master index
"()"
"--"
"-infinity"
"///"
"Canonical Embeddings of Plane Curves and Gonality"
"Daniel R. Grayson"
"David Eisenbud"
"Divisors"
"Elementary uses of Groebner bases"
"Factorization and characteristic sets library"
"Factory library"
"Fano varieties"
"GC garbage collector"
"GNU MP"
"Groebner bases"
"Homological Algebra 2"
"MP: Multi Protocol"
"Macaulay 2"
"Michael E. Stillman"
"String # ZZ"
"Weyl algebras"
"[]"
"acknowledgements"
"algebraic varieties"
"apply(Set,Function)"
"apply(Tally,Function)"
"arithmetic functions"
"assignment"
"associative algebras"
"bases of parts of modules"
"basic rings"
"binary method"
"classes"
"coherent sheaves"
"combinatorial functions"
"comparison"
"component example"
"copyright and license"
"debugging"
"editing Macaulay 2 code with emacs"
"emacs"
"enclosed"
"engine communication protocol"
"engine"
"executing other programs"
"exterior algebras"
"extracting information from chain complexes"
"finite fields"
"fraction fields"
"free modules"
"free resolutions of modules"
"functions"
"getting started"
"hashing"
"help functions"
"high level gb engine commands"
"how to get this program"
"hypertext"
"ideals"
"indeterminates"
"initialization file"
"internals"
"invoking the program"
"lists, arrays, and sequences"
"low level gb engine commands"
"making chain complexes by hand"
"making generic matrices"
"making matrices"
"making module maps"
"making modules from matrices"
"making random matrices"
"making ring maps"
"manipulating chain complexes"
"manipulating matrices"
"manipulating modules"
"manipulating polynomials"
"maps between chain complexes"
"maps between modules"
"maps between rings"
"mathematical overview"
"mathematics"
"multi-graded polynomial rings"
"not documented yet"
"numbers"
"obsolete functions and symbols"
"operators"
"plans for the future"
"polynomial rings with other monomial orderings"
"polynomial rings"
"programming overview"
"programming"
"quotient rings"
"reading the documentation"
"resources required"
"running Macaulay 2 in emacs"
"subclass"
"symmetric algebras"
"syntax"
"system"
"tensor products of rings"
"the authors"
"top level loop"
"top-method"
"transcendental functions"
"translating programs from Macaulay"
"transmitting a matrix"
"transmitting a monomial"
"transmitting a polynomial"
"transmitting a positive integer"
"transmitting a sequence"
"transmitting a vector"
"transmitting an integer mod n"
"transmitting an integer"
"using methods"
"{}"
(Hom,ChainComplex,Module)
(NewFromMethod,HashTable,List)
(NewMethod,ChainComplex)
(chainComplex,Matrix)
(chainComplex,Sequence)
(codim,CoherentSheaf)
(cohomology,ZZ,ChainComplex)
(cohomology,ZZ,ChainComplexMap)
(cohomology,ZZ,CoherentSheaf)
(cohomology,ZZ,Module)
(complete,ChainComplex)
(components,ChainComplex)
(cotangentSheaf,ProjectiveVariety)
(cotangentSheaf,ZZ,ProjectiveVariety)
(degrees,CoherentSheaf)
(dual,ChainComplex)
(dual,Matrix)
(dual,Module)
(exteriorPower,ZZ,CoherentSheaf)
(homology,ChainComplex)
(homology,Matrix,Matrix)
(homology,ZZ,ChainComplex)
(homology,ZZ,ChainComplexMap)
(isSubset,Set,Set)
(length,ChainComplex)
(map,Matrix)
(map,Module)
(map,Module,Matrix)
(map,Module,Module)
(map,Module,Module,Function)
(map,Module,Module,List)
(map,Module,Module,Matrix)
(map,Module,Module,RingElement)
(map,Module,Nothing,List)
(map,Module,RingElement)
