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ZZ -- the class of all integers
Functions and methods returning an integer :
# BasicList
-- length or cardinality
# HashTable
-- see
# BasicList
-- length or cardinality
# Set
-- see
# BasicList
-- length or cardinality
# String
-- see
# BasicList
-- length or cardinality
ZZ * ZZ
-- see
*
-- a binary operator, usually used for multiplication
+ ZZ
-- see
+
-- a unary or binary operator, usually used for addition
ZZ + ZZ
-- see
+
-- a unary or binary operator, usually used for addition
- ZZ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ZZ - ZZ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ZZ / ZZ
-- see
/
-- a binary operator, usually used for division
ZZ // ZZ
-- see
//
-- a binary operator, usually used for quotient
analyticSpread(Ideal)
-- see
analyticSpread
-- Compute the analytic spread of a module or ideal
analyticSpread(Ideal,RingElement)
-- see
analyticSpread
-- Compute the analytic spread of a module or ideal
analyticSpread(Module)
-- see
analyticSpread
-- Compute the analytic spread of a module or ideal
analyticSpread(Module,RingElement)
-- see
analyticSpread
-- Compute the analytic spread of a module or ideal
AtomicInt &= ZZ
-- atomic fetch and bitwise and
AtomicInt += ZZ
-- atomic fetch and add
AtomicInt -= ZZ
-- atomic fetch and subtract
AtomicInt ^^= ZZ
-- atomic fetch and bitwise xor
AtomicInt |= ZZ
-- atomic fetch and bitwise or
binomial
-- binomial coefficient
binomial(Constant,Constant)
-- see
binomial
-- binomial coefficient
binomial(Constant,Number)
-- see
binomial
-- binomial coefficient
binomial(Number,Constant)
-- see
binomial
-- binomial coefficient
binomial(Number,Number)
-- see
binomial
-- binomial coefficient
binomial(ZZ,ZZ)
-- see
binomial
-- binomial coefficient
changeBase(String,ZZ)
-- see
changeBase
-- change integer base
char
-- computes the characteristic of the ring or field
degree(SheafMap)
(missing documentation)
degreeLength
-- the length of the degree vector
depth
-- depth of a net
dim
-- compute the Krull dimension
dim(GaloisField)
-- see
dim(Ring)
-- compute the Krull dimension
euler
fileMode(String)
-- get file mode
gcd(ZZ,ZZ)
-- see
gcd
-- greatest common divisor
genus
height
-- height of a net
length
-- length of an object
length(Module)
-- Computes the length of a module
maxPosition(BasicList)
-- see
maxPosition
-- position of the largest element
minPosition(BasicList)
-- see
minPosition
-- position of the smallest element
multiplicity(Ideal)
-- see
multiplicity
-- Compute the Hilbert-Samuel multiplicity of an ideal
multiplicity(Ideal,RingElement)
-- see
multiplicity
-- Compute the Hilbert-Samuel multiplicity of an ideal
nextPrime
-- compute the smallest prime greater than or equal to a given number
numColumns
-- see
numColumns(Matrix)
-- number of columns in a matrix or mutable matrix
numgens
-- the number of generators
numRows
-- see
numRows(Matrix)
-- number of rows in a matrix or mutable matrix
pdim
-- calculate the projective dimension
powermod(ZZ,ZZ,ZZ)
-- see
powermod
-- powers of integers mod N
random(ZZ)
-- see
random(ZZ,ZZ)
-- get a random integer or real number
random(ZZ,ZZ)
-- get a random integer or real number
rank
-- compute the rank
regularity
-- compute the Castelnuovo-Mumford regularity
size2(CC)
-- see
size2
-- number of binary digits to the left of the point
size2(RR)
-- see
size2
-- number of binary digits to the left of the point
size2(RRi)
-- see
size2
-- number of binary digits to the left of the point
size2(ZZ)
-- see
size2
-- number of binary digits to the left of the point
width
-- width of a file or net
ZZ & ZZ
-- logical and
Methods that use an integer :
ZZ !
-- see
!
-- factorial
BasicList #? ZZ
-- see
#?
-- check existence of value in a list, hash table, database, or string
String #? ZZ
-- see
#?
