Symbol -- the class of all symbols

Description

Symbols are entered as an alphabetic character followed by a sequence of alphanumeric characters; case is significant. The single symbol character ' is regarded as alphabetic, so that symbols such as x' may be used.

Symbols are used as names for values to be preserved, as indeterminates in polynomial rings, and as keys in hash tables. They may have global scope, meaning they are visible from every line of code, or local scope, with visibility restricted to a single file or function body.

i1 : x

o1 = x

o1 : Symbol

i2 : ab12

o2 = ab12

o2 : Symbol

Types of symbol :

Keyword -- the class of all keywords

Functions and methods returning a symbol :

global -- get a global symbol
local -- get a local symbol
symbol -- get a symbol

Methods that use a symbol :

Symbol == Symbol -- see == -- equality
Symbol ? IndexedVariable -- see ? -- comparison operator
? Symbol -- view brief documentation of a symbol
about(Symbol) -- see about -- search the documentation
addHook(Symbol,Function) -- see addHook -- add a hook function to an object for later processing
autoload(Symbol,String) -- see autoload -- arrange for a function to be loaded automatically
baseName(Symbol) -- see baseName -- the base name of a generator
code(Symbol) -- see code -- display source code
concatenate(Symbol) -- see concatenate -- join strings
dictionary(Symbol) -- see dictionary -- determine the dictionary to which a symbol belongs
File << Symbol -- see File << Thing -- print to a file
findSynonyms(Symbol) -- find synonyms of symbols
frames(Symbol) -- see frames -- get the frames associated to a closure
help(Symbol) -- see help -- view documentation nodes
hooks(Symbol) -- see hooks -- list hooks attached to a key
installAssignmentMethod(Symbol,HashTable,Function) -- see installAssignmentMethod -- install methods assignment to the value of an operator
installAssignmentMethod(Symbol,HashTable,HashTable,Function) -- see installAssignmentMethod -- install methods assignment to the value of an operator
installAssignmentMethod(Symbol,HashTable,HashTable,Option) -- see installAssignmentMethod -- install methods assignment to the value of an operator
installAssignmentMethod(Symbol,HashTable,Option) -- see installAssignmentMethod -- install methods assignment to the value of an operator
localDictionaries(Symbol) -- see localDictionaries -- get local dictionaries
locate(Symbol) -- see locate -- locate source code
methods(Symbol) -- see methods -- list methods
package(Symbol) -- see package -- get containing package
runHooks(Symbol,Thing) -- see runHooks -- run the hook functions stored in an object
Symbol .. Symbol -- sequences of consecutive symbols
Symbol ..< Symbol -- sequences of consecutive symbols
Symbol _ Ring -- get a ring variable by name
Symbol _ Thing -- index variable
Symbol _ Thing = Thing -- assignment to an indexed variable
value(Symbol) -- retrieve the value of a symbol

Fixed objects of class Symbol :

