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.

Functions and methods returning a an integer :

# BasicList -- length

# File -- length

# HashTable -- length

# String -- length

binomial -- binomial coefficient

binomial(ZZ,ZZ)

char -- the characteristic of a field or ring

codim -- calculate the codimension

degreeLength -- the number of degrees

depth -- depth of a net

dim -- calculate the dimension

floor RR

gcd(ZZ,ZZ)

genus

height -- height of a net

length -- length

maxPosition BasicList -- position of largest element

minPosition BasicList -- position of smallest element

pdim -- calculate the projective dimension

precedence -- parsing precedence

random ZZ -- random integer

regularity -- compute the regularity

setrecursionlimit ZZ -- set the limit on recursion

width -- width of a file or net

xor(ZZ,ZZ)

ZZ !

ZZ & ZZ -- logical and

ZZ >> ZZ -- shift bits rightward

Methods for using an integer :

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

> ZZ -- greater than

>= ZZ -- greater than or equal

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

acos ZZ

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

asin ZZ

atan ZZ

BasicList # ZZ -- get element from list

BasicList #? ZZ -- check for element in list

basis(ZZ,Ideal)

basis(ZZ,Module)

basis(ZZ,Ring)

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

coefficients(ZZ,Matrix)

coefficients(ZZ,RingElement)

CoherentSheaf ^ ZZ

CoherentSheaf ^** ZZ -- tensor power

CoherentSheaf ZZ -- canonical twist of a coherent sheaf

conjugate ZZ

cos ZZ

cosh ZZ

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

degree ZZ

degreesMonoid ZZ

degreesRing ZZ

diff(ProjectiveHilbertPolynomial,ZZ) -- differentiate

divideByVariable(Matrix,RingElement,ZZ)

drop(BasicList,ZZ) -- drop some elements

EngineRing _ ZZ

exp ZZ

expression ZZ

Ext^ZZ(CoherentSheaf,CoherentSheaf)

Ext^ZZ(CoherentSheaf,SheafOfRings)

Ext^ZZ(CoherentSheaf,SumOfTwists)

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) -- compute an Ext module

Ext^ZZ(Module,Ring)

Ext^ZZ(SheafOfRings,CoherentSheaf)

Ext^ZZ(SheafOfRings,SheafOfRings)

Ext^ZZ(SheafOfRings,SumOfTwists)

exteriorPower(ZZ,CoherentSheaf) -- exterior power

exteriorPower(ZZ,Matrix) -- exterior power

exteriorPower(ZZ,Module)

factor ZZ

Fano(ZZ,Ideal)

Fano(ZZ,Ideal,Ring)

fittingIdeal(ZZ,Module)

gcdCoefficients(ZZ,ZZ)

generators(ZZ,Resolution)

getChangeMatrix(ZZ,Resolution)

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

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

ggPush ZZ

GradedModule _ ZZ

GradedModuleMap == ZZ

GradedModuleMap ^ ZZ

GradedModuleMap _ ZZ

Grassmannian(ZZ,ZZ)

Grassmannian(ZZ,ZZ,Ring)

HH^ZZ Sequence

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 SheafOfRings

HH^ZZ SumOfTwists -- coherent sheaf cohomology

HH_ZZ Sequence

HH_ZZ ChainComplex -- homology of a chain complex

HH_ZZ ChainComplexMap -- homology of a chain complex map

hilbertFunction(ZZ,CoherentSheaf)

hilbertFunction(ZZ,Ideal)

hilbertFunction(ZZ,Module)

hilbertFunction(ZZ,ProjectiveVariety)

hilbertFunction(ZZ,Ring)

Ideal == ZZ -- equality

Ideal ^ ZZ -- power of an ideal

Ideal _ ZZ

ideal ZZ

koszul(ZZ,Matrix) -- a differential in a Koszul complex

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)

lift(ZZZ,ZZ)

liftable(ZZ,Ring)

log ZZ

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

map(Module,ZZ)

