Macaulay2Doc : Table of Contents
Macaulay2Doc -- Macaulay2 documentation-
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rings-
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monoid -- make or retrieve a monoid
monomial orderings-
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GRevLex -- graded reverse lexicographical monomial order.
Lex -- lexicographical monomial order.
GLex -- graded lexicographic ordering
Weights -- assigning weights to the variables
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GroupLex -- defines a ring where some variables are inverted
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RevLex -- reverse lexicographic ordering
NCLex -- Non-commutative lexicographical order.
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modules-
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basis -- basis or generating set of all or part of a ring, ideal or module
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The Macaulay2 language-
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strings and nets/// -- delineate a string with slashes
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format -- format a string or a real number
lines -- split a string into lines
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stack -- join nets or string vertically
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String -- the class of all strings
Net -- the class of all nets and strings
lists and sequences-
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first -- first element of a list
last -- last element of a list
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unsequence -- extract the single element from a sequence of length 1
append -- append an element to a list
between -- insert something between elements of a list
delete -- delete elements of a list
drop -- drop some elements from a list or sequence
flatten -- flatten a list by unnesting lists
fold -- apply binary operator repeatedly
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mingle -- mingle elements of several lists
pack -- pack elements of a list into shorter ones
prepend -- add an element to the beginning of a list
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rsort -- sort a list or matrix in reverse order
sort -- sort a list or columns of a matrix
subtable -- extract a subtable from a table
table -- make a table (nested list)
take -- take some elements from a list
unique -- eliminate duplicates from a list
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position -- find first element of a list satisfying a condition
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VisibleList -- the class of all visible listsList -- the class of all lists -- {...}
Sequence -- the class of all sequences -- (...)
Array -- the class of all arrays -- [...]
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hash tables-
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keys -- keys used in a hash table
values -- values in a hash table
pairs -- list the pairs in a hash table, dictionary, or basic list
mutable -- whether something may be modified
remove -- remove an entry from a hash table
applyKeys -- apply a function to each key in a hash table
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applyPairs -- apply a function to each pair in a hash table
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operators-
:= -- assignment of method or new local variable
<- -- assignment with left side evaluated
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>= -- greater than or equal
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SPACE -- blank operator; often used for function application, making polynomial rings
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_ -- a binary operator, used for subscripting and access to elements
. -- access to elements whose key is a symbol
.? -- check for presence of elements whose key is a symbol
# -- length, or access to elements
#? -- check for presence of elements
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+ -- a unary or binary operator, usually used for addition
- -- a unary or binary operator, usually used for negation or subtraction
* -- a binary operator, usually used for multiplication
/ -- a binary operator, usually used for division
// -- a binary operator, usually used for quotient
% -- a binary operator, usually used for remainder and reduction
^ -- a binary operator, usually used for powers
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++ -- a binary operator, usually used for direct sum
** -- a binary operator, usually used for tensor product or Cartesian product
^** -- a binary operator, usually used for tensor or Cartesian power
~ -- a unary postfix operator
(*) -- a unary postfix operator, used for indicating a graded object
: -- a binary operator, uses include repetition; ideal quotients
.. -- a binary operator, used for sequences of consecutive items
..< -- a binary operator, used for sequences of consecutive items, not including the endpoint
<< -- a binary operator (file output, ...)
