- open private dictionary of a package
- debugError -- a function to debug
- debugging
- DebuggingMode -- name for an optional argument
- debuggingMode -- whether to enter the debugger when an error occurs
- debugLevel -- current level debugging
- Decompose -- name for an optional argument
- decompose -- minimal associated primes of an ideal
- decompose(Ideal) -- minimal associated primes of an ideal
- decompose(MonomialIdeal) -- minimal associated primes of an ideal
- deepSplice -- remove subsequences
- default -- default member of a family
- default(InexactFieldFamily) -- default member of a family
- defaultPrecision -- default precision of numbers
- definition of product (block) orders
- Degree
- 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)
- degreeLength -- the number of degrees
- degreeLength(GeneralOrderedMonoid) -- the number of degrees
- degreeLength(Ideal) -- the number of degrees
- degreeLength(Module) -- the number of degrees
- degreeLength(OrderedMonoid) -- the number of degrees
- degreeLength(Ring) -- the number of degrees
- DegreeLift -- name for an optional argument
- DegreeLimit -- name for an optional argument
- DegreeMap -- name for an optional argument
- DegreeOrder -- sort primarily by degree
- DegreeRank -- name for an optional argument
- Degrees -- name for an optional argument
- degrees -- degrees of generators
- degrees(CoherentSheaf) -- degrees of generators
- degrees(GeneralOrderedMonoid) -- degrees of generators
- degrees(Ideal) -- degrees of generators
- degrees(Matrix) -- degrees of target and source
- degrees(Module) -- degrees of generators
- degrees(Ring) -- degrees of generators
- degreesMonoid -- get the monoid of degrees
- degreesMonoid(GeneralOrderedMonoid) -- get the monoid of degrees
- degreesMonoid(List) -- get the monoid of degrees
- degreesMonoid(Module) -- get the monoid of degrees
- degreesMonoid(PolynomialRing) -- get the monoid of degrees
- degreesMonoid(QuotientRing) -- get the monoid of degrees
- degreesMonoid(ZZ) -- get the monoid of degrees
- degreesRing -- the ring of degrees
- degreesRing(GeneralOrderedMonoid) -- the ring of degrees
- degreesRing(List) -- the ring of degrees
- degreesRing(Module) -- the ring of degrees
- degreesRing(Ring) -- the ring of degrees
- degreesRing(ZZ) -- the ring of degrees
- delete -- delete elements of a list
- demark -- insert a string between elements of a list of strings
- denominator -- denominator of a fraction
- denominator(Divide) -- denominator of a fraction
- Dense -- name for an optional argument
- Density -- name for 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 -- real description
- describe(FractionField) -- real description
- describe(GaloisField) -- real description
- describe(GeneralOrderedMonoid) -- real description
- describe(PolynomialRing) -- real description
- describe(QuotientRing) -- real description
- describe(Thing) -- real description
- describe(Variety) -- real description
- Description -- name for an optional argument
- determinant -- determinant of a matrix
- determinant(..., Strategy => ...) -- choose between Bareiss and Cofactor algorithms
- determinant(Matrix) -- 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
- 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) -- differentiate or take difference
- diff(ProjectiveHilbertPolynomial,ZZ) -- differentiate or take difference
- 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
- 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 -- name for an optional argument
- division in polynomial rings with monomials less than 1
- do -- loop control
- document -- package item: documentation node
- document(..., BaseFunction => ...) -- function for a documented feature
- document(..., Caveat => ...) -- warnings
- document(..., Consequences => ...) -- side-effects of a function
- document(..., Headline => ...) -- make a headline for a documentation node
- document(..., Inputs => ...) -- inputs for a function
- document(..., Key => ...) -- key of a documentation node
- document(..., Outputs => ...) -- outputs for a function
- document(..., SeeAlso => ...) -- crossreferences in documentation
- document(..., SourceCode => ...) -- package item: documentation node
- document(..., Subnodes => ...) -- a menu of documentation nodes
- document(..., Usage => ...) -- shows the usage of a function
- document(List) -- package item: 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, Strategy => ...)
- dual(MonomialIdeal,List) -- the Alexander dual
- dual(MonomialIdeal,List, Strategy => ...)
- dual(MonomialIdeal,RingElement) -- the Alexander dual
- dual(MonomialIdeal,RingElement, Strategy => ...)
- dumpdata -- dump state of the system to a file
- 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(QQ) -- exponential integral
- eint(RR) -- exponential integral
- eint(ZZ) -- exponential integral
- 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 -- package item: start a new package
- encapDirectory -- encapsulated installation directory
- Encapsulate -- name for an optional argument
- EncapsulateDirectory -- name for an optional argument
- 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
- epkg
- equality and containment
- equality and containment of modules
- Equation -- the class of all equation expressions
- Equation == Equation -- equality
- Equation == Expression -- equality
- Equation == Holder -- equality
- erase -- remove a global symbol
- erf -- error function
- erf(QQ) -- error function
- erf(RR) -- error function
- erf(ZZ) -- error function
- erfc -- complementary error function
- erfc(QQ) -- complementary error function
- erfc(RR) -- complementary error function
- erfc(ZZ) -- 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(String) -- hypertext EXAMPLE item
- EXAMPLE(VisibleList) -- hypertext EXAMPLE item
- examples -- list the examples in documentation
- examples of specifying alternate monomial orders
- examples(Thing) -- list the examples in documentation
- Exclude -- name for an optional argument
- exec -- execute another program
- exit -- exit the program
- exp -- exponential function
- exp(CC) -- exponential function
- exp(Constant) -- exponential function
- exp(QQ) -- exponential function
- exp(RingElement) -- exponential function
- exp(RR) -- exponential function
- exp(ZZ) -- exponential function
- expm1 -- exponential minus 1
- expm1(QQ) -- exponential minus 1
- expm1(RR) -- exponential minus 1
- expm1(ZZ) -- exponential minus 1
- exponents -- list the exponents in a polynomial
- exponents(MonoidElement) -- list the exponents in a polynomial
- exponents(RingElement) -- list the exponents in a polynomial
- export -- package item: export functions
- export(List) -- package item: export functions
- export(String) -- package item: export functions
- export(Symbol) -- package item: export functions
- exportMutable -- package item: export writable variables
- exportMutable(List) -- package item: export writable variables
- exportMutable(Symbol) -- package item: export writable variables
- Expression -- the class of all expressions
- expression -- convert to an expression
- Expression * Expression -- the class of all expressions