! -- factorial
!= -- inequality
# -- length or access to elements
#? -- check existence of value in a list, hash table, database, or string
% -- a binary operator, usually used for remainder and reduction
%= -- augmented assignment for %
& -- a binary operator
&= -- augmented assignment for &
(*) -- 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
**= -- augmented assignment for **
*= -- augmented assignment for *
+ -- a unary or binary operator, usually used for addition
++ -- a binary operator, usually used for direct sum
++= -- augmented assignment for ++
+= -- augmented assignment for +
, -- the comma, used for separating entries in a list or sequence
- -- a unary or binary operator, usually used for negation or subtraction
-= -- augmented assignment for -
-> -- 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
..<= -- augmented assignment for ..<
..= -- augmented assignment for ..
.? -- check for presence of elements whose key is a symbol
/ -- a binary operator, usually used for division
// -- a binary operator, usually used for quotient
//= -- augmented assignment for //
/= -- augmented assignment for /
: -- a binary operator, uses include repetition; ideal quotients
:= -- assignment of method or new local variable
; -- expression separator
< -- less than
<- -- assignment with left side evaluated
<< -- a binary operator (file output, ...)
<<= -- augmented assignment for <<
<= -- less than or equal
<== -- a unary and binary operator
<=== -- a unary and binary operator
<==> -- a binary operator
<==>= -- augmented assignment for <==>
= -- assignment
=!= -- strict inequality
== -- equality
===> -- a binary operator
===>= -- augmented assignment for ===>
==> -- a binary operator
==>= -- augmented assignment for ==>
=> -- produce an Option
> -- greater than
>= -- greater than or equal
>> -- a binary operator, uses include bit shifting, or attaching optional inputs to functions
>>= -- augmented assignment for >>
? -- comparison operator
?? -- null coalescing operator
??= -- augmented assignment for ??
@ -- a binary operator
@= -- augmented assignment for @
@@ -- a binary operator
@@= -- augmented assignment for @@
\ -- a binary operator
\= -- augmented assignment for \
\\ -- a binary operator
\\= -- augmented assignment for \\
^ -- 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
^**= -- augmented assignment for ^**
^= -- augmented assignment for ^
^^ -- logical exclusive-or
^^= -- augmented assignment for ^^
_ -- a binary operator, used for subscripting and access to elements
_* -- a unary postfix operator, used for indicating pushforward maps
_= -- augmented assignment for _
| -- a binary operator, often used for horizontal concatenation
|- -- a binary operator
|-= -- augmented assignment for |-
|= -- augmented assignment for |
|| -- a binary operator, often used for vertical concatenation
||= -- augmented assignment for ||
~ -- a unary postfix operator
Acknowledgement -- acknowledgements listed in a documentation node
AdditionalPaths -- list of non-standard paths to search for a program
AfterEval -- top level method applied after evaluation
AfterNoPrint -- top level method applied after not printing
AfterPrint -- top level method applied after printing
Algorithm -- an optional argument
Alignment -- an optional argument
AllCodimensions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
and -- conjunction
argument -- specify the function in a scripted functor for an argument
Ascending -- specify ascending order
Authors -- an optional argument
AuxiliaryFiles -- an optional argument
Bareiss
Base
BaseFunction -- the basename of a function in a documentation node
baseRings -- store the list of base rings of a ring
BaseRow -- an optional argument
BasisElementLimit -- an optional argument
Bayer -- value of an optional argument
BeforePrint -- top level method applied before printing results
Binomial -- value of an optional argument
BKZ -- compute BKZ reduced basis instead of an LLL reduced basis
Body -- an optional argument
Boxes -- an optional argument
break -- break from a loop
cache -- a key under which to store cache tables
CacheExampleOutput -- an optional argument
catch -- catch a thrown exception
Caveat -- warnings or limitations listed in a documentation node
Center -- value of an optional argument
Certification -- an optional argument
ChangeMatrix -- an optional argument
CheckDocumentation -- an optional argument
ClosestFit -- an optional argument
CodimensionLimit -- an optional argument
CoefficientRing -- an optional argument
Cofactor
CohenEngine -- use the original Macaulay2 LLL algorithm
CohenTopLevel -- use the Macaulay2 language LLL algorithm
Complement -- a Strategy option value
CompleteIntersection -- value of an optional argument
ConductorElement -- Specifies a particular non-zerodivisor in the conductor.
Configuration -- an optional argument
Consequences -- side-effects of a function in a documentation node
Constants -- an optional argument
continue -- continue with the next iteration of a loop
Contributors -- non-author contributors listed in a documentation node
Date -- an optional argument
dd -- differential in a chain complex
DebuggingMode -- an optional argument
Decompose -- value of an optional argument
Default -- value of an optional argument
Degree -- specify the degree of a map
DegreeGroup -- an optional argument
DegreeLift -- an optional argument
DegreeLimit -- an optional argument
DegreeMap -- an optional argument
DegreeOrder -- sort primarily by degree