(map,Module,ZZ,Function)
(map,Module,ZZ,List)
(matrix,List)
(matrix,Matrix)
(matrix,Ring,List)
(module,CoherentSheaf)
(product,List)
(product,List,Function)
(product,List,List,Function)
(product,Set)
(product,Tally)
(product,ZZ,Function)
(quote " ",ChainComplex,Array)
(quote " ",CoherentSheaf,ZZ)
(quote " ",ProjectiveHilbertPolynomial,ZZ)
(quote " ",Ring,OrderedMonoid)
(quote %,Matrix,Matrix)
(quote %,Matrix,RingElement)
(quote &,ZZ,ZZ)
(quote **,CoherentSheaf,CoherentSheaf)
(quote **,Matrix,Matrix)
(quote **,Matrix,Module)
(quote **,Matrix,Ring)
(quote **,Module,Module)
(quote **,Module,Ring)
(quote **,Monoid,Monoid)
(quote **,Ring,Ring)
(quote **,Set,Set)
(quote **,Tally,Tally)
(quote *,Ideal,Ideal)
(quote *,Set,Set)
(quote ++,ChainComplex,ChainComplex)
(quote ++,CoherentSheaf,CoherentSheaf)
(quote ++,Matrix,Matrix)
(quote ++,Module,Module)
(quote ++,Set,Set)
(quote +,Ideal,Ideal)
(quote +,List,List)
(quote +,Module,Module)
(quote +,Set,Set)
(quote +,Tally,Tally)
(quote -,Set,Set)
(quote -,Tally,Tally)
(quote /,CoherentSheaf,CoherentSheaf)
(quote /,Ideal,Ideal)
(quote /,List,Function)
(quote /,Module,Ideal)
(quote /,Module,Module)
(quote /,Ring,Ideal)
(quote //,Matrix,Matrix)
(quote //,Matrix,RingElement)
(quote /^,Thing,ZZ)
(quote :,Module,Module)
(quote :,ZZ,Thing)
(quote <<,File,Thing)
(quote <<,Nothing,Thing)
(quote <<,String,Thing)
(quote <<,Thing)
(quote <<,ZZ,ZZ)
(quote ==,Module,Module)
(quote =>,Thing,Thing)
(quote >>,ZZ,ZZ)
(quote ?,Tally,Tally)
(quote \,Function,List)
(quote ^,Ideal,ZZ)
(quote ^,Matrix,Array)
(quote ^,Matrix,List)
(quote ^,Module,Array)
(quote ^,Module,List)
(quote ^,Net,ZZ)
(quote ^,Ring,List)
(quote ^,Ring,ZZ)
(quote _,ChainComplex,ZZ)
(quote _,ChainComplexMap,ZZ)
(quote _,List,List)
(quote _,List,ZZ)
(quote _,Matrix,Array)
(quote _,Matrix,List)
(quote _,Matrix,Sequence)
(quote _,Matrix,ZZ)
(quote _,Module,Array)
(quote _,Module,List)
(quote _,Module,ZZ)
(quote _,Monoid,ZZ)
(quote _,Ring,List)
(quote _,Ring,String)
(quote _,Ring,ZZ)
(quote _,RingElement,RingElement)
(quote _,SchurRing,List)
(quote _,Sequence,ZZ)
(quote _,Tally,Thing)
(quote _,Vector,ZZ)
(quote _,ZZ,Monoid)
(quote _,ZZ,Ring)
(quote |,List,List)
(quote |,Matrix,Matrix)
(quote |,String,String)
(quote |,ZZ,ZZ)
(quote ||,Matrix,Matrix)
(quote ||,Net,Net)
(quote ~,Module)
(quote ~,Ring)
(rank,CoherentSheaf)
(resolution,Ideal)
(resolution,Matrix)
(resolution,Module)
(ring,CoherentSheaf)
(sheaf,Module)
(sheaf,Module,Variety)
(sheaf,Ring)
(subsets,List)
(subsets,Set)
(subsets,Set,ZZ)
(subsets,ZZ,ZZ)
(sum,ChainComplex)
(sum,ChainComplexMap)
(sum,List)
(sum,List,Function)
(sum,List,List,Function)
(sum,Set)
(sum,Tally)
(sum,ZZ,Function)
(variety,CoherentSheaf)
Adjacent
AffineVariety
AfterEval
AfterNoPrint
AfterPrint
Algorithm
Array
Ascending
Associative
AssociativeExpression
BIG
BLOCKQUOTE
BODY
BOLD
BR
BasicList
BasisElementLimit
Bayer
BeforePrint
BinaryOperation
BinaryPowerMethod
Boolean
CC
CENTER
CITE
CODE
ChainComplex
ChainComplexMap
ChangeMatrix
CodimensionLimit
CoherentSheaf
Command
CompleteIntersection
ConversionFormat
ConvertApply
ConvertFixedRepeat
ConvertInteger
ConvertJoin
ConvertList
ConvertMissing
ConvertRepeat
ConvertToExpression
DFN
DL
Database
Degree
DegreeLimit
DegreeOrder
Degrees
Descending
Divide
Documentation
DoubleArrow
DownArrow