- Expression ** Expression -- the class of all expressions
- Expression + Expression -- the class of all expressions
- Expression - Expression -- the class of all expressions
- Expression / Expression -- the class of all expressions
- Expression == Equation -- equality
- Expression == Expression -- the class of all expressions
- Expression ^ Expression -- the class of all expressions
- Expression _ Expression -- the class of all expressions
- Expression Expression -- 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 and Cofactor 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
- 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 -- name for 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
- findSynonyms -- find synonyms of symbols
- findSynonyms(Symbol) -- find synonyms of symbols
- fine control of a Groebner basis computation
- finite field extensions
- finite fields
- First -- name for 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 list by unnesting lists
- flatten(Matrix) -- puts the columns of a matrix into a single row
- flatten(VisibleList) -- flatten a list by unnesting lists
- flattenRing -- write a ring as a (quotient) of a polynomial ring over ZZ or a prime field
- flattenRing(..., CoefficientRing => ...) -- write a ring as a (quotient) of a polynomial ring over ZZ or a prime field
- flattenRing(..., Result => ...) -- write a ring as a (quotient) of a polynomial ring over ZZ or a prime field
- flattenRing(Ideal) -- write a ring as a (quotient) of a polynomial ring over ZZ or a prime field
- flattenRing(Ring) -- write a ring as a (quotient) of a polynomial ring over ZZ or a prime field
- Flexible
- flip -- matrix of commutativity of tensor product
- flip(Module,Module) -- matrix of commutativity of tensor product
- floor -- floor function
- floor(CC) -- floor function
- floor(QQ) -- floor function
- floor(RR) -- floor function
- flush -- flush output to file
- fold -- apply binary operator repeatedly
- fold(Function,Thing,VisibleList) -- apply binary operator repeatedly
- fold(Function,VisibleList) -- apply binary operator repeatedly
- fold(VisibleList,Function) -- apply binary operator repeatedly
- fold(VisibleList,Thing,Function) -- apply binary operator repeatedly
- FollowLinks -- name for 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
- ForestNode -- a type of basic list used to represent a forest, i.e., a list of rooted trees
- fork -- fork the process
- Format -- name for an optional argument
- format -- format a string or a real number
- format and display of matrices in Macaulay2
- 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
- fromDual -- ideal from inverse system
- Function -- the class of all functions
- Function @@ Function -- composition of functions
- Function \ Ideal -- apply a function to generators of an ideal
- Function \ Tally -- 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
- Gamma(QQ) -- Gamma function
- Gamma(RR) -- Gamma function
- Gamma(ZZ) -- 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 -- name for 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
- 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(GeneralOrderedMonoid) -- list of generators
- 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(MonomialIdeal) -- the generator matrix of an ideal
- generators(Ring) -- the list of generators of a ring
- Generic -- name for 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
- getPackage -- download a package from the repository
- getPackage(..., Configuration => ...) -- download a package from the repository
- getPackage(..., CurrentVersion => ...) -- download a package from the repository
- getPackage(..., DebuggingMode => ...) -- download a package from the repository
- getPackage(..., Repository => ...) -- download a package from the repository
- getPackage(..., UserMode => ...) -- download a package from the repository
- getPackage(..., Version => ...) -- download a package from the repository
- getPackage(String) -- download a package from the repository
- 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(..., 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
- 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
- globalReleaseFunction -- the standard method for the global variable release hook
- GlobalReleaseHook
- 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(ModuleMap) -- 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
- 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 hash table
- HashTable #? Thing -- check for value in hash table
- 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 -- name for an optional argument
- Headline -- make a headline for a documentation node
- Heft -- name for an optional argument
- heft -- heft vector of ring, module, graded module, or resolution
- heft vectors
- heft(GradedModule) -- heft vector of ring, module, graded module, or resolution
- heft(Module) -- heft vector of ring, module, graded module, or resolution
- heft(Resolution) -- heft vector of ring, module, graded module, or resolution
- heft(Ring) -- heft vector of ring, module, graded module, or resolution
- Height -- name for 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 -- help command
- help(Array) -- help command
- help(DocumentTag) -- help command
- help(List) -- help command
- help(Sequence) -- help command
- help(String) -- help command
- help(Symbol) -- help command
- help(Thing) -- help command
- Hermitian -- name for 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 ChainComplex -- homology of a chain complex
- HH_ZZ ChainComplexMap -- homology of a chain complex map
- Hilbert -- name for 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 / OneExpression
- Holder == Equation -- equality
- Holder == Holder -- equality
- 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 -- package item: start a new package
- Homogeneous
- 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(Matrix) -- get the homomorphism from element of Hom
- homomorphisms (maps) between modules -- including elements of modules
- horizontalJoin -- join nets or strings horizontally
- horizontalJoin(BasicList) -- join nets or strings horizontally
- HorizontalSpace -- name for an optional argument
- how Macaulay2 finds its files
- html -- convert hypertext 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
- hypertext(List) -- prepare hypertext for display
- hypertext(Sequence) -- prepare hypertext for display
- 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 + 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 -- ideal or submodule quotient
- Ideal : RingElement -- ideal or submodule quotient
- Ideal == Ideal -- equality
- Ideal == Module -- equality
- Ideal == MonomialIdeal -- equality
- Ideal == Ring -- equality
- Ideal == ZZ -- equality
- Ideal ^ ZZ -- power
- Ideal _ List -- map from free module to some generators
- Ideal _ ZZ
- Ideal _* -- get the list of generators of an ideal
- ideal quotients and saturation
- 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 -- name for 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
- ImmutableType -- the class of immutable types
- 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 => ...)