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

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

mathML ZZ

Matrix * 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

mingens(ZZ,Resolution)

minors(ZZ,Matrix) -- ideal generated by minors

Module == ZZ

Module ^ ZZ -- make a direct sum of several copies of a module

Module ^** ZZ -- tensor power

Module _ ZZ -- get a generator

Monoid _ ZZ -- get a generator of a monoid

Net ^ ZZ -- raise a net

net ZZ

new Eliminate from ZZ

newDegreesMonoid ZZ

newDegreesRing ZZ

pack(BasicList,ZZ)

pack(ZZ,BasicList)

pad(String,ZZ)

pad(ZZ,String)

partitions ZZ

partitions(ZZ,ZZ)

peek2(Sequence,ZZ)

peek2(List,ZZ)

peek2(BasicList,ZZ)

peek2(HashTable,ZZ)

peek2(Net,ZZ)

peek2(Nothing,ZZ)

peek2(String,ZZ)

peek2(Symbol,ZZ)

peek2(Thing,ZZ)

pfaffians(ZZ,Matrix)

precedence ZZ

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

ProjectiveHilbertPolynomial ZZ -- value of polynomial

projectiveHilbertPolynomial ZZ

projectiveHilbertPolynomial(ZZ,ZZ)

promote(Matrix,ZZ)

promote(ZZ,EngineRing)

promote(ZZ,QQ)

promote(ZZ,Ring)

promote(ZZ,RingElement)

promote(ZZ,ZZ)

QQ == ZZ

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

read(File,ZZ) -- read from a file

realPart ZZ

Ring / ZZ

Ring == ZZ

Ring ^ ZZ -- make a free module

Ring _ ZZ -- get a variable by number

RR == ZZ

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

Schur ZZ

see ZZ

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

select(ZZ,HashTable,Function) -- select a limited number of pairs from a hash table

selectInSubring(ZZ,Matrix)

setRandomSeed ZZ -- set starting point for random number generator

sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves

SheafOfRings ^ ZZ

SheafOfRings ZZ

sin ZZ

sinh ZZ

someTerms(RingElement,ZZ,ZZ)

sqrt ZZ

String # ZZ -- get character from string

String #? ZZ -- check for character in string

String ^ ZZ

String _ ZZ

String | ZZ

subsets(Sequence,ZZ)

subsets(List,ZZ)

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

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

substitute(Matrix,ZZ)

substring(String,ZZ)

substring(String,ZZ,ZZ)

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

symmetricPower(ZZ,Matrix) -- symmetric power

take(BasicList,ZZ) -- take some elements from a list

tan ZZ

tanh ZZ

texMath ZZ

Thing /^ ZZ -- divided power

toHandle ZZ

Tor_ZZ(Module,Module)

truncate(ZZ,Ideal)

truncate(ZZ,Module)

truncateOutput ZZ

vars ZZ

Vector == ZZ

Vector _ ZZ -- get a component

wedgeProduct(ZZ,ZZ,Module)

ZZ % GroebnerBasis

ZZ % Ideal

ZZ % MonomialIdeal

ZZ % RingElement

ZZ % ZZ

ZZ * CC

ZZ * ChainComplexMap

ZZ * GradedModuleMap

ZZ * Ideal

ZZ * InfiniteNumber

ZZ * Matrix

ZZ * Module

ZZ * MonomialIdeal

ZZ * ProjectiveHilbertPolynomial

ZZ * RingElement

ZZ * Vector

ZZ ** Matrix

ZZ + CC

ZZ + Matrix

ZZ ++ Matrix

ZZ - CC

ZZ - Matrix

ZZ / CC

ZZ // Matrix

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 == Ring

ZZ == RingElement

ZZ == RR

ZZ == Vector

ZZ _ EngineRing

ZZ _ Module

ZZ _ Monoid -- get unit element

ZZ _ Ring

ZZ | Matrix

ZZ | String

ZZ | ZZ -- logical or

ZZ || Matrix

Fixed objects of class ZZ :

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