EM
EXAMPLE
Eliminate
Elimination
EliminationOrder
EmptyMarkUpType
End
Engine
EngineRing
Entity
Equation
ExampleTABLE
Expression
Ext
Fano
Field
File
FindOne
FractionField
Function
FunctionApplication
GBtype
GF
GLex
GRevLex
GaloisField
GeneralOrderedGroup
GeneralOrderedMonoid
GlobalAssignHook
GlobalReleaseHook
GradedModule
GradedModuleMap
Grassmannian
GroebnerBasis
H1
H2
H3
H4
H5
H6
HEAD
HH
HR
HREF
HTML
Handle
HardDegreeLimit
HashTable
HeaderType
Holder
Hom
IMG
ITALIC
Ideal
IndeterminateNumber
IndexedVariable
IndexedVariableTable
InfiniteNumber
InverseMethod
Inverses
Iterate
KBD
LISTING
LengthLimit
Lex
Limit
Linear
List
LongPolynomial
MENU
Manipulator
MarkUpList
MarkUpType
Matrix
MatrixExpression
MinimalGenerators
MinimalMatrix
MinorsComputation
Minus
Module
ModuleMap
Monoid
MonoidElement
MonomialIdeal
MonomialOrder
MonomialSize
Monomials
MutableHashTable
MutableList
NL
NOINDENT
Net
NewFromMethod
NewMethod
NewOfFromMethod
NewOfMethod
NoPrint
NonAssociativeProduct
NonLinear
Nothing
Numeric
OL
OO
OneExpression
Option
OptionTable
Options
OptionsRegistry
Order
OrderedMonoid
PARA
PRE
PairLimit
PairsRemaining
PfaffiansComputation
PolynomialRing
Position
Power
PrimitiveElement
Print
Product
ProductOrder
ProductRing
Proj
Projective
ProjectiveHilbertPolynomial
ProjectiveVariety
PushforwardComputation
PutAnnotationPacket
PutCommonMetaOperatorPacket
PutCommonMetaTypePacket
PutCommonOperatorPacket
PutOperatorPacket
QQ
QuotientRing
RR
Resolution
RevLex
RightArrow
Ring
RingElement
RingMap
RowExpression
SAMP
SEEALSO
SEQ
SHIELD
SMALL
STRONG
SUB
SUP
Schur
SchurRing
ScriptedFunction
ScriptedFunctor
SelfInitializingType
Sequence
Set
SimplePowerMethod
SingleArgumentDispatch
SkewCommutative
Sort
SortStrategy
SparseMonomialVectorExpression
SparseVectorExpression
Spec
StopBeforeComputation
StopWithMinimalGenerators
Strategy
String
SubringLimit
Subscript
Sum
Superscript
Symbol
SymbolTable
Syzygies
SyzygyLimit
SyzygyMatrix
SyzygyRows
TABLE
TEST
TEX
TITLE
TO
TT
Tally
TeX
Thing
Time
Tor
TotalPairs
Type
UL
UNDERLINE
Unmixed
UseHilbertFunction
VAR
Variable
VariableBaseName
VariableOrder
Variables
Variety
Vector
Verify
WeylAlgebra
WrapperType
WritePacket
XMP
ZZ
ZeroExpression
abs
accumulate
acos
addEndFunction
addStartFunction
adjoint
adjoint1
adjust
alarm
all
ambient
ancestor
ann
annihilator
any
append
apply
applyKeys
applyPairs
applyTable
apropos
argument
ascii
asin
assert
assign
atan
autoload
backtrace
baseName
baseRings
basictype
basis
benchmark
betti
between
binomial
borel
browse
buckets
callgg
chainComplex
char
characters
class
clearAll
close
closeLink
code
codim
coefficientRing
coefficients
cohomology
coimage
coker
cokernel
collectGarbage
columnate
combine
commandLine
complement
complete
components
compress
concatenate
cone
conjugate
content
contract
convert
copy
cos
cosh
cotangentSheaf
cover
currentDirectory
dd
decompose
deepSplice
degree
degreeLength
degrees
degreesMonoid
degreesRing
delete
demark
denominator
depth
describe
det
diff
difference
dim
directSum
divideByVariable
doc
document
drop
dual
dumpdata
edit
eeLift
eePop
eePopBool
eePopInt
eePopIntarray
eePromote
elements
endl
engineMemory
engineStack
entries
environment
erase
error
errorDepth
euler
evaluate
even
examine
examples
exec
exit
exp
expand
exponents
expression
extend
exteriorPower
factor
false
first
firstkey