- 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 ^ ZZ -- a binary operator, usually used for powers
- InexactFieldFamily Array -- the standard way to 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 + ZZ -- a unary or binary operator, usually used for addition
- InfiniteNumber - InfiniteNumber -- a unary or binary operator, usually used for negation or subtraction
- InfiniteNumber - ZZ -- a unary or binary operator, usually used for negation or subtraction
- InfiniteNumber // ZZ -- a binary operator, usually used for quotient
- InfiniteNumber == InfiniteNumber -- equality
- InfiniteNumber == ZZ -- equality
- infinity -- infinity
- info -- convert hypertext to info format
- InfoDirSection -- package item: start a new package
- infoHelp -- view online doc with info
- information about a map of modules
- informing others about your package
- inheritance
- Inhomogeneous
- initial help
- initialization file
- input -- read Macaulay2 commands and echo
- Inputs -- inputs for a function
- 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
- installHilbertFunction -- install a Hilbert function without computation
- installHilbertFunction(Ideal,RingElement) -- install a Hilbert function without computation
- installHilbertFunction(Matrix,RingElement) -- install a Hilbert function without computation
- installHilbertFunction(Module,RingElement) -- install a Hilbert function without computation
- installing methods
- installMethod -- install methods
- installPackage -- load and install a package and its documentation
- installPackage(..., AbsoluteLinks => ...) -- 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(..., Encapsulate => ...) -- load and install a package and its documentation
- installPackage(..., EncapsulateDirectory => ...) -- 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(..., MakeInfo => ...) -- load and install a package and its documentation
- installPackage(..., MakeLinks => ...) -- load and install a package and its documentation
- installPackage(..., PackagePrefix => ...) -- 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 -- name for 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
- interpreterDepth -- nesting depth of the interpreter
- intersect -- compute an intersection
- intersect(List) -- compute an intersection
- intersect(Sequence) -- compute an intersection
- Intersection -- value for an optional argument
- intersection of ideals
- inverse -- compute the inverse
- inverse systems
- inverse(Matrix) -- compute the inverse
- InverseMethod -- compute reciprocals
- inversePermutation -- inverse permutation
- Inverses -- name for 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
- 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
- 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(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
- 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
- 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 someting is a polynomial ring
- isPolynomialRing(PolynomialRing) -- whether someting is a polynomial ring
- isPolynomialRing(Thing) -- whether someting is a polynomial ring
- isPrime -- whether a integer, polynomial, or ideal is prime
- isPrime(Ideal) -- whether a integer, polynomial, or ideal is prime
- isPrime(ZZ) -- whether a integer, polynomial, or ideal is prime
- isPrimitive -- whether an element is a primitive element of a finite field
- isPseudoprime -- whether an integer is a pseudoprime
- isPseudoprime(ZZ) -- whether an integer is a pseudoprime
- 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(QQ) -- whether a number is real
- isReal(RR) -- 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(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 rectangular list of lists
- 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
- Iterate -- a Strategy option value for saturate
- 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 -- name for an optional argument
- join -- join lists
- KeepZeroes -- name for an optional argument
- kernel -- kernel of a ringmap, matrix, or chain complex
- kernel and image 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
- keys(HashTable) -- keys used in a hash table
- Keyword -- the class of all keywords
- 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 leading coefficient
- leadCoefficient(RingElement) -- the leading coefficient
- leadComponent -- the leading component of a vector or matrix
- leadComponent(Matrix) -- the leading component of a vector or matrix
- leadComponent(Vector) -- the leading component of a vector or matrix
- leadMonomial -- the leading monomial
- leadMonomial(RingElement) -- the leading monomial
- 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 for an optional argument
- left shift
- length -- length
- 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) -- length
- 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 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(ZZ,type of ZZ) -- lift to another ring
- liftable -- whether lifting to another ring is possible
- Limit -- name for an optional argument
- limitFiles
- limitProcesses
- Linear -- a Strategy option value for saturate
- 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 -- 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 << Thing -- print to a file
- 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
- 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(QQ) -- logarithm of the Gamma function
- lngamma(RR) -- logarithm of the Gamma function
- lngamma(ZZ) -- logarithm of the Gamma function
- load -- read Macaulay2 commands
- loaddata -- load state of the system from a file
- loadDepth -- the load depth
- LoadDocumentation -- when loading a package, load the documentation, too
- loadedFiles
- loadedPackages -- 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(String) -- load a package
- Local -- name for 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(Function) -- locate source code
- locate(Nothing) -- locate source code
- locate(Pseudocode) -- locate source code
- locate(Sequence) -- locate source code
- locate(Symbol) -- locate source code
- log -- logarithm function
- log(CC) -- logarithm function
- log(QQ) -- logarithm function
- log(QQ,CC) -- logarithm function
- log(QQ,QQ) -- logarithm function
- log(QQ,RR) -- logarithm function
- log(QQ,ZZ) -- logarithm function
- log(RR) -- logarithm function
- log(RR,CC) -- logarithm function
- log(RR,QQ) -- logarithm function
- log(RR,RR) -- logarithm function
- log(RR,ZZ) -- logarithm function
- log(ZZ) -- logarithm function
- log(ZZ,CC) -- logarithm function
- log(ZZ,QQ) -- logarithm function
- log(ZZ,RR) -- logarithm function
- log(ZZ,ZZ) -- logarithm function
- log1p -- logarithm of 1+x
- log1p(QQ) -- logarithm of 1+x
- log1p(RR) -- logarithm of 1+x
- log1p(ZZ) -- logarithm of 1+x
- LongPolynomial
- 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 -- name for an optional argument
- makeDocumentTag -- convert a documentation key to a documentation tag
- makeDocumentTag(DocumentTag) -- convert a documentation key to a documentation tag
- makeDocumentTag(String) -- convert a documentation key to a documentation tag
- makeDocumentTag(Thing) -- convert a documentation key to a documentation tag
- MakeInfo -- name for an optional argument
- MakeLinks -- name for an optional argument
- makePackageIndex
- makePackageIndex(List)
- makePackageIndex(Sequence)
- 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 => ...) -- set 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
- mapping over hash tables -- apply a function to each element of a hash table
- mapping over lists -- apply a function to each element of a list
- 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(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 -- calculate the normal form of ring elements and matrices
- Matrix % Matrix -- calculate the normal form of ring elements and matrices
- Matrix % Module -- calculate the normal form of ring elements and matrices
- Matrix % MonomialIdeal -- calculate the normal form of ring elements and matrices
- Matrix % RingElement -- calculate the 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 * ZZ -- 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 | RingElement -- join matrices horizontally
- Matrix | ZZ -- join matrices horizontally
- Matrix || Matrix -- join matrices vertically
- Matrix || RingElement -- join matrices vertically
- Matrix || ZZ -- 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(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 -- maximum of elements of a list
- max(GradedModule) -- maximum of elements of a list
- max(VisibleList) -- maximum of elements of a list
- maxAllowableThreads -- the maximum possibl number of simultaneously running tasks
- maxExponent
- MaximalRank -- name for an optional argument
- maxPosition -- position of largest element
- maxPosition(BasicList) -- position of largest element
- MaxReductionCount -- name for an optional argument
- member -- test membership in a list or set
- member(Thing,Set) -- test membership in a list or set
- member(Thing,VisibleList) -- test membership in a list or set
- 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
- merge -- merge hash tables
- merge(HashTable,HashTable,Function) -- merge 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
- 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 -- calculate the normal form of ring elements and matrices
- methods(Command) -- list methods
- methods(Sequence) -- list methods
- methods(Thing) -- list methods
- methods(Type) -- list methods
- Michael E. Stillman
- min -- minimum of elements of a list
- min(GradedModule) -- minimum of elements of a list
- min(VisibleList) -- minimum of elements of a list
- minExponent
- mingens -- minimal generator matrix
- mingens(..., Strategy => ...)
