master index

master index

Canonical Embeddings of Plane Curves and Gonality

Daniel R. Grayson

Elementary uses of Groebner bases

Factorization and characteristic sets library

Factory library

GC garbage collector

MP: Multi Protocol

Michael E. Stillman

acknowledgements

algebraic varieties

arithmetic functions

assigning values

associative algebras

bases of parts of modules

coherent sheaves

combinatorial functions

communicating with programs

component example

conditional execution

copyright and license

creating and writing files

editing Macaulay 2 code with emacs

engine communication protocol

executing other programs

exterior algebras

extracting information from chain complexes

fraction fields

free resolutions of modules

getting input from the user

getting started

high level gb engine commands

how to get this program

inheritance from parents

initialization file

installing methods

invoking the program

language and programming overview

local variables in a file

local variables in a function

low level gb engine commands

making a new method function

making chain complexes by hand

making functions with a variable number of arguments

making functions

making generic matrices

making matrices

making module maps

making modules from matrices

making new functions with optional arguments

making new types

making random matrices

making ring maps

manipulating chain complexes

manipulating matrices

manipulating modules

manipulating polynomials

mapping over hash tables

mapping over lists

maps between chain complexes

maps between modules

maps between rings

mathematical overview

method functions with a variable number of arguments

method functions with optional arguments

multi-graded polynomial rings

not documented yet

numbered variables

obsolete functions and symbols

polynomial rings with other monomial orderings

polynomial rings

printing and formatting for new types

printing to the screen

reading the documentation

replacements for commands and scripts from Macaulay

resources required

running Macaulay 2 in emacs

subscripted variables

symmetric algebras

tensor products of rings

transcendental functions

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

two dimensional formatting

using functions with optional arguments

using functions

viewing the symbols defined so far

what a class is

(Hom,ChainComplex,Module)

(NewFromMethod,HashTable,List)

(NewMethod,ChainComplex)

(chainComplex,GradedModule)

(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)

(exteriorPower,ZZ,CoherentSheaf)

(homology,ChainComplex)

(homology,Matrix,Matrix)

(homology,ZZ,ChainComplex)

(homology,ZZ,ChainComplexMap)

(isSubset,Set,Set)

(length,ChainComplex)

(map,ChainComplex,ChainComplex,Function)

(map,Module,Matrix)

(map,Module,Module)

(map,Module,Module,Function)

(map,Module,Module,List)

(map,Module,Module,Matrix)

(map,Module,Module,RingElement)

(map,Module,Module,ZZ)

(map,Module,Nothing,List)

(map,Module,RingElement)

(map,Module,ZZ,Function)

(map,Module,ZZ,List)

(matrix,Matrix)

(matrix,Ring,List)

(max,ChainComplex)

(min,ChainComplex)

(module,CoherentSheaf)

(product,List,Function)

(product,List,List,Function)

(product,Tally)

(product,ZZ,Function)

(quote " ",ChainComplex,Array)

(quote " ",CoherentSheaf,ZZ)

(quote " ",Module,Array)

(quote " ",ProjectiveHilbertPolynomial,ZZ)

(quote " ",Ring,OrderedMonoid)

(quote %,Matrix,Matrix)

(quote %,Matrix,RingElement)

(quote &,ZZ,ZZ)

(quote **,ChainComplex,ChainComplex)

(quote **,ChainComplex,ChainComplexMap)

(quote **,ChainComplex,GradedModule)

(quote **,ChainComplexMap,ChainComplex)

(quote **,ChainComplexMap,ChainComplexMap)

(quote **,CoherentSheaf,CoherentSheaf)

(quote **,GradedModule,ChainComplex)

(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 @,List,Function)

(quote @,OptionTable,Function)

(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)

(rank,CoherentSheaf)

(resolution,Ideal)

(resolution,Matrix)

(resolution,Module)

(ring,CoherentSheaf)

(sheaf,Module,Variety)

(subsets,Set,ZZ)

(subsets,ZZ,ZZ)

(sum,ChainComplex)

