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

Description

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

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.

In Macaulay2, there are several kinds of lists, the main difference being their notation. These include Array and Sequence. See VisibleList.

Functions and methods returning a list :

Thing * List, see * -- a binary operator, usually used for multiplication
- List -- negation of a vector
apply(ZZ,Function) -- apply a function to {0,..., n-1}
ascii(String) -- ASCII character conversion
associatedPrimes -- find the associated primes of an ideal
associatedPrimes(Ideal), see associatedPrimes -- find the associated primes of an ideal
associatedPrimes(MonomialIdeal), see associatedPrimes -- find the associated primes of an ideal
between(Thing,VisibleList) -- insert something between elements of a list
characters(String), see characters -- get characters from a string
compositions -- compositions of an integer
degree(Matrix)
eulers -- list the sectional Euler characteristics
List << Thing, see File << Thing -- print to a file
genera -- list of the successive linear sectional arithmetic genera
irreducibleDecomposition(MonomialIdeal) -- express a monomial ideal as an intersection of irreducible monomial ideals
keys(HashTable) -- keys used in a hash table
lines(String), see lines -- split a string into lines
lines(String,String), see lines -- split a string into lines
List + List -- sum of two vectors
List - List -- difference of two vectors
List / Thing -- vector division
List | List -- join lists, sequences or arrays
localDictionaries(Dictionary), see localDictionaries -- get local dictionaries
localDictionaries(Function), see localDictionaries -- get local dictionaries
localDictionaries(Pseudocode), see localDictionaries -- get local dictionaries
localDictionaries(Symbol), see localDictionaries -- get local dictionaries
mingle(BasicList), see mingle -- mingle elements of several lists
pack(BasicList,ZZ), see pack -- pack elements of a list into shorter ones
pack(ZZ,BasicList), see pack -- pack elements of a list into shorter ones
pairs(HashTable), see pairs -- list the pairs in a hash table
partitions(ZZ) -- list the partitions of an integer
partitions(ZZ,ZZ) -- list the partitions of an integer
permutations(ZZ), see permutations -- produce all permutations of a list
primaryDecomposition -- irredundant primary decomposition of an ideal
primaryDecomposition(Ideal), see primaryDecomposition -- irredundant primary decomposition of an ideal
regex(String,String) -- regular expression matching
regex(String,ZZ,String) -- regular expression matching
searchPath(List,String) -- search a path for a file
searchPath(String) -- missing documentation
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
separate(String), see separate -- split a string into pieces
separate(String,String), see separate -- split a string into pieces
List - Set, see Set - Set -- set difference
subsets(List) -- produce all the subsets
subsets(List,ZZ) -- produce all the subsets
subsets(Sequence,ZZ), see subsets(List,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
toList(BasicList) -- list of elements
toList(Set) -- list of elements
transpose(List) -- transposes a table
unique -- eliminate duplicates from a list
unstack(Net), see unstack -- list the rows of a net
values(HashTable) -- 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
List / RingMap, see VisibleList / Function -- apply a function to elements of a list
RingMap \ List, see VisibleList / Function -- apply a function to elements of a list

Methods that use a list :