>> -- a binary operator, uses include bit shifting, or attaching optional inputs to functions
| -- a binary operator, often used for horizontal concatenation
|| -- a binary operator, often used for vertical concatenation
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<==> -- a binary operator
===> -- a binary operator
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<=== -- a unary and binary operator
<== -- a unary and binary operator
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, -- the comma, used for separating entries in a list or sequence
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catch -- catch a thrown exception
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new -- new objects and new typesnewClass -- set the class and parent of an object
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file manipulation -- Unix file manipulation functions-
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fileTime -- get or set file modified time
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realpath -- convert a filename to one passing through no symbolic links
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system facilities-
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input -- read Macaulay2 commands and echo
load -- read Macaulay2 commands
needs -- read Macaulay2 commands if necessary
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dumpdata -- dump state of the system to a file
loaddata -- load state of the system from a file
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exec -- execute another program
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getenv -- get value of environment variable
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path -- list of directories to look in
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run -- run an external command
sleep -- sleep for a while
time -- time a computation
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wait -- wait for child process
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version -- information about this version of the program
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Type -- the class of all types
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" -- delineate a string with quotation marks
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- List -- negation of a vector
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>= ZZ -- greater than or equal
^* -- a unary postfix operator, used for indicating pullback maps
_* -- a unary postfix operator, used for indicating pushforward maps
abs -- absolute value function
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acosh -- inverse hyperbolic cosine
acot -- compute the inverse cotangent
addHook -- add a hook function to an object for later processing
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Adjacent -- the class of all adjacent expression pairs
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AfterEval -- top level method applied after evaluation
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AfterPrint -- top level method applied after printing
agm -- arithmetic-geometric mean
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all -- whether all elements satisfy a specified condition
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ambient -- ambient free module of a subquotient, or ambient ring
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antipode -- antipode for skew commuting polynomial rings
any -- whether any elements satisfy a specified condition
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apply -- apply a function to each element
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applyTable -- apply a function to elements of a table
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argument -- specify the function in a scripted functor for an argument
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ascii -- ASCII character conversion
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asinh -- inverse hyperbolic sine
assert -- assert something is true
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atan -- compute the arctangent
atan(RR) -- compute the arctangent of a number
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backtrace -- whether a backtrace is displayed following an error message
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Bag -- the class of all bags
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baseName -- the base name of a generator
baseRings -- store the list of base rings of a ring
BaseRow -- name for an optional argument
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Bayer -- a Strategy option value for saturate
BeforePrint -- top level method applied before printing results
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BesselJ -- Bessel function of the first kind
BesselY -- Bessel function of the second kind
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betti(Module) -- show the degrees of the generators and relations of a module or a coherent sheaf
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Binomial -- name for an optional argument
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Boolean -- the class of Boolean values
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Boxes -- name for an optional argument
break -- break from a loop
cache -- a key under which to store cache tables
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cacheValue -- cache values of functions in their arguments
capture(String) -- evaluate Macaulay2 code and capture the output (under development)
CC -- the class of all complex numbers
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Center -- value for an optional argument
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char -- computes the characteristic of the ring or field
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clean -- Set to zero elements that are approximately zero
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code -- display source code
codim -- compute the codimension
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cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
columnAdd -- add a multiple of one column to another
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Command -- the class of all commands
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commonest -- the most common elements of a list or tally
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comodule -- submodule to quotient module
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complement(Matrix) -- find the minimal generators for cokernel of a matrix (low level form)
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compress -- extract nonzero columns from a matrix
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cone -- mapping cone of a chain map
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continue -- continue with the next iteration of a loop
contract -- contract one matrix by another
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copyright -- a string containing the copyright notice for Macaulay2
Core -- the core part of Macaulay2
cos -- compute the cosine
cosh -- compute the hyperbolic cosine
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coth -- hyperbolic cotangent
cover -- get the covering free module
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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
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csch -- hyperbolic cosecant
current -- the pseudocode that produced an error
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Database -- the class of all database files
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dd -- differential in a chain complex
debug -- open private dictionary of a package
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debuggingMode -- whether to enter the debugger when an error occurs
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default -- default member of a family
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Degrees -- name for an optional argument
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demark -- insert a string between elements of a list of strings
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Dense -- name for an optional argument
Density -- name for an optional argument
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dictionary -- determine the dictionary to which a symbol belongs
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diff -- differentiate or take difference
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dim -- compute the Krull dimension
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Divide -- the class of all divide expressions
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dual -- dual module or map
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eint -- exponential integral
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else -- condition testing
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End -- module of endomorphisms
end -- stop loading a file
endl -- end an output line
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Engine -- specify whether a ring is handled by the engine
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EngineRing -- the class of rings handled by the engine
entries -- lists the entries of a matrix
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Equation -- the class of all equation expressions
erase -- remove a global symbol
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erfc -- complementary error function
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euler -- Euler characteristic
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eulers -- list the sectional Euler characteristics
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even -- tell whether an integer is even
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examples -- list the examples in documentation
Exclude -- name for an optional argument
exp -- exponential function
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expm1 -- exponential minus 1
exponents -- list the exponents in a polynomial
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Ext -- compute an Ext module
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extend -- extend a module map to a chain map, if possible
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factor -- factor a ring element or a ZZ-module
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File -- the class of all files
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fileExitHooks -- a list of hooks (functions) to execute when the current file has been loaded
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FileName -- name for an optional argument
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fillMatrix -- fill a mutable matrix with random numbers
findHeft -- find a heft vector for a list of degrees
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FindOne -- find a primitive element
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First -- name for an optional argument
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flattenRing -- write a ring as a (quotient) of a polynomial ring over ZZ or a prime field
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flush -- flush output to file
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forceGB -- declare that the columns of a matrix are a Gröbner basis
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ForestNode -- a type of basic list used to represent a forest, i.e., a list of rooted trees
Format -- name for an optional argument
frac -- construct a fraction field
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frames -- get the frames associated to a closure
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Function _ Thing -- attach the first argument to a function of two or more arguments
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gb -- compute a Gröbner basis
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gbSnapshot -- the Gröbner basis matrix as so far computed
gbTrace -- provide tracing output during various computations in the engine.