-- check existence of value in a list, hash table, database, or string
CC % ZZ
-- see
%
-- a binary operator, usually used for remainder and reduction
QQ % ZZ
-- see
%
-- a binary operator, usually used for remainder and reduction
RR % ZZ
-- see
%
-- a binary operator, usually used for remainder and reduction
ZZ % MonomialIdeal
-- see
%
-- a binary operator, usually used for remainder and reduction
ZZ % ZZ
-- see
%
-- a binary operator, usually used for remainder and reduction
CC * ZZ
-- see
*
-- a binary operator, usually used for multiplication
ProjectiveHilbertPolynomial * ZZ
-- see
*
-- a binary operator, usually used for multiplication
QQ * ZZ
-- see
*
-- a binary operator, usually used for multiplication
RR * ZZ
-- see
*
-- a binary operator, usually used for multiplication
RRi * ZZ
-- see
*
-- a binary operator, usually used for multiplication
ZZ * CC
-- see
*
-- a binary operator, usually used for multiplication
ZZ * ProjectiveHilbertPolynomial
-- see
*
-- a binary operator, usually used for multiplication
ZZ * QQ
-- see
*
-- a binary operator, usually used for multiplication
ZZ * RR
-- see
*
-- a binary operator, usually used for multiplication
ZZ * RRi
-- see
*
-- a binary operator, usually used for multiplication
CC + ZZ
-- see
+
-- a unary or binary operator, usually used for addition
ChainComplexMap + ZZ
-- see
+
-- a unary or binary operator, usually used for addition
ProjectiveHilbertPolynomial + ZZ
-- see
+
-- a unary or binary operator, usually used for addition
QQ + ZZ
-- see
+
-- a unary or binary operator, usually used for addition
RR + ZZ
-- see
+
-- a unary or binary operator, usually used for addition
RRi + ZZ
-- see
+
-- a unary or binary operator, usually used for addition
ZZ + CC
-- see
+
-- a unary or binary operator, usually used for addition
ZZ + ChainComplexMap
-- see
+
-- a unary or binary operator, usually used for addition
ZZ + ProjectiveHilbertPolynomial
-- see
+
-- a unary or binary operator, usually used for addition
ZZ + QQ
-- see
+
-- a unary or binary operator, usually used for addition
ZZ + RR
-- see
+
-- a unary or binary operator, usually used for addition
ZZ + RRi
-- see
+
-- a unary or binary operator, usually used for addition
CC - ZZ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ProjectiveHilbertPolynomial - ZZ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
QQ - ZZ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
RR - ZZ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
RRi - ZZ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ZZ - CC
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ZZ - ProjectiveHilbertPolynomial
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ZZ - QQ
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ZZ - RR
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
ZZ - RRi
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
CC / ZZ
-- see
/
-- a binary operator, usually used for division
QQ / ZZ
-- see
/
-- a binary operator, usually used for division
RR / ZZ
-- see
/
-- a binary operator, usually used for division
RRi / ZZ
-- see
/
-- a binary operator, usually used for division
ZZ / CC
-- see
/
-- a binary operator, usually used for division
ZZ / QQ
-- see
/
-- a binary operator, usually used for division
ZZ / RR
-- see
/
-- a binary operator, usually used for division
ZZ / RRi
-- see
/
-- a binary operator, usually used for division
CC // ZZ
-- see
//
-- a binary operator, usually used for quotient
InfiniteNumber // ZZ
-- see
//
-- a binary operator, usually used for quotient
QQ // ZZ
-- see
//
-- a binary operator, usually used for quotient
RR // ZZ
-- see
//
-- a binary operator, usually used for quotient
ZZ // MonomialIdeal
-- see
//
-- a binary operator, usually used for quotient
CC == ZZ
-- see
==
-- equality
ChainComplex == ZZ
-- see
==
-- equality
ChainComplexMap == ZZ
-- see
==
-- equality
GradedModuleMap == ZZ
-- see
==
-- equality
Ideal == ZZ
-- see
==
-- equality
Matrix == ZZ
-- see
==
-- equality
Module == ZZ
-- see
==
-- equality
MonomialIdeal == ZZ
-- see
==
-- equality
MutableMatrix == ZZ
-- see
==
-- equality
ProjectiveHilbertPolynomial == ZZ
-- see
==
-- equality
QQ == ZZ
-- see
==
-- equality
Ring == ZZ
-- see
==
-- equality
RingElement == ZZ
-- see
==
-- equality
RingMap == ZZ
-- see
