List -- the class of all lists -- {...}

Description

Lists in Macaulay2 consist of elements of any type, enclosed in braces, and separated by commas.

i1 : L = {a,1,b,2}

o1 = {a, 1, b, 2}

o1 : List

The length of a list has two notations, the version with the # is faster when writing programs.

i2 : #L, length L

o2 = (4, 4)

o2 : Sequence

The first entry of the list has index 0. Indexing is performed using #.

i3 : L#2

o3 = b

o3 : Symbol

Lists in Macaulay2 are immutable. See MutableList for making and using lists that you may modify.

To convert lists to and from other types of BasicList, in addition to toList, one may use new.

i4 : new Array from {a,b,c}

o4 = [a, b, c]

o4 : Array

i5 : new List from [a,b,c]

o5 = {a, b, c}

o5 : List

For an overview of lists and sequences, see lists and sequences.

Types of list:

VerticalList -- a type of visible self-initializing list that prints vertically

Functions and methods returning a list:

List * Thing -- see * -- a binary operator, usually used for multiplication
Thing * List -- see * -- a binary operator, usually used for multiplication
- List -- see - -- a unary or binary operator, usually used for negation or subtraction
List // Number -- see // -- a binary operator, usually used for quotient
List // RingElement -- see // -- a binary operator, usually used for quotient
apply(ZZ,Function) -- apply a function to {0,..., n-1}
applyPairs(BasicList,Function) -- see applyPairs -- apply a function to each pair in a hash table
applyPairs(Dictionary,Function) -- see applyPairs -- apply a function to each pair in a hash table
between(Thing,VisibleList) -- see between -- insert something between elements of a list
commonest -- the most common elements of a list or tally
compositions -- list the compositions of an integer
decompose(Ideal)
degree(Matrix) (missing documentation)
degrees -- degrees of generators
elements(Set) -- see elements -- list of elements
findHeft -- find a heft vector for a list of degrees
frames(CompiledFunction) -- see frames -- get the frames associated to a closure
frames(CompiledFunctionClosure) -- see frames -- get the frames associated to a closure
frames(FunctionClosure) -- see frames -- get the frames associated to a closure
frames(PseudocodeClosure) -- see frames -- get the frames associated to a closure
frames(Sequence) -- see frames -- get the frames associated to a closure
frames(Symbol) -- see frames -- get the frames associated to a closure
Monoid _* -- see generators of rings, ideals, and modules
Function \ Ideal -- see Ideal / Function -- apply a function to generators of an ideal
Ideal / Function -- apply a function to generators of an ideal
independentSets(Ideal) -- see independentSets -- some size-maximal independent subsets of variables modulo an ideal
independentSets(MonomialIdeal) -- see independentSets -- some size-maximal independent subsets of variables modulo an ideal
keys(Database) -- see keys -- keys used in a hash table, dictionary, or database
keys(Dictionary) -- see keys -- keys used in a hash table, dictionary, or database
keys(HashTable) -- see keys -- keys used in a hash table, dictionary, or database
leadComponent(Matrix) -- see leadComponent -- the leading component(s) of a vector or matrix
lines(String) -- see lines -- split a string into lines
lines(String,String) -- see lines -- split a string into lines
