ZZ -- the class of all integers

ZZ -- the class of all integers

The ring ZZ is a member of the class Ring. Each object of class ZZ is called an integer.

Making an integer :

# BasicList -- length

# File -- length

# HashTable -- length

# String -- length

ZZ !

ZZ & ZZ -- logical and

ZZ >> ZZ -- shift bits rightward

binomial(ZZ,ZZ)

floor RR

gcd(ZZ,ZZ)

precedence -- parsing precedence

random ZZ -- random integer

xor(ZZ,ZZ)

Methods for using an integer :

(...) _ ZZ -- get element from list

BasicList # ZZ -- get element from list

BasicList #? ZZ -- check for element in list

CC * ZZ

CC + ZZ

CC - ZZ

CC / ZZ

CC == ZZ

CC ^ ZZ

ChainComplex == ZZ

ChainComplex ^ ZZ

ChainComplex _ ZZ -- get component

ChainComplexMap + ZZ

ChainComplexMap == ZZ

ChainComplexMap ^ ZZ

ChainComplexMap _ ZZ -- get component

CoherentSheaf ZZ -- canonical twist of a coherent sheaf

EngineRing _ ZZ

Ext(ZZ,Ideal,Ideal)

Ext(ZZ,Ideal,Module)

Ext(ZZ,Ideal,Ring)

Ext(ZZ,Matrix,Ideal)

Ext(ZZ,Matrix,Module)

Ext(ZZ,Matrix,Ring)

Ext(ZZ,Module,Ideal)

Ext(ZZ,Module,Matrix)

Ext(ZZ,Module,Module)

Ext(ZZ,Module,Ring)

Ext(ZZ,Ring,Ideal)

Ext(ZZ,Ring,Module)

Ext(ZZ,Ring,Ring)

Fano(ZZ,Ideal)

Fano(ZZ,Ideal,Ring)

GF ZZ -- make a finite field of a given order

GF(ZZ,ZZ) -- make a finite field of a given prime power order

GradedModule _ ZZ

GradedModuleMap == ZZ

GradedModuleMap ^ ZZ

GradedModuleMap _ ZZ

Grassmannian(ZZ,ZZ)

Grassmannian(ZZ,ZZ,Ring)

HH^ZZ (...)

HH^ZZ ChainComplex -- cohomology of a chain complex

HH^ZZ ChainComplexMap -- cohomology of a chain complex map

HH^ZZ CoherentSheaf -- coherent sheaf cohomology

HH^ZZ Module -- local cohomology

HH_ZZ (...)

HH_ZZ ChainComplex -- homology of a chain complex

HH_ZZ ChainComplexMap -- homology of a chain complex map

Ideal == ZZ

Ideal ^ ZZ -- power of an ideal

Ideal _ ZZ

InfiniteNumber * ZZ

InfiniteNumber + ZZ

InfiniteNumber - ZZ

Matrix * ZZ

Matrix + ZZ

Matrix ++ ZZ

Matrix - ZZ

Matrix // ZZ

Matrix == ZZ

Matrix ^ ZZ

Matrix _ ZZ -- get a column from a matrix

Matrix | ZZ

Matrix || ZZ

Module == ZZ

Module ^ ZZ

Module _ ZZ -- get a generator

Monoid _ ZZ -- get a generator of a monoid

MonomialIdeal == ZZ

MonomialIdeal ^ ZZ

Net ^ ZZ -- raise a net

ProjectiveHilbertPolynomial ZZ -- value of polynomial

QQ == ZZ

RR == ZZ

Ring / ZZ

Ring ^ ZZ -- make a free module

Ring _ ZZ -- get a variable by number

RingElement % ZZ

RingElement * ZZ

RingElement + ZZ

RingElement ++ ZZ

RingElement - ZZ

RingElement / ZZ

RingElement // ZZ

RingElement == ZZ

RingElement ^ ZZ

RingElement _ ZZ

RingMap ZZ

Schur ZZ

String # ZZ -- get character from string

String #? ZZ -- check for character in string

String ^ ZZ

String _ ZZ

String | ZZ

Thing /^ ZZ -- divided power

Tor(ZZ,Module,Module)