- 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
- minimal primes of an ideal
- MinimalGenerators
- MinimalMatrix -- name for an optional argument
- minimalPresentation -- compute a minimal presentation
- 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
- minimalPrimes -- minimal associated primes of an ideal
- minimalPrimes(Ideal) -- minimal associated primes of an ideal
- minimalPrimes(MonomialIdeal) -- minimal associated primes of an ideal
- Minimize -- name for an optional argument
- minimizeFilename -- minimize a file name
- minors -- ideal generated by minors
- minors(..., First => ...) -- ideal generated by minors
- minors(..., Limit => ...) -- ideal generated by minors
- minors(..., Strategy => ...) -- choose between Bareiss and Cofactor algorithms
- minors(ZZ,Matrix) -- ideal generated by minors
- minPosition -- position of smallest element
- minPosition(BasicList) -- position of 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 -- ideal or submodule quotient
- Module : Module -- ideal or submodule quotient
- Module : RingElement -- ideal or submodule quotient
- 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
- ModuleMap -- the class of all maps between modules
- 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(..., DegreeLift => ...) -- make or retrieve a monoid
- monoid(..., DegreeMap => ...) -- make or retrieve a monoid
- monoid(..., DegreeRank => ...) -- make or retrieve a monoid
- monoid(..., Degrees => ...) -- make or retrieve a monoid
- monoid(..., Global => ...) -- make or retrieve a monoid
- monoid(..., Heft => ...) -- make or retrieve a monoid
- monoid(..., Inverses => ...) -- make or retrieve a monoid
- monoid(..., Join => ...) -- make or retrieve a monoid
- monoid(..., Local => ...) -- make or retrieve a monoid
- monoid(..., MonomialOrder => ...) -- make or retrieve a monoid
- monoid(..., MonomialSize => ...) -- make or retrieve a monoid
- monoid(..., SkewCommutative => ...) -- make or retrieve a monoid
- monoid(..., VariableBaseName => ...) -- make or retrieve a monoid
- monoid(..., Variables => ...) -- make or retrieve a monoid
- monoid(..., Weights => ...) -- make or retrieve a monoid
- monoid(..., WeylAlgebra => ...) -- make or retrieve a monoid
- monoid(Array) -- make or retrieve a monoid
- monoid(List) -- make or retrieve a monoid
- monoid(PolynomialRing) -- make or retrieve a monoid
- monoid(QuotientRing) -- make or retrieve a monoid
- MonoidElement -- the class of all monoid elements
- MonoidElement == MonoidElement -- equality
- Monomial -- name for 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 : MonomialIdeal -- ideal or submodule quotient
- MonomialIdeal == Ideal -- equality
- MonomialIdeal == MonomialIdeal -- equality
- MonomialIdeal == Ring -- equality
- MonomialIdeal == ZZ -- equality
- MonomialIdeal ^ ZZ -- power
- 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(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 -- name for 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
- mpack
- MPFR
- MPIR
- multidegree -- multidegree
- multidegree(Ideal) -- multidegree
- multidegree(Module) -- multidegree
- multidegree(Ring) -- multidegree
- mutable -- whether something may be modified
- mutable matrices
- mutable(Thing) -- whether something may be modified
- 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 -- package item: start a new package
- 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(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
- 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 -- package item: start a new package
- newPackage(..., Authors => ...) -- package item: start a new package
- newPackage(..., AuxiliaryFiles => ...) -- package item: start a new package
- newPackage(..., CacheExampleOutput => ...) -- package item: start a new package
- newPackage(..., Certification => ...) -- package item: start a new package
- newPackage(..., Configuration => ...) -- package item: start a new package
- newPackage(..., Date => ...) -- package item: start a new package
- newPackage(..., DebuggingMode => ...) -- package item: start a new package
- newPackage(..., Headline => ...) -- package item: start a new package
- newPackage(..., HomePage => ...) -- package item: start a new package
- newPackage(..., InfoDirSection => ...) -- package item: start a new package
- newPackage(..., PackageExports => ...) -- package item: start a new package
- newPackage(..., PackageImports => ...) -- package item: start a new package
- newPackage(..., Reload => ...) -- package item: start a new package
- newPackage(..., Version => ...) -- package item: start a new package
- newPackage(String) -- package item: start a new package
- newRing -- make a copy of a ring, with some features changed
- newRing(..., Constants => ...) -- 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
- nextkey -- the next key in a database
- NonAssociativeProduct -- the class of all nonassociative product expressions
- 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
- 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 + Matrix -- a unary or binary operator, usually used for addition
- Number - Constant -- 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 // Matrix -- a binary operator, usually used for quotient
- Number // RingElement -- a binary operator, usually used for quotient
- 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
- numbered variables
- 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(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,VisibleList) -- convert to floating point
- 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(GeneralOrderedMonoid) -- number of generators of a monoid
- numgens(Ideal) -- number of generators of an ideal
- numgens(Module) -- number of generators of a module
- 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
- operators
- Option -- the class of all pairs x => y
- Option ++ Option -- direct sum of modules or maps
- optional argument documentation template
- optional argument name documentation template
- Options -- name for an optional argument
- options -- get options
- options(Command) -- get optional arguments and default values for a function that accepts them
- options(Function) -- get optional arguments and default values for a function that accepts them
- options(GeneralOrderedMonoid) -- get values used for optional arguments