List ** List -- Cartesian product of two lists
List + List -- sum of two vectors
List - List -- difference of two vectors
List | List -- join lists, sequences or arrays
localDictionaries(Dictionary) -- see localDictionaries -- get local dictionaries
localDictionaries(FunctionClosure) -- see localDictionaries -- get local dictionaries
localDictionaries(PseudocodeClosure) -- see localDictionaries -- get local dictionaries
localDictionaries(Symbol) -- see localDictionaries -- get local dictionaries
localDictionaries(CompiledFunction) (missing documentation)
localDictionaries(CompiledFunctionClosure) (missing documentation)
localDictionaries(Sequence) (missing documentation)
locate(List) -- see locate -- locate source code
List / Number -- see Matrix / Number -- scalar division
List / RingElement -- see Matrix / Number -- scalar division
mingle(BasicList) -- see mingle -- mingle elements of several lists
pack(BasicList,ZZ) -- see pack -- pack elements of a list or string into several shorter lists or strings
pack(String,ZZ) -- see pack -- pack elements of a list or string into several shorter lists or strings
pack(ZZ,BasicList) -- see pack -- pack elements of a list or string into several shorter lists or strings
pack(ZZ,String) -- see pack -- pack elements of a list or string into several shorter lists or strings
pairs(BasicList) -- see pairs -- list the pairs in a hash table, dictionary, or basic list
pairs(Dictionary) -- see pairs -- list the pairs in a hash table, dictionary, or basic list
pairs(HashTable) -- see pairs -- list the pairs in a hash table, dictionary, or basic list
partitions -- list the partitions of an integer
permutations(ZZ) -- see permutations -- produce all permutations of a list
positions -- which elements of a list satisfy a condition
regex -- evaluate a regular expression search
searchPath(List,String) -- search a path for a file
searchPath(String) -- see searchPath(List,String) -- search a path for a file
select(String,String) -- see select(String,String,String) -- select and reformat substrings matching a regular expression
select(String,String,String) -- select and reformat substrings matching a regular expression
select(ZZ,Function) -- select integers
selectPairs(BasicList,Function) -- see selectPairs -- select a part of a hash table by pairs
selectPairs(ZZ,BasicList,Function) -- see selectPairs -- select a part of a hash table by pairs
separate -- split a string into substrings using a regular expression
List - Set -- see Set - Set -- set difference
subsets -- produce the subsets of a set or list
take(Thing,List) -- see take -- take some elements from a list or sequence
take(Thing,ZZ) -- see take -- take some elements from a list or sequence
toList(BasicList) -- see toList -- create a list
toList(Set) -- see toList -- create a list
toList(String) -- see toList -- create a list
toList(Pseudocode) (missing documentation)
transpose(List) -- see transpose -- transpose a matrix or table
unique -- eliminate duplicates from a list
unstack(Net) -- see unstack -- list the rows of a net
unstack(String) -- see unstack -- list the rows of a net
values(Dictionary) -- see values -- values in a hash table
values(HashTable) -- see values -- values in a hash table
List / Command -- see VisibleList / Function -- apply a function to elements of a list
List / Function -- see VisibleList / Function -- apply a function to elements of a list