gcd -- greatest common divisor
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genera -- list of the successive linear sectional arithmetic genera
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genera(Ideal) -- list of the successive linear sectional arithmetic genera
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genera(Ring) -- list of the successive linear sectional arithmetic genera
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generators -- provide matrix or list of generators
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Generic -- name for an optional argument
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genus -- arithmetic genus
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get -- get the contents of a file
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getNetFile -- get the sequence of completed lines (nets) from a net file
getNonUnit -- retrieve a previously discovered non-unit
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getSymbol -- make a global user symbol from a string
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GF -- make a finite field
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groupID -- the process group identifier
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hash -- hash code of an object
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HeaderType -- 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
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Height -- name for an optional argument
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HH -- general homology and cohomology functor
hh -- Hodge numbers of a smooth projective variety
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Hilbert -- name for an optional argument
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hold -- hold something in a holder expression
Holder -- the class of all holder expressions
Hom -- module of homomorphisms
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homogenize -- homogenize with respect to a variable
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html -- convert hypertext to html format
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Ideal -- the class of all ideals
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Ideal _* -- get the list of generators of an ideal
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ii -- the square root of -1
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in -- a keyword used in for-loops
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independentSets -- some size-maximal independent subsets of variables modulo an ideal
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index -- numeric index of a ring variable
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indices -- indices of a polynomial; also components for a direct sum
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info -- convert hypertext to info format
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Inverses -- name for an optional argument
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isANumber -- whether a number is not not-a-number
isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
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isField -- whether something is a field
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isIdeal -- whether something is an ideal
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isModule -- whether something is a module
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isOpen -- whether a file or database is open
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isPrime -- whether a integer, polynomial, or ideal is prime
isPrimitive -- whether an element is a primitive element of a finite field
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isReal -- whether a number is real
isRing -- whether something is a ring
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isSquareFree -- whether something is square free monomial ideal
isSubmodule -- whether a module is evidently a submodule of a free module
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isSubset -- whether one object is a subset of another
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isTable -- whether something is a rectangular list of lists
isUnit -- whether a ring element is a unit
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Iterate -- a Strategy option value for saturate
jacobian -- the Jacobian matrix of partial derivatives
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jacobian(Matrix) -- the matrix of partial derivatives of polynomials in a matrix
jacobian(Ring) -- the Jacobian matrix of the polynomials defining a quotient ring
Join -- name for an optional argument
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kernel -- kernel of a ringmap, matrix, or chain complex
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Keyword -- the class of all keywords
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koszul -- Koszul complex or specific matrix in the Koszul complex
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lcm -- least common multiple
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Left -- value for an optional argument
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LengthLimit -- stop when the resolution reaches this length
lift -- lift to another ring
liftable -- whether lifting to another ring is possible
Limit -- name for an optional argument
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Linear -- a Strategy option value for saturate
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List .. List -- rectangular sequences of consecutive lists and sequences
List ..< List -- rectangular sequences of consecutive lists and sequences
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listSymbols -- compact display of symbols and their values
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lngamma -- logarithm of the Gamma function
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Local -- name for an optional argument
local -- get a local symbol
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log -- logarithm function
log1p -- logarithm of 1+x
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MakeInfo -- name for an optional argument
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mathML -- convert to MathML format
Matrix -- the class of all matrices
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Matrix % GroebnerBasis -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis
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matrix(List) -- create a matrix from a doubly-nested list of ring elements or matrices
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matrix(Ring,List) -- create a matrix from a doubly nested list of ring elements or matrices
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max -- maximum of elements of a list
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member -- test membership in a list or set
memoize -- record results of function evaluation for future use
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min -- minimum of elements of a list
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mingens -- minimal generator matrix
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minimalBetti(Ideal) -- minimal betti numbers of (the mininimal free resolution of) a homogeneous ideal or module
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Minimize -- name for an optional argument
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Minus -- the class of all minus expressions
minus -- additive inverse
mod -- reduce modulo an integer
Module -- the class of all modules
module -- make or get a module
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ModuleMap -- the class of all maps between modules