- options(Monoid) -- get values used for optional arguments
- options(Package) -- get options
- 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 for a function that accepts them
- 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
- override -- override default values for optional arguments
- overview documentation template
- pack -- pack elements of a list into shorter ones
- pack(BasicList,ZZ) -- pack elements of a list into shorter ones
- pack(ZZ,BasicList) -- pack elements of a list into shorter ones
- Package -- the class of all packages
- package -- get containing package
- package documentation template
- package(Dictionary) -- get containing package
- package(DocumentTag) -- get containing package
- package(Function) -- get containing package
- package(HashTable) -- get containing package
- package(Sequence) -- get containing package
- package(Symbol) -- get containing package
- package(Thing) -- get containing package
- PackageDictionary -- the dictionary for names of packages
- PackageExports -- package item: start a new package
- PackageImports -- package item: start a new package
- PackagePrefix -- name for an optional argument
- packages
- packages provided with Macaulay2
- packing monomials for efficiency
- pad -- pad a string with spaces
- pad(String,ZZ) -- pad a string with spaces
- pad(ZZ,String) -- pad a string with spaces
- pager -- display with paging
- PairLimit -- name for an optional argument
- pairs -- list the pairs in a hash table
- pairs(HashTable) -- list the pairs in a hash table
- PairsRemaining -- whether to display the number of S-pairs remaining
- parallel programming with threads and tasks
- parent -- parent type of an object
- Parenthesize
- pari
- parsing precedence, in detail
- part -- select terms of a polynomial by degree or weight
- part(InfiniteNumber,InfiniteNumber,RingElement) -- select terms of a polynomial by degree or weight
- part(InfiniteNumber,InfiniteNumber,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- part(InfiniteNumber,ZZ,RingElement) -- select terms of a polynomial by degree or weight
- part(InfiniteNumber,ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- part(List,RingElement) -- sum of terms of a polynomial of a given degree(s)
- part(Nothing,Nothing,RingElement) -- select terms of a polynomial by degree or weight
- part(Nothing,Nothing,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- part(Nothing,ZZ,RingElement) -- select terms of a polynomial by degree or weight
- part(Nothing,ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,InfiniteNumber,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,InfiniteNumber,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,Nothing,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,Nothing,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,ZZ,RingElement) -- select terms of a polynomial by degree or weight
- part(ZZ,ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree or weight
- 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,Tally) -- partition a set or list by values of a function
- partition(Function,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 a polynomial degree by degree
- parts(RingElement) -- display 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 into 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 the quotient of the ambient ring by an ideal into a polynomial
- poincare(Module) -- assemble degrees of an module into a polynomial
- poincare(Ring) -- assemble degrees of an ring into a polynomial
- poincareN -- assemble degrees into polynomial
- poincareN(ChainComplex) -- assemble degrees into polynomial
- polynomial rings
- PolynomialRing -- the class of all ordered monoid rings
- Position -- monomial ordering
- position -- find first element of a list satisfying a condition
- position(..., Reverse => ...) -- search the list in reverse order
- position(VisibleList,Function) -- find first element of a list satisfying a condition
- position(VisibleList,VisibleList,Function) -- find first element of a list satisfying a condition
- positions -- which elements of a list satisfy a condition
- positions(VisibleList,Function) -- which elements of a list satisfy a condition
- Postfix
- 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
- precision(InexactField)
- precision(InexactNumber)
- precision(Matrix)
- precision(MutableMatrix)
- precision(Number)
- precision(PolynomialRing)
- precision(QuotientRing)
- precision(Ring)
- precision(RingElement)
- Prefix
- prefixDirectory -- the prefix directory
- prefixPath -- absolute locations of Macaulay2 files
- preimage -- preimage of an ideal under a ring map
- preimage(RingMap,Ideal) -- preimage of an ideal under a ring 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
- primary decomposition
- PrimaryTag -- for internal use only: a symbol used in storing documentation
- PrimitiveElement -- specify a primitive element
- Print -- top level method for printing results
- print -- print something
- 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(Tally) -- 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
- 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 + ProjectiveHilbertPolynomial -- a unary or binary operator, usually used for addition
- ProjectiveHilbertPolynomial - ProjectiveHilbertPolynomial -- a unary or binary operator, usually used for negation or subtraction
- ProjectiveHilbertPolynomial == ProjectiveHilbertPolynomial -- 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 -- prune, e.g., compute a minimal presentation
- 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)
- PushforwardComputation -- a type of list used internally
- 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 * 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 + 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 - 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 / 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 == ZZ -- equality
- quit -- quit the program
- Quotient -- value for an optional argument
- quotient -- quotient or division
- quotient rings
- quotient' -- matrix quotient (opposite)
- quotient'(Matrix,Matrix) -- matrix quotient (opposite)
- quotient(..., BasisElementLimit => ...)
- quotient(..., DegreeLimit => ...)
- quotient(..., MinimalGenerators => ...) -- Decides whether quotient computes and outputs a trimmed set of generators; default is true
- quotient(..., PairLimit => ...)