List .. List, see .. -- a binary operator, uses include ranges; sequence of consecutive items
List ? List, see ? -- comparison operator
ascii(List) -- ASCII character conversion
basis(InfiniteNumber,List,Ideal), see basis -- basis of all or part of a module or ring
basis(InfiniteNumber,List,Module), see basis -- basis of all or part of a module or ring
basis(InfiniteNumber,List,Ring), see basis -- basis of all or part of a module or ring
basis(List,Ideal), see basis -- basis of all or part of a module or ring
basis(List,InfiniteNumber,Ideal), see basis -- basis of all or part of a module or ring
basis(List,InfiniteNumber,Module), see basis -- basis of all or part of a module or ring
basis(List,InfiniteNumber,Ring), see basis -- basis of all or part of a module or ring
basis(List,List,Ideal), see basis -- basis of all or part of a module or ring
basis(List,List,Module), see basis -- basis of all or part of a module or ring
basis(List,List,Ring), see basis -- basis of all or part of a module or ring
basis(List,Module), see basis -- basis of all or part of a module or ring
basis(List,Ring), see basis -- basis of all or part of a module or ring
basis(List,ZZ,Ideal), see basis -- basis of all or part of a module or ring
basis(List,ZZ,Ring), see basis -- basis of all or part of a module or ring
basis(ZZ,List,Ideal), see basis -- basis of all or part of a module or ring
basis(ZZ,List,Ring), see basis -- basis of all or part of a module or ring
chainComplex(List) -- make a chain complex
columnPermute(MutableMatrix,ZZ,List), see columnPermute -- permute some columns
diagonalMatrix(List), see diagonalMatrix(Ring,List) -- make a diagonal matrix from a list
diagonalMatrix(Ring,List) -- make a diagonal matrix from a list
directSum(List), see directSum -- direct sum of modules or maps
document(List), see document -- package item: documentation node
drop(BasicList,List)
dual(MonomialIdeal,List) -- the Alexander dual
eliminate(List,Ideal), see eliminate
export(List), see export -- package item: export functions
exportMutable(List), see exportMutable -- package item: export writable variables
gcd(List), see gcd -- greatest common divisor
gcdLLL(List), see gcdLLL -- compute the gcd of integers, and small multipliers
gradedModule(List), see gradedModule -- make a graded module
gradedModuleMap(List), see gradedModuleMap -- make a map of graded modules
hashTable(List), see hashTable -- make a hash table
HeaderType List -- missing documentation
hilbertFunction(List,Ideal) -- compute the Hilbert function of the quotient of the ambient ring by an ideal
hilbertFunction(List,Module) -- compute the Hilbert function of a module
hilbertFunction(List,ProjectiveVariety) -- compute the Hilbert function of a projective variety
hilbertFunction(List,Ring) -- compute the Hilbert function of a ring
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
hypertext(List), see hypertext -- prepare hypertext for display
Ideal _ List -- missing documentation
ideal(List) -- make an ideal
intersect(List), see intersect -- compute an intersection
List >> Function -- attaching options to a function
listSymbols(List), see listSymbols -- compact display of symbols and their values
makePackageIndex(List), see makePackageIndex
map(Module,Module,List) -- create a matrix by giving a sparse or dense list of entries
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
Matrix ^ List -- select rows
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
max(List), see max -- maximum of elements of a list
memoize(Function,List), see memoize -- record results of function evaluation for future use
min(List), see min -- minimum of elements of a list
Module / List, see Module / Module -- quotient module
Module ^ List -- projection onto summand
Module _ List -- missing documentation
monomialIdeal(List), see monomialIdeal(Matrix) -- monomial ideal of lead terms
mutableMatrix(List), see mutableMatrix -- make a mutable matrix
netTable(List) -- a table of boxes
new BR from List -- missing documentation
new DocumentTag from List -- missing documentation
new HashTable from List -- make a hash table from a list
new HR from List -- missing documentation
new HREF from List -- missing documentation
new MarkUpType from List -- missing documentation
new Module from List -- missing documentation
new TO from List -- missing documentation
new TO2 from List -- missing documentation
new TOH from List -- missing documentation
ofClass(List), see ofClass -- English phrases for types
part(List,RingElement), see part -- sum of monomials of a polynomial of a given degree
plethysm(List,RingElement) -- missing documentation
product(List) -- product of elements
random(List,Ring) -- a random ring element of a given degree
Ring / List, see Ring / Ideal -- make a quotient ring
Ring ^ List -- make a free module
Ring _ List -- make a monomial from a list of exponents
rowPermute(MutableMatrix,ZZ,List), see rowPermute -- permute some rows
rsort(List), see rsort -- sort a list or matrix in reverse order
Set - List, see Set - Set -- set difference
SheafOfRings ^ List -- make a graded free coherent sheaf
sort(List) -- sort a list
standardPairs(MonomialIdeal,List), see standardPairs -- find the standard pairs of a monomial ideal
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
take(BasicList,List)
TEST(List), see TEST -- package item: register a test of the package
truncate(List,Ideal), see truncate -- truncate the module at a specified degree
truncate(List,Module), see truncate -- truncate the module at a specified degree
undocumented(List), see undocumented
unique(List), see unique -- eliminate duplicates from a list
vars(List) -- a sequence of variables
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 -- missing documentation

Fixed objects of class List :

commandLine -- the command line arguments
environment -- the environment variables

For the programmer

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