fittingIdeal
flag
flatten
flip
floor
flush
fold
forceGB
forceGB => ChangeMatrix
fork
format
formatDocumentTag
frac
fraction
frame
fromDual
gb
gb => ChangeMatrix
gb => CodimensionLimit
gb => DegreeLimit
gb => PairLimit
gb => StopBeforeComputation
gb => StopWithMinimalGenerators
gb => Strategy
gb => SyzygyLimit
gbTrace
gcd
gcdCoefficients
gcdDegree
genera
generatorSymbols
generators
genericMatrix
genericSkewMatrix
genericSymmetricMatrix
gens
get
getDocumentationTag
getMatrix
getWWW
getc
getchange
getenv
gg
ggGF
ggINT
ggINTARRAY
ggMONOMIAL
ggMOelim
ggMOgeneral
ggMOglex
ggMOgproduct
ggMOgrevlex
ggMOlex
ggMOproduct
ggMOrevlex
ggMOwtfcn
ggPush
ggSTRING
ggZ
ggZn
ggadd
ggaddress
ggautoreduce
ggbetti
ggbinomialGB
ggbinomialGBaddgens
ggbinomialGBenlarge
ggborel
ggcalc
ggcharp
ggcodim
ggcoeffs
ggcompare
ggconcat
ggcontract
ggcopy
ggdegree
ggdenominator
ggderef
ggdets
ggdiff
ggdim
ggdirectsum
ggdiv
ggdivides
ggdivmod
ggdrop
ggdup
ggduplicate
ggelem
ggelim
ggev
ggexterior
ggexteriorproduct
ggfactor
ggfactor1
ggfactor2
ggflip
ggforget
ggfractionfield
ggfree
ggfromint
gggb
gggcd
gggcdextended
gggetchange
gggetcoeff
gggetcols
gggetgb
gggetideal
gggetmingens
gggetring
gggetrows
gggetshift
gggetsubring
gggetsubringGB
gggetsyz
gggetterms
gggetvalue
ggheap
gghermite
gghilb
gghomogenize
gghomogenize1
ggiden
ggindex
gginitial
ggintersect
ggisborel
ggisequal
ggishomogeneous
ggissubset
ggisunit
ggiszero
ggkbasis
ggkbasisIn
ggkbasisOut
ggker
ggkoszul
gglcm
ggleadcoeff
ggleadcomp
ggleadmonom
ggleadterm
gglength
gglift
ggmatrix
ggmem
ggminleadterms
ggmod
ggmodtensor
ggmonideal
ggmonoid
ggmonsyz
ggmult
ggnegate
ggnmonoms
ggnone
ggnumerator
ggpairs
ggpfaffs
ggpick
ggpolyring
ggpop
ggpoppem
ggpower
ggprimes
ggpromote
ggqring
ggquit
ggradical
ggrandom
ggrandomint
ggrandommax
ggrandomseed
ggreceive
ggreduce
ggremaining
ggremote
ggremove
ggres
ggresNmap
ggresNmodule
ggreshape
ggresmap
ggresmodule
ggringmap
ggsagbi
ggsat
ggschur
ggsearch
ggsee
ggselect
ggsend
ggsetshift
ggshift
ggsimplify
ggskeleton
ggsortcolumns
ggsparsevector
ggstack
ggstats
ggsubduction
ggsubmatrix
ggsubmodule
ggsubtract
ggsymm
ggtensor
ggterm
ggtermideal
ggtest
ggtonet
ggtostring
ggtracing
ggtranspose
ggtruncate
ggvar
ggvector
ggweylalgebra
ggzero
ggzeromat
ggzeromonoid
globalAssignFunction
globalReleaseFunction
gradedModule
gradedModuleMap
graphIdeal
graphRing
group
handle
hash
hashTable
heap
height
help
hilbertFunction
hilbertPolynomial
hilbertSeries
hold
homogenize
homology
homomorphism
horizontalJoin
html
id
ideal
identity
ii
image
imaginaryPart
incomparable
indeterminate
index
indexComponents
inducedMap
inducedMap => Degree
inducedMap => Verify
inducesWellDefinedMap
infinity
input
installMethod
instance
integrate
intersect
irreducibleCharacteristicSeries
isAffineRing
isBorel
isCommutative
isDirectSum
isField
isFreeModule
isHomogeneous
isIdeal
isInjective
isIsomorphism
isModule
isPolynomialRing
isPrime
isPrimitive
isQuotientModule
isQuotientOf
isQuotientRing
isRing
isSubmodule
isSubset
isSurjective
isTable
isWellDefined
jacobian
join
ker
kernel
keys
koszul
last
lcmDegree
leadCoefficient
leadComponent
leadMonomial
leadTerm
length
lift
liftable
lineNumber
lines
linkFilename
linkFilenameKeys
listForm
listUserSymbols
load
loaddata
locate
log
look
lookup
lookupCount
map
match
mathML
matrix
max
maxPosition