Methods that use a list:

# List -- length or cardinality of a list, hash table, dictionary, set, or string
List #? ZZ -- see #? -- check existence of value in a list, hash table, database, or string
>= List
List ? List -- see ? -- comparison operator
basis(InfiniteNumber,List,Ideal) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(InfiniteNumber,List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(InfiniteNumber,List,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(InfiniteNumber,List,Ring) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,Ideal) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,InfiniteNumber,Ideal) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,InfiniteNumber,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,InfiniteNumber,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,InfiniteNumber,Ring) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,List,Ideal) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,List,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,List,Ring) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,Ring) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,RingMap) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Ideal) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Ring) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Ideal) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Ring) -- see basis -- basis or generating set of all or part of a ring, ideal or module
capture(List) -- see capture -- evaluate Macaulay2 code and capture the output
check(List) -- see check -- perform tests of a package
check(List,Package) -- see check -- perform tests of a package
check(List,String) -- see check -- perform tests of a package
code(List) -- see code -- display source code
columnPermute(MutableMatrix,ZZ,List) -- see columnPermute -- permute some columns
commonRing(List) -- see commonRing -- find smallest containing ring
degreesMonoid(List) -- see degreesRing(List) -- the ring or monoid of degrees
degreesRing(List) -- the ring or monoid of degrees
diagonalMatrix(List) -- see diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
diagonalMatrix(Ring,List) -- see diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
diagonalMatrix(RingFamily,List) -- see diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
diagonalMatrix(RingFamily,ZZ,ZZ,List) -- see diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
diagonalMatrix(ZZ,ZZ,List) -- see diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
directProduct(List) -- see directProduct -- direct product
directSum(List) -- see directSum -- direct sum of modules or maps
document(List) -- see document -- create a documentation node
makeDocumentTag(List) -- see DocumentTag -- the class of all document tags
drop(BasicList,List) -- see drop -- drop some elements from a list or sequence
dual(MonomialIdeal,List) -- the Alexander dual
examples(List) -- see examples -- list the examples in documentation
export(List) -- see export -- export symbols from a package
exportFrom(Package,List) -- see exportFrom -- export symbols from a package's private dictionary
exportFrom(String,List) -- see exportFrom -- export symbols from a package's private dictionary
exportMutable(List) -- see exportMutable -- export mutable symbols from a package
findFiles(List) -- see findFiles -- find files recursively
findHeft(List) -- see findHeft -- find a heft vector for a list of degrees
findProgram(String,List) -- see findProgram -- load external program
gcd(List) -- see gcd -- greatest common divisor
Ring _ List -- see get a monomial by exponent vector -- make a monomial from a list of exponents
gradedModule(List)
HeaderType List -- see HeaderType -- a class of lists with abbreviated constructors
headlines(List) -- see headlines -- display a table of documentation headlines
help(List) -- see help -- view documentation nodes
hilbertFunction(List,Ideal) -- see hilbertFunction -- the Hilbert function
hilbertFunction(List,Module) -- see hilbertFunction -- the Hilbert function
hilbertFunction(List,Ring) -- see hilbertFunction -- the Hilbert function
homogenize(Matrix,RingElement,List) -- see homogenize -- homogenize with respect to a variable
homogenize(Module,RingElement,List) -- see homogenize -- homogenize with respect to a variable
homogenize(RingElement,RingElement,List) -- see homogenize -- homogenize with respect to a variable
homogenize(Vector,RingElement,List) -- see homogenize -- homogenize with respect to a variable
hooks(List) -- see hooks -- list hooks attached to a key
ideal(List) -- make an ideal
importFrom(Package,List) -- see importFrom -- import symbols to the current private dictionary
importFrom(String,List) -- see importFrom -- import symbols to the current private dictionary
intersect(List) -- see intersect -- compute an intersection
lcm(List) -- see lcm -- least common multiple
List # ZZ -- get value from list, hash table, database, dictionary, or string
List .. List -- rectangular sequences of consecutive lists and sequences
List ..< List -- rectangular sequences of consecutive lists and sequences
List << List -- component-wise comparison of lists
List ^ List (missing documentation)
listSymbols(List) -- see listSymbols -- compact display of symbols and their values
makePackageIndex(List) -- see makePackageIndex -- create an index of installed packages
map(Module,Module,List) -- create a matrix by giving a sparse or dense list of entries