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Monoid -- the class of all monoids
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Monomial -- name for an optional argument
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MonomialIdeal -- the class of all monomial ideals handled by the engine
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Monomials -- whether to display the number of monomial
monomials -- matrix of monomials in a ring element or matrix
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net -- format for printing, as a net
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NetFile -- the class of all net files
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newline -- the new line character sequence
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newRing -- make a copy of a ring, with some features changed
nextkey -- the next key in a database
nextPrime -- compute the smallest prime greater than or equal to a given number
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NoPrint -- top level method for non-printing results
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notify -- whether to notify the user when a file is loaded
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null -- the unique member of the empty class
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Number -- the class of all numbers
number -- count how many elements of a list satisfy a condition
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numeric -- convert to floating point
numgens -- the number of generators
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odd -- tell whether an integer is odd
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ofClass -- English phrases for types
on -- trace a function each time it's run
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oo -- the last output value
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ooo -- the next to the last output value
oooo -- the third to the last output value
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Option -- the class of all pairs x => y
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Options -- name for an optional argument
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options(Function) -- get optional arguments and default values for a function that accepts them
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OptionTable -- the class of hash tables for optional arguments
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Order -- specify the order of a Hilbert series required
order -- a key used internally
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override -- override default values for optional arguments
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Package -- the class of all packages
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pad -- pad a string with spaces
pager -- display with paging
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part -- select terms of a polynomial by degree or weight
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Partition -- a type of list representing a partition of a natural number
partition -- partition a set or list by values of a function
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pdim -- calculate the projective dimension
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pdim(Module) -- calculate the projective dimension of a module
peek -- examine contents of an object
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permanents -- ideal generated by square permanents of a matrix
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poincare -- assemble degrees into polynomial
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poincare(Ideal) -- assemble degrees of the quotient of the ambient ring by an ideal into a polynomial
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poincareN -- assemble degrees into polynomial
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Power -- the class of all power expressions
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prefixPath -- absolute locations of Macaulay2 files
preimage -- preimage of an ideal under a ring map
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PrimaryTag -- for internal use only: a symbol used in storing documentation
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Print -- top level method for printing results
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printingLeadLimit -- maximum number of leading zeroes to use when printing real numbers
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printingSeparator -- string used to separate mantissa from exponent when printing real numbers
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printingTrailLimit -- maximum number of additional trailing digits to use when printing real numbers
printString -- lowlevel function to print a string, net, or symbol
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Product -- the class of all product expressions
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Projective -- whether to produce a projective Hilbert polynomial
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prune -- prune, e.g., compute a minimal presentation
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pseudocode -- produce the pseudocode for a function
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QQ -- the class of all rational numbers
Quotient -- value for an optional argument
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random -- get a random element
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Range -- can be assigned a integral interval
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Reduce -- name for an optional argument
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registerFinalizer -- register a string that will be displayed when an object is garbage collected
regularity -- compute the Castelnuovo-Mumford regularity
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Reload -- name for an optional argument
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remainder' -- matrix quotient and remainder (opposite)
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removeHook -- remove a hook function from an object
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Resolution -- the class of all resolution computations
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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
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Result -- name for an optional argument
return -- return from a function
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Reverse -- name for an optional argument
Right -- value for an optional argument
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Ring -- the class of all rings
ring -- get the associated ring of an object
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Ring _ List -- make a monomial from a list of exponents
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Ring Array -- the standard way to make a polynomial ring
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RingElement -- the class of all ring elements handled by the engine
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RingFamily _* -- a unary postfix operator, used for indicating pushforward maps
RingMap -- the class of all ring maps
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rowAdd -- add a multiple of one row to another
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rowMult -- multiply a row by a ring element
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RR -- the class of all real numbers
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runHooks -- run the hook functions stored in an object
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same -- whether everything in a list is the same
saturate -- saturation of ideal or submodule