- quotient(..., Strategy => ...) -- Possible strategies are: Iterate, Linear, and Quotient
- quotient(Ideal) -- submodule to quotient module
- quotient(Ideal,Ideal) -- ideal or submodule quotient
- quotient(Ideal,RingElement) -- ideal or submodule quotient
- quotient(Matrix,GroebnerBasis) -- matrix quotient
- quotient(Matrix,Matrix) -- matrix quotient
- quotient(Module) -- submodule to quotient module
- quotient(Module,Ideal) -- ideal or submodule quotient
- quotient(Module,Module) -- ideal or submodule quotient
- quotient(Module,RingElement) -- ideal or submodule quotient
- quotient(MonomialIdeal,MonomialIdeal) -- ideal or submodule quotient
- quotientRemainder -- matrix quotient and remainder
- quotientRemainder' -- matrix quotient and remainder (opposite)
- quotientRemainder'(Matrix,Matrix) -- matrix quotient and remainder (opposite)
- quotientRemainder(Matrix,GroebnerBasis) -- matrix quotient and remainder
- quotientRemainder(Matrix,Matrix) -- matrix quotient and remainder
- quotientRemainder(Number,RingElement) -- quotient and remainder
- quotientRemainder(RingElement,Number) -- quotient and remainder
- quotientRemainder(RingElement,RingElement) -- quotient and remainder
- QuotientRing -- the class of all quotient rings
- radical -- the radical of an ideal
- radical of an ideal
- radical(..., CompleteIntersection => ...) -- the radical of an ideal
- radical(..., Strategy => ...) -- the radical of an ideal
- radical(..., Unmixed => ...) -- the radical of an ideal
- radical(Ideal) -- the radical of an ideal
- radical(MonomialIdeal) -- the radical of an ideal
- random -- get a random element
- random and generic matrices
- random(..., Density => ...) -- make a random module map
- random(..., Height => ...) -- random element of a type
- random(..., MaximalRank => ...) -- make a random module map
- random(..., UpperTriangular => ...) -- make a random module map
- random(GaloisField) -- random element of a type
- random(List) -- shuffle a list randomly
- random(List,Ring) -- random element of a type
- random(Module,Module) -- make a random module map
- random(QuotientRing) -- random element of a type
- random(RingFamily) -- random element of a type
- random(RR) -- random real number
- random(RR,RR) -- random real number
- random(Type) -- random element of a type
- random(ZZ) -- random integer
- random(ZZ,Ring) -- random element of a type
- random(ZZ,ZZ) -- random integer in a range
- 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
- ranges and repetitions
- 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
- 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
- RealField -- the class of all real fields
- realPart -- real part
- realpath -- convert a filename to one passing through no symbolic links
- recursionDepth -- the current recursion depth
- recursionLimit -- set the limit on recursion
- Reduce -- name for an optional argument
- reduceHilbert -- reduce a Hilbert series expression
- reduceHilbert(Divide) -- reduce a Hilbert series expression
- regex
- regex(String,String)
- regex(String,ZZ,String)
- regex(String,ZZ,ZZ,String)
- registerFinalizer -- register a string that will be displayed when an object is garbage collected
- regular expressions
- regularity -- compute the Castelnuovo-Mumford regularity
- regularity(..., Weights => ...)
- 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
- relations -- the defining relations
- relations(Module) -- the defining relations
- relativizeFilename -- relativize a file name
- Reload -- name for 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 -- name for an optional argument
- remove -- remove an entry from a hash table
- remove(HashTable,Thing) -- remove an entry from a hash table
- removeDirectory -- remove a directory
- removeFile -- remove a file
- removeHook -- remove a hook function from an object
- removeHook(HashTable,Thing,Function) -- remove a hook function from an object
- removeHook(Symbol,Function) -- remove a hook function from an object
- removeLowestDimension -- remove components of lowest dimension
- removeLowestDimension(Ideal) -- remove components of lowest dimension
- removeLowestDimension(Module) -- remove components of lowest dimension
- reorganize -- reorganize a database file
- replace -- replacement in strings and lists
- replace(String,String,String) -- regular expression replacement of substrings
- replace(ZZ,Thing,VisibleList) -- copy a list, replacing an element
- replacements for commands and scripts from Macaulay
- Repository -- download a package from the repository
- RerunExamples -- name for 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(..., 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 are obtained
- 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 projective resolution of a module
- resolution(MonomialIdeal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal
- restart -- restart Macaulay2
- Result -- name for an optional argument
- return -- return from a function
- returnCode
- Reverse -- name for an optional argument
- reverse -- reverse a list
- reverse(BasicList) -- reverse a list
- RevLex -- reverse lexicographic ordering
- Right -- value for an optional argument
- 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 ** Matrix -- tensor product
- Ring ** Module -- tensor product
- Ring ** Ring -- tensor product
- 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 ^ List -- make a free module
- Ring ^ ZZ -- make a free module
- Ring _ List -- make a monomial from a list of exponents
- Ring _ String -- get a ring variable by name
- 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 OrderedMonoid -- 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(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 -- calculate the normal form of ring elements and matrices
- RingElement % Matrix -- calculate the normal form of ring elements and matrices
- RingElement % MonomialIdeal -- calculate the normal form of ring elements and matrices
- RingElement % Number -- a binary operator, usually used for remainder and reduction
- RingElement % RingElement -- calculate the 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 ^ Ring -- lift to another ring
- RingElement ^ RingFamily -- lift to another ring
- 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 _* -- 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 of a module map via a ring map
- RingMap ** Module -- tensor product of a module 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
- 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
- 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 * 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 + 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 - 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 / 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 == ZZ -- equality
- RR >> 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
- RunExamples -- name for an optional argument
- runHooks -- run the hook functions stored in an object
- runHooks(HashTable,Thing,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
- same -- whether everything in a list is the same
- saturate -- saturation of ideal or submodule
- saturate(..., BasisElementLimit => ...)
- saturate(..., DegreeLimit => ...)
- saturate(..., MinimalGenerators => ...) -- whether to compute minimal generators
- saturate(..., PairLimit => ...)
- saturate(..., Strategy => ...)