DegreeRank -- an optional argument
Degrees -- an optional argument
Dense -- an optional argument
Density -- an optional argument
Descending -- specify descending order
DivideConquer -- an optional argument
DividedPowers -- Option for inverseSystem
do -- loop control
Dynamic
elapsedTime -- time a computation using time elapsed
elapsedTiming -- time a computation using time elapsed
else -- condition testing
end -- stop loading a file
Engine -- specify whether a ring is handled by the engine
ExampleFiles -- data files corresponding to a documentation node
Exclude -- an optional argument
FastNonminimal -- compute a non-minimal graded free resolution
FileName -- an optional argument
FindOne -- find a primitive element
First -- an optional argument
FlatMonoid
FollowLinks -- an optional argument
for -- for loops
fpLLL (missing documentation)
from -- loop control
Homogeneous2 -- see gb -- compute a Gröbner basis
LinearAlgebra -- see gb -- compute a Gröbner basis
Sugarless -- see gb -- compute a Gröbner basis
Toric -- see gb -- compute a Gröbner basis
UseSyzygies -- see gb -- compute a Gröbner basis
GBDegrees -- an optional argument
Generic -- an optional argument
Givens -- use Givens rotations instead of Gram-Schmidt during LLL
GLex -- graded lexicographic ordering
global -- get a global symbol
GlobalAssignHook -- hook for assignment to global variables
GlobalReleaseHook
GlobalSectionLimit (missing documentation)
Gorenstein -- Constructing Gorenstein Rings and Modules
GRevLex -- graded reverse lexicographical monomial order.
GroupLex -- defines a ring where some variables are inverted
GroupRevLex
HardDegreeLimit -- compute only up to this degree
Headline -- headline of a documentation node
Heft -- an optional argument
Height -- an optional argument
Hermite (missing documentation)
Hermitian -- an optional argument
Hilbert -- an optional argument
Homogeneous -- a Strategy option value
HorizontalSpace -- an optional argument
if -- condition testing
IgnoreExampleErrors -- an optional argument
in -- a keyword used in for-loops
incomparable -- a result indicating incomparability
Index -- Optional input for idealizer
indexComponents -- specify keys for components of a direct sum
InfoDirSection -- an optional argument
Inhomogeneous -- a Strategy option value
Inputs -- inputs for a function in a documentation node
InstallPrefix -- an optional argument
Intersection -- value of an optional argument
InverseMethod -- compute reciprocals
Inverses -- an optional argument
Invertible -- an optional argument
Iterate -- value of an optional argument
Jacobian
Join -- an optional argument
Jupyter -- top level printing method used in the Jupyter kernel
Keep -- an optional argument for various functions
KeepFiles -- whether to keep temporary files
KeepZeroes -- an optional argument
Key -- key of a documentation node
Keywords -- an optional argument
Left -- value of an optional argument
LengthLimit -- stop when the resolution reaches this length
Lex -- lexicographical monomial order.
Limit -- an optional argument
Linear -- value of an optional argument
list -- loop control
LoadDocumentation -- an optional argument
Local -- an optional argument
local -- get a local symbol
LongPolynomial -- a Strategy option value
MakeDocumentation -- an optional argument
MakeHTML -- an optional argument
MakeInfo -- an optional argument
MakeLinks -- an optional argument
MakePDF -- an optional argument
MaximalRank -- an optional argument
MaxReductionCount -- an optional argument
Dispatch -- see method -- make a new method function
TypicalValue -- see method -- make a new method function
MinimalGenerators -- whether to compute minimal generators and return a trimmed set of generators
MinimalMatrix -- an optional argument
minimalPresentationMap -- see minimalPresentation(Ring) -- compute a minimal presentation of a quotient ring
minimalPresentationMapInv -- see minimalPresentation(Ring) -- compute a minimal presentation of a quotient ring
Tries -- see minimalReduction(...,Tries=>...) -- Set the number of random tries to compute a minimal reduction
Minimize -- an optional argument
MinimumVersion -- the minimum required version of a program
WeylAlgebra -- see monoid(...,WeylAlgebra=>...) -- specify differential operators in the ring
Monomial -- value of an optional argument
Down -- see MonomialOrder -- monomial ordering
Global -- see MonomialOrder -- monomial ordering
MonomialOrder -- monomial ordering
Position -- see MonomialOrder -- monomial ordering
Up -- see MonomialOrder -- monomial ordering
Monomials -- whether to display the number of monomial
MonomialSize -- an optional argument
NCLex -- Non-commutative lexicographical order.
new -- new objects and new types
NewFromMethod
NewMethod
NewOfFromMethod
NewOfMethod
Email -- see newPackage -- the preamble of a package
HomePage -- see newPackage -- the preamble of a package
Name -- see newPackage -- the preamble of a package
NoPrint -- top level method for non-printing results
not -- negation
NTL -- use the all-integer LLL strategy from NTL library
of -- a keyword
CallLimit -- see on -- trace a function each time it's run
GenerateAssertions -- see on -- trace a function each time it's run
Binary -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
Flexible -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
Postfix -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
Prefix -- see operatorAttributes -- a hashtable with information about Macaulay2 operators
OptionalComponentsPresent -- an optional argument