member
memoize
merge
mergePairs
method
methods
min
minPosition
mingens
mingle
minors
minprimes
minus
mod
modifyRing
module
modulo
modulus
monoid
monomialCurve
monomialIdeal
mutable
name
needs
net
netRows
newClass
newCoordinateSystem
newHandle
newline
nextkey
notImplemented
null
nullhomotopy
number
numerator
numgens
odd
on
oo
ooo
oooo
openDatabase
openDatabaseOut
openFiles
openIn
openLink
openOut
options
order
original
pack
pad
pairs
parent
partitions
path
pathSeparator
pdim
peek
pfaffians
phase
pi
plus
poincare
poincareComputation
poincareN
pop
position
positions
power
precedence
prepend
presentation
print
printExamples
printString
processArgs
processID
product
profile
profileSummary
projectiveHilbertPolynomial
promote
protect
prune
pruningMap
pseudoRemainder
pushForward
pushForward => StopBeforeComputation
pushForward => StopWithMinimalGenerators
pushForward => Strategy
pushForward1
pushForward1 => DegreeLimit
pushForward1 => MonomialOrder
pushForward1 => PairLimit
pushForward1 => StopBeforeComputation
pushForward1 => StopWithMinimalGenerators
pushForward1 => Strategy
pushForward1 => UseHilbertFunction
quit
quote !
quote !=
quote " "
quote #
quote #?
quote %
quote &
quote &&
quote *
quote **
quote +
quote ++
quote ,
quote -
quote ->
quote .
quote ..
quote .?
quote /
quote //
quote /^
quote :
quote :=
quote ;
quote <
quote <-
quote <<
quote <=
quote =
quote =!=
quote ==
quote ===
quote =>
quote >
quote >=
quote >>
quote ?
quote @
quote @@
quote \
quote ^
quote ^^
quote _
quote and
quote do
quote else
quote from
quote global
quote if
quote local
quote new
quote not
quote of
quote or
quote quote
quote shield
quote then
quote time
quote timing
quote try
quote while
quote |
quote ||
quote ~
quotient
quotient => MinimalGenerators
quotient => Strategy
radical
random
rank
read
realPart
regularity
relations
reloaded
remove
removeLowestDimension
reorganize
res
reshape
resolution
resolution => Algorithm
resolution => DegreeLimit
resolution => HardDegreeLimit
resolution => LengthLimit
resolution => PairLimit
resolution => SortStrategy
resolution => StopBeforeComputation
resolution => SyzygyLimit
restart
returnCode
reverse
ring
rsort
run
runStartFunctions
same
saturate
saturate => DegreeLimit
saturate => MinimalGenerators
saturate => Strategy
scan
scanKeys
scanPairs
see
seeParsing
select
selectInSubring
sendToEngine
sendgg
seq
sequence
set
setrecursionlimit
sheaf
sin
singularLocus
sinh
size
sleep
someTerms
sort
sortColumns
sortColumns => DegreeOrder
sortColumns => MonomialOrder
source
splice
sqrt
standardForm
stats
status
stderr
stdin
stdout
string
submatrix
submodule
subquotient
subscript
subsets
substitute
substring
subtable
sum
super
superscript
symbol
symbolTable
symmetricAlgebra
symmetricPower
syms
syz
syz => ChangeMatrix
syz => CodimensionLimit
syz => StopBeforeComputation
syz => StopWithMinimalGenerators
syz => Strategy
syzygyScheme
table
take
tally
tan
tanh
target
tensor
terms
tex
texMath
text
times
tmpname
toDual
toHandle
toList
toSequence
toString
top
topCoefficients
topicList
topics
trace
transnet
transpose
trim
true
truncate
ultimate
uniform
unique
unlist
use
userSymbols
value
values
variety
vars
vector
version
verticalJoin
wait
wedgeProduct
width
writeMessage
writePacket
writeRawPacket
xor
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