- saturate(Ideal) -- saturation of ideal or submodule
- saturate(Ideal,Ideal) -- saturation of ideal or submodule
- saturate(Ideal,RingElement) -- saturation of ideal or submodule
- saturate(Module) -- saturation of ideal or submodule
- saturate(Module,Ideal) -- saturation of ideal or submodule
- saturate(Module,RingElement) -- saturation of ideal or submodule
- saturate(MonomialIdeal,MonomialIdeal) -- saturation of ideal or submodule
- saturate(MonomialIdeal,RingElement) -- saturation of ideal or submodule
- saving polynomials and matrices in files
- scan -- apply a function to each element
- scan(BasicList,Function) -- apply a function to each element of a list
- scan(ZZ,Function) -- apply a function to 0 .. n-1
- 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 pairs in a hash table
- scanPairs(HashTable,Function) -- apply a function to pairs in a hash table
- scanValues -- apply a function to each value in a hash table
- scanValues(HashTable,Function) -- apply a function to each value in a hash table
- 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 Schryer 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 Pluecker ideal of a Schubert variety
- Schubert(..., CoefficientRing => ...) -- find the Pluecker ideal of a Schubert variety
- Schubert(..., Variable => ...) -- find the Pluecker ideal of a Schubert variety
- Schubert(ZZ,ZZ,VisibleList) -- find the Pluecker 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(QQ) -- secant
- sec(RR) -- secant
- sec(ZZ) -- secant
- sech -- hyperbolic secant
- sech(CC) -- hyperbolic secant
- sech(QQ) -- hyperbolic secant
- sech(RR) -- hyperbolic secant
- sech(ZZ) -- hyperbolic secant
- SeeAlso -- crossreferences in documentation
- 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(HashTable,Function) -- select part of a hash table
- select(String,String) -- select substrings matching a regular expression from a string
- select(String,String,String) -- select substrings matching a regular expression from a string
- 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 pieces
- separate(String) -- split a string into pieces
- separate(String,String) -- split a string into pieces
- SeparateExec -- name for an optional argument
- separateRegexp -- separate a string into pieces, with separators determined by a regular expression
- separateRegexp(String,String) -- separate a string into pieces, with separators determined by a regular expression
- separateRegexp(String,ZZ,String) -- separate a string into pieces, with separators determined by 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
- 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() -- 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
- 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 TeX, hypertext, or a URL, in an external application
- show(URL) -- display various TeX, hypertext, or a URL, in an external application
- showClassStructure -- display class structure
- showHtml -- convert hypertext to html and display with a browser
- showStructure -- display parent structure
- showTex -- convert to TeX and display on screen
- showTex(..., Format => ...) -- convert to TeX and display on screen
- 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(QQ) -- compute the sine
- sin(RR) -- compute the sine
- sin(ZZ) -- 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
- Singular-Libfac
- 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(QQ) -- compute the hyperbolic sine
- sinh(RR) -- compute the hyperbolic sine
- sinh(ZZ) -- 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(ZZ) -- number of binary digits to the left of the point
- SizeLimit -- name for an optional argument
- SkewCommutative -- make or retrieve a monoid
- 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 a linear equation
- solve(..., ClosestFit => ...) -- solve a linear equation
- solve(..., MaximalRank => ...) -- solve a linear equation
- solve(Matrix,Matrix) -- solve a linear equation
- solve(MutableMatrix,MutableMatrix) -- solve a linear equation
- someTerms -- select some terms of a polynomial
- someTerms(RingElement,ZZ,ZZ) -- select some terms of a polynomial
- Sort
- 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 -- name for an optional argument
- SourceRing -- name for an optional argument
- SPACE -- blank operator; often used for function application, making polynomial rings
- 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
- splice(BasicList) -- remove subsequences
- sqrt -- square root function
- sqrt(CC) -- square root function
- sqrt(QQ) -- square root function
- sqrt(RR) -- square root function
- sqrt(ZZ) -- 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(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 -- name for an optional argument
- stopIfError -- whether to stop the program when an error occurs
- StopWithMinimalGenerators -- name for an optional argument
- Strategy -- name for an optional argument
- String -- the class of all strings
- String # ZZ -- get character from string
- String #? ZZ -- check for character in string
- String .. String -- a sequence of consecutive strings
- String ..< String -- a sequence of consecutive strings, not including the endpoint
- 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 _ Sequence -- substring
- String _ ZZ -- get element from string
- String | String -- join strings or nets
- String | ZZ -- join strings or nets
- strings and nets
- sublists -- process interspersed sublists of a list
- sublists(VisibleList,Function) -- process interspersed sublists of a list
- sublists(VisibleList,Function,Function) -- process interspersed sublists of a list
- sublists(VisibleList,Function,Function,Function) -- process interspersed sublists of a list
- sublists(VisibleList,Function,Function,Nothing) -- process interspersed sublists of a list
- sublists(VisibleList,Function,Nothing) -- process interspersed sublists of a list
- sublists(VisibleList,Function,Nothing,Function) -- process interspersed sublists of a list
- sublists(VisibleList,Function,Nothing,Nothing) -- process interspersed sublists of a list
- submatrix
- submatrix' -- 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,Nothing,VisibleList) -- select part of a matrix
- submatrix(Matrix,VisibleList) -- select columns
- submatrix(Matrix,VisibleList,Nothing) -- select part of a matrix
- submatrix(Matrix,VisibleList,VisibleList) -- select part of a matrix
- 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 all the subsets
- subsets(List) -- produce all the subsets
- subsets(List,ZZ) -- produce all the subsets
- subsets(Sequence,ZZ) -- produce all the subsets
- subsets(Set) -- produce all the subsets
- subsets(Set,ZZ) -- produce all the subsets
- subsets(ZZ) -- produce all the subsets
- subsets(ZZ,ZZ) -- produce all the subsets
- 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(Tally) -- 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
- 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
- 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
- SYNOPSIS(..., BaseFunction => ...)
- SYNOPSIS(..., Consequences => ...)
- SYNOPSIS(..., Heading => ...)
- SYNOPSIS(..., Inputs => ...)
- SYNOPSIS(..., Outputs => ...)
- SYNOPSIS(..., Usage => ...)