Options -- an optional argument
or -- disjunction
Order -- specify the order of a Hilbert series required
order -- a key used internally
Outputs -- outputs for a function in a documentation node
PackageExports -- an optional argument
PackageImports -- an optional argument
PairLimit -- an optional argument
PairsRemaining -- whether to display the number of S-pairs remaining
ParallelF4 (missing documentation)
ParallelizeByDegree -- see parallelism in engine computations -- parallelism in engine computations
PlaneCurveSingularities -- Using the Rees Algebra to resolve plane curve singularities
Precision -- name of an optional argument.
Increment -- see primaryComponent -- find a primary component corresponding to an associated prime
PrimitiveElement -- specify a primitive element
Print -- top level method for printing results
Projective -- whether to produce a projective Hilbert polynomial
Prune -- value of an optional argument
pruningMap
pullbackMaps (missing documentation)
pushoutMaps (missing documentation)
Quotient -- value of an optional argument
Radical -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
RadicalCodim1 -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
RaiseError -- whether to raise an error
Range -- can be assigned a integral interval
RealFP -- use double precision real numbers
RealQP -- use quadruple precision real numbers
RealQP1 -- use a combination of double precision and quad precision real numbers
RealRR -- use arbitrary precision real numbers
RealXD -- use extended exponent real numbers
Reduce -- an optional argument
References -- references listed in a documentation node
POSIX -- see regex -- evaluate a regular expression search
Reload -- an optional argument
RemakeAllDocumentation -- an optional argument
RerunExamples -- an optional argument
Result -- an optional argument
return -- return from a function
returnCode
Reverse -- an optional argument
RevLex -- reverse lexicographic ordering
Right -- value of an optional argument
RunDirectory -- the directory from which to run a program
RunExamples -- an optional argument
SaturationMap (missing documentation)
SeeAlso -- cross-references to other documentation nodes
SeparateExec -- an optional argument
shield -- shield evaluation from interrupts
SimplifyFractions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
SizeLimit -- an optional argument
SkewCommutative -- an optional argument
Sort -- a Strategy option value
SortStrategy -- specify a strategy for sorting S-pairs
SourceCode -- sources displayed in a documentation node
SourceRing -- an optional argument
SPACE -- blank operator; often used for function application, making polynomial rings
Standard -- the standard top level printing method
StartWithOneMinor -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
step -- step by single lines in the debugger
StopBeforeComputation -- an optional argument
StopIteration -- stop iteration
StopWithMinimalGenerators -- an optional argument
EisenbudHunekeVasconcelos -- see strategies for computing primary decomposition
GTZ -- see strategies for computing primary decomposition
ShimoyamaYokoyama -- see strategies for computing primary decomposition
Strategy -- an optional argument
Strict -- Forces strict equality of degrees
Subnodes -- a menu of documentation nodes
SubringLimit -- stop after finding enough elements of a subring
subscript -- specify the function in a scripted functor for a subscript
superscript -- specify the function in a scripted functor for a superscript
symbol -- get a symbol
Heading -- see SYNOPSIS -- a standardized synopsis for use in documentation nodes
Syzygies -- an optional argument
SyzygyLimit -- an optional argument
SyzygyMatrix -- an optional argument
SyzygyRows -- an optional argument
Test -- value of an optional argument
TeXmacs -- the TeXmacs top level printing method
then -- condition testing
=== -- see Thing === Thing -- strict equality
threadVariable -- create a symbol whose value in one thread is not shared with others
Threshold -- the LLL threshold, in interval (1/4,1]
throw -- throw an exception
time -- time a computation
timing -- time a computation
to -- loop control
Torsion -- value of an optional argument
TorsionFree (missing documentation)
TotalPairs -- whether to display the total number of S-pairs
Trim -- Choose whether to trim (or find minimal generators) for the ideal or module.
Truncate -- an optional argument
try -- catch an error
Undo -- an optional argument
Unique -- do not return repeated polynomial roots
Unmixed -- value of an optional argument
UpdateOnly -- only copies of newer files should replace files
UpperTriangular -- an optional argument
Usage -- ways to use a function in a documentation node
UseCachedExampleOutput -- an optional argument
UseHilbertFunction -- an optional argument
UserMode -- an optional argument
Variable -- specify a name for a variable
VariableBaseName -- an optional argument
Variables -- an optional argument
Vasconcelos -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
Verbose -- request verbose feedback
Verbosity -- an optional argument
Verify -- an optional argument
Version -- an optional argument
VerticalSpace -- an optional argument
WebApp -- the web app top level printing method
Weights -- assigning weights to the variables
when -- a keyword
while -- while loops
Wrap -- a key for methods for wrapping printed output
xor -- exclusive disjunction

For the programmer

The object Symbol is a type, with ancestor class Thing.