map(Module,Module,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,List) -- create a matrix by giving a doubly nested list of ring elements
map(Module,ZZ,List) -- create a matrix by giving a sparse or dense list of entries
map(Ring,Ring,List) -- make a ring map
match(List,String) -- see match -- regular expression matching
Matrix ^ List -- select rows
MutableMatrix ^ List -- see Matrix ^ List -- select rows
Vector ^ List -- see Matrix ^ List -- select rows
Matrix _ List -- select columns
MutableMatrix _ List -- see Matrix _ List -- select columns
matrix(List) -- create a matrix from a doubly-nested list of ring elements or matrices
matrix(Ring,List) -- create a matrix from a doubly nested list of ring elements or matrices
matrix(RingFamily,List) -- see matrix(Ring,List) -- create a matrix from a doubly nested list of ring elements or matrices
memoize(Function,List) -- see memoize -- record results of function evaluation for future use
Module / List -- see Module / Module -- quotient module
Module ^ List -- projection onto summand
Ideal _ List -- see Module _ List -- map from free module to some generators
Module _ List -- map from free module to some generators
monoid(List) -- see monoid -- make or retrieve a monoid
monomialIdeal(List) -- see monomialIdeal(Matrix) -- monomial ideal of lead monomials
MultigradedBettiTally List (missing documentation)
mutableMatrix(List) -- see mutableMatrix -- make a mutable matrix
mutableMatrix(Ring,List) -- see mutableMatrix -- make a mutable matrix
mutableMatrix(RingFamily,List) -- see mutableMatrix -- make a mutable matrix
new HashTable from List -- make a hash table from a list
new OptionTable from List (missing documentation)
norm(List) -- see norm
ofClass(List) -- see ofClass -- English phrases for types
options(List) -- see options(Function) -- get the optional arguments and default values of a function or method
OptionTable ++ List -- see OptionTable ++ OptionTable
List >> Function -- see OptionTable >> Function -- attaching options to a function
part(List,RingElement) -- see part -- select terms of a polynomial by degree(s) or weight(s)
part(List,Ideal) (missing documentation)
part(List,Matrix) (missing documentation)
part(List,Module) (missing documentation)
part(List,Ring) (missing documentation)
product(List) -- product of elements
pullback(List) (missing documentation)
pushout(List) (missing documentation)
random(List) -- shuffle a list randomly
random(List,Module) -- get a random vector in the module
random(List,Ideal) -- see random(ZZ,Ideal) -- get a random homogeneous element from a graded ideal
random(List,Ring) -- see random(ZZ,Ring) -- get a random homogeneous element from a graded ring
Ring / List -- see Ring / Ideal -- make a quotient ring
Ring ^ List -- make a free module
RingFamily ^ List -- see Ring ^ List -- make a free module
InexactFieldFamily List -- see Ring List -- make a local polynomial ring
Ring List -- make a local polynomial ring
rowPermute(MutableMatrix,ZZ,List) -- see rowPermute -- permute some rows
rsort(List) -- see rsort -- sort a list or matrix in reverse order
rsort(List,Function) -- see rsort -- sort a list or matrix in reverse order
scanLines(Function,List) -- see scanLines -- apply a function to each line of a file
selectVariables(List,PolynomialRing) -- see selectVariables -- make a subring of a polynomial ring generated by selected variables
Set - List -- see Set - Set -- set difference
sort(List) -- sort a list
sort(List,Function) -- see sort(List) -- sort a list
span(List) -- construct smallest interval
standardPairs(MonomialIdeal,List) -- see standardPairs -- find the standard pairs of a monomial ideal
submatrixByDegrees(Matrix,List,List) -- see submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
subsets(List) -- see subsets -- produce the subsets of a set or list
subsets(List,ZZ) -- see subsets -- produce the subsets of a set or list
substitute(Ideal,List) -- see substitute -- substituting values for variables
substitute(Matrix,List) -- see substitute -- substituting values for variables
substitute(Module,List) -- see substitute -- substituting values for variables
substitute(RingElement,List) -- see substitute -- substituting values for variables
substitute(Vector,List) -- see substitute -- substituting values for variables
sum(List) -- sum the elements of a list
SYNOPSIS(List) -- see SYNOPSIS -- a standardized synopsis for use in documentation nodes
take(BasicList,List) -- see take -- take some elements from a list or sequence
tensor(List) -- see tensor -- tensor product
truncate(List,Ideal)
truncate(List,List,Matrix) (missing documentation)
truncate(List,Matrix)
truncate(List,Module)
truncate(List,Ring)
truncate(Nothing,List,Matrix) (missing documentation)
undocumented(List) -- see undocumented -- declare that something need not be documented
union(List) -- see union -- compute the union
vars(List) -- a sequence of variables
vector(List) -- see vector -- make a vector
vector(Module,List) -- see vector -- make a vector
vector(Ring,List) -- see vector -- make a vector
vector(RingFamily,List) -- see vector -- make a vector
List / SelfInitializingType -- see VisibleList / Function -- apply a function to elements of a list
VisibleList _ List -- get some entries of a list
weightRange(List,RingElement) -- see weightRange -- the pair of lowest and highest weights of the monomials
WrapperType List -- see WrapperType -- a class of lists with abbreviated constructors

For the programmer

The object List is a type, with ancestor classes VisibleList < BasicList < Thing.