Vector == ZZ

Vector _ ZZ -- get a component

ZZ % GroebnerBasis

ZZ % Ideal

ZZ % RingElement

ZZ % ZZ

ZZ * CC

ZZ * ChainComplexMap

ZZ * GradedModuleMap

ZZ * Ideal

ZZ * InfiniteNumber

ZZ * Matrix

ZZ * Module

ZZ * ProjectiveHilbertPolynomial

ZZ * RingElement

ZZ * Vector

ZZ + CC

ZZ + ChainComplexMap

ZZ + InfiniteNumber

ZZ + Matrix

ZZ + RingElement

ZZ ++ Matrix

ZZ ++ RingElement

ZZ - CC

ZZ - InfiniteNumber

ZZ - Matrix

ZZ - RingElement

ZZ / CC

ZZ / RingElement

ZZ // Matrix

ZZ // RingElement

ZZ : Thing -- repeat an item

ZZ << ZZ -- shift bits leftward

ZZ == CC

ZZ == ChainComplex

ZZ == ChainComplexMap

ZZ == GradedModuleMap

ZZ == Ideal

ZZ == Matrix

ZZ == Module

ZZ == MonomialIdeal

ZZ == QQ

ZZ == RR

ZZ == RingElement

ZZ == Vector

ZZ _ EngineRing

ZZ _ Module

ZZ _ Monoid -- get unit element

ZZ _ Ring

ZZ | Matrix

ZZ | String

ZZ | ZZ -- logical or

ZZ || Matrix

acos ZZ

apply(ZZ,Function) -- apply function to 0 .. n-1

asin ZZ

atan ZZ

basis(ZZ,Ideal)

basis(ZZ,Module)

basis(ZZ,Ring)

conjugate ZZ

cos ZZ

cosh ZZ

cotangentSheaf(ZZ,ProjectiveVariety) -- make an exterior power of the cotangent sheaf

degreesMonoid ZZ

degreesRing ZZ

diff(ProjectiveHilbertPolynomial,ZZ) -- differentiate

divideByVariable(Matrix,RingElement,ZZ)

drop(BasicList,ZZ) -- drop some elements

exp ZZ

expression ZZ

exteriorPower(ZZ,CoherentSheaf) -- exterior power

exteriorPower(ZZ,Matrix)

exteriorPower(ZZ,Module)

factor ZZ

fittingIdeal(ZZ,Module)

gcdCoefficients(ZZ,ZZ)

generators(ZZ,Resolution)

getChangeMatrix(ZZ,Resolution)

ggPush ZZ

hilbertFunction(ZZ,Ideal)

hilbertFunction(ZZ,Module)

hilbertFunction(ZZ,Ring)

ideal ZZ

imaginaryPart ZZ

isPrime ZZ

isUnit ZZ

koszul(ZZ,Matrix)

leadTerm(ZZ,Ideal)

leadTerm(ZZ,Matrix)

leadTerm(ZZ,ZZ,Resolution)

lift(Ideal,ZZ)

lift(Matrix,ZZ)

lift(QQ,ZZ)

lift(RingElement,ZZ)

lift(ZZ,Ring)

lift(ZZ,ZZ)

liftable(ZZ,Ring)

log ZZ

map(Module,Module,ZZ) -- make a map

map(Module,ZZ)

map(Module,ZZ,Function) -- make a map

map(Module,ZZ,{...}) -- make a map

mathML ZZ

mingens(ZZ,Resolution)

minors(ZZ,Matrix)

monomialIdeal(ZZ,Matrix) -- make a monomial ideal

net ZZ

new Eliminate from ZZ

pack(BasicList,ZZ)

pack(ZZ,BasicList)

pad(String,ZZ)

pad(ZZ,String)

partitions ZZ

partitions(ZZ,ZZ)

peek2((...),ZZ)

peek2(BasicList,ZZ)

peek2(HashTable,ZZ)

peek2(Net,ZZ)

peek2(Nothing,ZZ)

peek2(String,ZZ)

peek2(Symbol,ZZ)

peek2(Thing,ZZ)

peek2({...},ZZ)

pfaffians(ZZ,Matrix)

precedence ZZ

product(ZZ,Function) -- product of consecutive values of a function

projectiveHilbertPolynomial ZZ

projectiveHilbertPolynomial(ZZ,ZZ)

promote(Matrix,ZZ)

promote(ZZ,EngineRing)

promote(ZZ,QQ)

promote(ZZ,Ring)

promote(ZZ,RingElement)

promote(ZZ,ZZ)

random(ZZ,Ring) -- a random ring element of a given degree

realPart ZZ

scan(ZZ,Function) -- apply a function to 0 .. n-1

see ZZ

select(ZZ,BasicList,Function) -- select elements from a list

select(ZZ,HashTable,Function) -- select from a hash table

selectInSubring(ZZ,Matrix)

sin ZZ

sinh ZZ

someTerms(RingElement,ZZ,ZZ)

sqrt ZZ

subsets((...),ZZ)

subsets(Set,ZZ) -- produce all the subsets

subsets(ZZ,ZZ) -- produce all the subsets

subsets({...},ZZ)

substitute(Matrix,ZZ)

substring(String,ZZ)

substring(String,ZZ,ZZ)

sum(ZZ,Function) -- sum consecutive values of a function

symmetricPower(ZZ,Matrix)

take(BasicList,ZZ)

tan ZZ

tanh ZZ

texMath ZZ

toHandle ZZ

truncate(ZZ,Ideal)

truncate(ZZ,Module)

vars ZZ

wedgeProduct(ZZ,ZZ,Module)

{...} _ ZZ -- get element from list

Fixed objects of class ZZ :

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