(sum,ChainComplexMap)

(sum,List,Function)

(sum,List,List,Function)

(sum,ZZ,Function)

(variety,CoherentSheaf)

AssociativeExpression

BasisElementLimit

BinaryOperation

BinaryPowerMethod

ChainComplexMap

CodimensionLimit

CompleteIntersection

ConversionFormat

ConvertFixedRepeat

ConvertToExpression

EliminationOrder

EmptyMarkUpType

FunctionApplication

GeneralOrderedGroup

GeneralOrderedMonoid

GlobalAssignHook

GlobalReleaseHook

GradedModuleMap

HardDegreeLimit

IndeterminateNumber

IndexedVariable

IndexedVariableTable

MatrixExpression

MinimalGenerators

MinorsComputation

MutableHashTable

NewOfFromMethod

NonAssociativeProduct

OptionsRegistry

PfaffiansComputation

PrimitiveElement

ProjectiveHilbertPolynomial

ProjectiveVariety

PushforwardComputation

PutAnnotationPacket

PutCommonMetaOperatorPacket

PutCommonMetaTypePacket

PutCommonOperatorPacket

PutOperatorPacket

ScriptedFunction

ScriptedFunctor

SelfInitializingType

SimplePowerMethod

SingleArgumentDispatch

SkewCommutative

SparseMonomialVectorExpression

SparseVectorExpression

StopBeforeComputation

StopWithMinimalGenerators

UseHilbertFunction

VariableBaseName

addStartFunction

coefficientRing

compactMatrixForm

currentDirectory

divideByVariable

forceGB => ChangeMatrix

formatDocumentTag

gb => ChangeMatrix

gb => CodimensionLimit

gb => DegreeLimit

gb => PairLimit

gb => StopBeforeComputation

gb => StopWithMinimalGenerators

gb => SyzygyLimit

gcdCoefficients

generatorExpressions

generatorSymbols

genericSkewMatrix

genericSymmetricMatrix

getDocumentationTag

ggColumnAddMultiple

ggColumnInterchange

ggRowAddMultiple

ggRowInterchange

ggSmithNormalForm

ggbinomialGBaddgens

ggbinomialGBenlarge

ggexteriorproduct

ggfindGoodUnitPivot

ggfractionfield

gggetColumnChange

ggishomogeneous

globalAssignFunction

globalReleaseFunction

gradedModuleMap

hilbertFunction

hilbertPolynomial

indexComponents

inducedMap => Degree

inducedMap => Verify

inducesWellDefinedMap

irreducibleCharacteristicSeries

isPolynomialRing

isQuotientModule

leadCoefficient

linkFilenameKeys

listUserSymbols

newCoordinateSystem

openDatabaseOut

poincareComputation

projectiveHilbertPolynomial

pseudoRemainder

pushForward => StopBeforeComputation

pushForward => StopWithMinimalGenerators

pushForward => Strategy

pushForward1 => DegreeLimit

pushForward1 => MonomialOrder

pushForward1 => PairLimit

pushForward1 => StopBeforeComputation

pushForward1 => StopWithMinimalGenerators

pushForward1 => Strategy

pushForward1 => UseHilbertFunction

!

#

%

&

*

+

,

-

.

/

:

;

<

=

>

?

@

\

^

_

|

~

quotient => MinimalGenerators

quotient => Strategy

removeLowestDimension

resolution => Algorithm

resolution => DegreeLimit

resolution => HardDegreeLimit

resolution => LengthLimit

resolution => PairLimit

resolution => SortStrategy

resolution => StopBeforeComputation

resolution => SyzygyLimit

runEndFunctions

runStartFunctions

saturate => DegreeLimit

saturate => MinimalGenerators

saturate => Strategy

selectInSubring

setrecursionlimit

sortColumns => DegreeOrder

sortColumns => MonomialOrder

symmetricAlgebra

syz => ChangeMatrix

syz => CodimensionLimit

syz => StopBeforeComputation

syz => StopWithMinimalGenerators

syz => Strategy

tensorAssociativity

topCoefficients