- 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 -- name for an optional argument
- SyzygyLimit -- name for an optional argument
- SyzygyMatrix -- name for an optional argument
- SyzygyRows -- name for an optional argument
- syzygyScheme -- construct a syzygy scheme
- Table -- the class of all table expressions
- table -- make a table (nested list)
- take -- take some elements from a list
- take(BasicList,List) -- take some elements from a list
- take(BasicList,ZZ) -- take some elements from a list
- Tally -- the class of all tally results
- tally -- tally the elements of a list or sequence
- Tally ** Tally -- Cartesian product of tallies
- Tally + Tally -- union of tallies
- Tally - Tally -- difference of tallies
- Tally / Command -- apply a function to elements of a list
- Tally / Function -- apply a function to elements of a list
- Tally ? Tally -- comparison operator
- Tally ^** ZZ -- Cartesian power of sets and tallies
- Tally _ Thing -- get a count from a tally
- tally(VisibleList) -- tally the elements of a list, sequence, or array
- tan -- compute the tangent
- tan(CC) -- compute the tangent
- tan(QQ) -- compute the tangent
- tan(RR) -- compute the tangent
- tan(ZZ) -- 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(QQ) -- compute the hyperbolic tangent
- tanh(RR) -- compute the hyperbolic tangent
- tanh(ZZ) -- 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(..., DegreeLift => ...) -- tensor product
- tensor(..., DegreeMap => ...) -- tensor product
- tensor(..., DegreeRank => ...) -- tensor product
- tensor(..., Degrees => ...) -- tensor product
- tensor(..., Global => ...) -- tensor product
- tensor(..., Heft => ...) -- tensor product
- tensor(..., Inverses => ...) -- tensor product
- tensor(..., Join => ...) -- tensor product
- tensor(..., Local => ...) -- tensor product
- tensor(..., MonomialOrder => ...) -- tensor product
- tensor(..., MonomialSize => ...) -- tensor product
- tensor(..., SkewCommutative => ...) -- tensor product
- tensor(..., VariableBaseName => ...) -- tensor product
- tensor(..., Variables => ...) -- tensor product
- tensor(..., Weights => ...) -- tensor product
- tensor(..., WeylAlgebra => ...) -- tensor product
- tensor(CoherentSheaf,CoherentSheaf) -- tensor product
- tensor(Module,Module) -- tensor product
- tensor(Monoid,Monoid) -- tensor product
- tensor(Ring,Ring) -- tensor product
- tensor(Ring,RingMap,Matrix) -- tensor product via a ring map
- tensor(Ring,RingMap,Module) -- tensor product via a ring map
- tensor(RingMap,Matrix) -- tensor product via a ring map
- tensor(RingMap,Module) -- tensor product via a ring map
- 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 -- package item: register a test of the package
- TEST(List) -- package item: register a test of the package
- TEST(String) -- package item: register a test of the package
- 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 * List -- a binary operator, usually used for multiplication
- Thing // Command -- apply a function
- Thing // Function -- apply a function
- Thing // SelfInitializingType -- apply a function
- Thing =!= Thing -- strict inequality
- Thing === Thing -- strict equality
- Thing => Thing -- produce an Option
- 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
- toDual -- inverse system
- toExternalString -- convert to a readable string
- toField -- declare that a ring is a field
- toField(Ring) -- declare that a ring is a field
- toList -- list of elements
- toList(BasicList) -- list of elements
- toList(Set) -- list of elements
- 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
- topComponents -- compute top dimensional component
- topComponents(Ideal) -- compute top dimensional component
- topComponents(Module) -- compute top dimensional component
- topLevelMode -- the current top level mode
- Tor -- Tor module
- Tor_ZZ(Module,Module) -- compute a Tor module
- Toric -- compute a Gröbner basis
- toRR -- convert to high-precision real number
- toSequence -- convert to sequence
- toSequence(BasicList) -- 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
- TreeNode -- a type of basic list used to represent a rooted tree
- trim -- minimize generators and relations
- trim(..., Strategy => ...)
- true
- truncate -- truncate the module at a specified degree
- truncate(List,Ideal) -- truncate the module at a specified degree
- truncate(List,Module) -- truncate the module at a specified degree
- truncate(ZZ,Ideal) -- truncate the module at a specified degree
- truncate(ZZ,Module) -- truncate the module at a specified degree
- 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 -- name for an optional argument
- undocumented
- undocumented(List)
- undocumented(Thing)
- uniform -- test whether elements of a list are of the same class
- uninstallPackage -- uninstall a package
- uninstallPackage(..., InstallPrefix => ...) -- uninstall a package
- uninstallPackage(..., PackagePrefix => ...) -- uninstall a package
- uninstallPackage(String) -- uninstall a package
- unique -- eliminate duplicates from a list
- unique(List) -- eliminate duplicates from a list
- unique(Sequence) -- eliminate duplicates from a list
- Unmixed -- name for 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 -- name for an optional argument
- URL -- a type representing a URL
- Usage -- shows the usage of a function
- 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
- UseHilbertFunction
- UserMode -- name for an optional argument
- userSymbols -- a list of the user's symbols
- UseSyzygies -- compute a Gröbner basis
- using functions
- using functions with optional inputs
- using Macaulay2 with emacs
- using Macaulay2 with emacs after it has been set up
- using Macaulay2 with TeXmacs
- using packages
- using sockets
- utf8 -- encode and decode unicode utf-8-encoded strings
- 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 -- make or retrieve a monoid
- Variables -- name for an optional argument
- variables
- varieties
- Variety -- the class of all algebraic varieties
- variety -- get the variety
- variety(CoherentSheaf) -- get the variety
- variety(Ideal) -- the closed projective subvariety defined by an ideal
- variety(SheafOfRings) -- get the variety
- vars -- variables
- vars(GeneralOrderedMonoid) -- row matrix of the variables
- vars(List) -- a sequence of variables
- 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(List) -- make a vector
- Verbose -- request verbose feedback
- Verify -- verify that a map is well-defined
- Version -- package item: start a new package
- version -- information about this version of the program
- VerticalList -- a type of visible self-initializing list that prints vertically
- VerticalSpace -- name for an optional argument
- viewHelp -- view online doc with a web browser
- viewing the symbols defined so far
- VirtualTally
- VirtualTally - VirtualTally
- 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
- 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 -- name for an optional argument
- what a class is
- what is a Groebner basis?
- what is a subquotient module?
- 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
- Wikipedia -- link to a Wikipedia entry
- Wikipedia(String) -- link to a Wikipedia entry
- 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 -- logical exclusive-or
- xor(ZZ,ZZ) -- logical exclusive-or
- youngest -- the youngest member of a sequence
- zero -- whether something is zero
- ZeroExpression -- the class of all zero expressions
- zeta -- Riemann zeta function
- zeta(QQ) -- Riemann zeta function
- zeta(RR) -- Riemann zeta function
- zeta(ZZ) -- 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 * 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 + InfiniteNumber -- 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 + ZZ -- a unary or binary operator, usually used for addition
- ZZ - CC -- a unary or binary operator, usually used for negation or subtraction
- ZZ - InfiniteNumber -- 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 - 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 / ZZ -- a binary operator, usually used for division
- ZZ // InfiniteNumber -- a binary operator, usually used for quotient
- 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 == InfiniteNumber -- equality
- ZZ == Module -- equality
- ZZ == MonomialIdeal -- equality
- ZZ == MutableMatrix -- equality
- ZZ == QQ -- equality
- ZZ == Ring -- equality
- ZZ == RingElement -- equality
- ZZ == RingMap -- equality
- ZZ == RR -- equality
- ZZ == ZZ -- equality
- ZZ >> ZZ
- ZZ _ Module -- integers or zero element
- ZZ | Matrix -- join matrices horizontally
- ZZ | String -- join strings or nets
- ZZ | ZZ -- logical or
- ZZ || Matrix -- join matrices vertically