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scan -- apply a function to each element
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scanKeys -- apply a function to each key in a hash table or database
scanLines -- apply a function to each line of a file
scanPairs -- apply a function to pairs in a hash table
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scanValues -- apply a function to each value in a hash table
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
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sech -- hyperbolic secant
seeParsing -- display parsing precedence table for Macaulay2 operators
select -- select from a list, hash table, or string
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separateRegexp -- separate a string into pieces, with separators determined by a regular expression
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serialNumber -- serial number of a dictionary, task, symbol, mutable hash table, or mutable list,
Set -- the class of all sets
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sheaf -- make a coherent sheaf
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shield -- shield evaluation from interrupts
show -- display various TeX, hypertext, or a URL, in an external application
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showHtml -- convert hypertext to html and display with a browser
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showTex -- convert to TeX and display on screen
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sinh -- compute the hyperbolic sine
size -- the size of an object
size2 -- number of binary digits to the left of the point
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solve -- solve linear equation(s)
someTerms -- select some terms of a polynomial
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splitWWW -- separate an http response into header and body
sqrt -- square root function
Standard -- the standard top level printing method
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stashValue -- stash values of functions in their arguments
status -- status of a resolution computation
stderr -- the standard error output file
stdio -- the standard input output file
step -- step by single lines in the debugger
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stopIfError -- whether to stop the program when an error occurs
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Strategy -- name for an optional argument
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sublists -- process interspersed sublists of a list
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submatrix' -- exclude rows and/or columns of a matrix
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submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
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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
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Sum -- the class of all sum expressions
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super -- get the ambient module
Superscript -- the class of all superscript expressions
superscript -- specify the function in a scripted functor for a superscript
support -- list of variables occurring in a polynomial or matrix
support(Ideal) -- list of variables occurring in the generators of an ideal
SVD -- singular value decomposition of a matrix
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Symbol -- the class of all symbols
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synonym -- synonym for members of a class
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Syzygies -- name for an optional argument
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Table -- the class of all table expressions
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Tally -- the class of all tally results
tally -- tally the elements of a list or sequence
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tan -- compute the tangent
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tanh -- compute the hyperbolic tangent
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terms -- provide a list of terms of a polynomial
tex -- convert to TeX format
TeXmacs -- the TeXmacs top level printing method
texMath -- convert to TeX math format
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then -- condition testing
Thing -- the class of all things
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throw -- throw an exception
Time -- the class of all timing results
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toCC -- convert to high-precision complex number
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topCoefficients -- first variable and its coefficient of a polynomial or matrix
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toRR -- convert to high-precision real number
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TotalPairs -- whether to display the total number of S-pairs
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TreeNode -- a type of basic list used to represent a rooted tree
trim -- minimize generators and relations
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truncate -- truncate the module at a specified degree
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tutorial -- convert documentation from tutorial format
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ultimate -- ultimate value for an iteration
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Undo -- name for an optional argument
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uniform -- test whether elements of a list are of the same class
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Unique -- do not return repeated polynomial roots
Unmixed -- name for an optional argument
UpdateOnly -- only copies of newer files should replace files
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URL -- a type representing a URL
Usage -- shows the usage of a function
use -- install or activate object
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use(Ring) -- install ring variables and ring operations
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UserMode -- name for an optional argument
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utf8 -- encode and decode unicode utf-8-encoded strings
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Variable -- specify a name for a variable
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variety(Ideal) -- the closed projective subvariety defined by an ideal
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Vector -- the class of all elements of free modules that are handled by the engine
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Verbose -- request verbose feedback
Verify -- verify that a map is well-defined
VerticalList -- a type of visible self-initializing list that prints vertically
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viewHelp -- view online doc with a web browser
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weightRange -- the pair of lowest and highest weights of the monomials
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width -- width of a file or net
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Wrap -- a key for methods for wrapping printed output
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WrapperType -- a class of lists with abbreviated constructors
xor -- logical exclusive-or
youngest -- the youngest member of a sequence
zero -- whether something is zero
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zeta -- Riemann zeta function
ZZ -- the class of all integers
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ZZ .. ZZ -- sequences of consecutive integers
ZZ ..< ZZ -- sequences of consecutive integers
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