==
-- equality
RR == ZZ
-- see
==
-- equality
RRi == ZZ
-- see
==
-- equality
ZZ == CC
-- see
==
-- equality
ZZ == ChainComplex
-- see
==
-- equality
ZZ == ChainComplexMap
-- see
==
-- equality
ZZ == GradedModuleMap
-- see
==
-- equality
ZZ == Ideal
-- see
==
-- equality
ZZ == Module
-- see
==
-- equality
ZZ == MonomialIdeal
-- see
==
-- equality
ZZ == MutableMatrix
-- see
==
-- equality
ZZ == ProjectiveHilbertPolynomial
-- see
==
-- equality
ZZ == QQ
-- see
==
-- equality
ZZ == Ring
-- see
==
-- equality
ZZ == RingElement
-- see
==
-- equality
ZZ == RingMap
-- see
==
-- equality
ZZ == RR
-- see
==
-- equality
ZZ == RRi
-- see
==
-- equality
ZZ == ZZ
-- see
==
-- equality
> ZZ
>= ZZ
ZZ ^^ ZZ
-- see
^^
-- logical exclusive-or
help(ZZ)
-- see
about
-- search the documentation
infoHelp(ZZ)
-- see
about
-- search the documentation
viewHelp(ZZ)
-- see
about
-- search the documentation
abs(ZZ)
-- see
abs
-- absolute value function
all(ZZ,Function)
-- see
all(BasicList,Function)
-- whether all elements of a list satisfy a specified condition
any(ZZ,Function)
-- see
any(BasicList,Function)
-- whether any elements of a list satisfy a specified condition
apply(ZZ,Function)
-- apply a function to {0,..., n-1}
BasicList # ZZ
-- get value from list, hash table, database, or string
String # ZZ
-- see
BasicList # ZZ
-- get value from list, hash table, database, or string
basis(InfiniteNumber,ZZ,Ideal)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(InfiniteNumber,ZZ,Matrix)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(InfiniteNumber,ZZ,Module)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(InfiniteNumber,ZZ,Ring)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Ideal)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Matrix)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Module)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(List,ZZ,Ring)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,Ideal)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,InfiniteNumber,Ideal)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,InfiniteNumber,Matrix)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,InfiniteNumber,Module)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,InfiniteNumber,Ring)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Ideal)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Matrix)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Module)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,List,Ring)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,Matrix)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,Module)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,Ring)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,ZZ,Ideal)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,ZZ,Matrix)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,ZZ,Module)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
basis(ZZ,ZZ,Ring)
-- see
basis
-- basis or generating set of all or part of a ring, ideal or module
BesselJ(ZZ,Constant)
-- see
BesselJ
-- Bessel function of the first kind
BesselJ(ZZ,Number)
-- see
BesselJ
-- Bessel function of the first kind
BesselY(ZZ,Constant)
-- see
BesselY
-- Bessel function of the second kind
BesselY(ZZ,Number)
-- see
BesselY
-- Bessel function of the second kind
BettiTally ZZ
-- see
BettiTally
-- the class of all Betti tallies
hilbertPolynomial(ZZ,BettiTally)
-- see
BettiTally
-- the class of all Betti tallies
hilbertSeries(ZZ,BettiTally)
-- see
BettiTally
-- the class of all Betti tallies
lift(BettiTally,type of ZZ)
-- see
BettiTally
-- the class of all Betti tallies
ZZ * BettiTally
-- see
BettiTally
-- the class of all Betti tallies
binomial(RingElement,ZZ)
-- see
binomial
-- binomial coefficient
ChainComplex ^ ZZ
-- access member, cohomological degree
ChainComplex _ ZZ
-- component
GradedModule _ ZZ
-- see
ChainComplex _ ZZ
-- component
ChainComplex _ ZZ = Thing
-- install component of chain complex
ChainComplexMap ^ ZZ
-- iterated composition
GradedModuleMap ^ ZZ
-- see
ChainComplexMap ^ ZZ
-- iterated composition
ChainComplexMap _ ZZ
-- component map
GradedModuleMap _ ZZ
-- see
ChainComplexMap _ ZZ
-- component map
ChainComplexMap _ ZZ = Thing
-- install component of chain complex map
changeBase(String,ZZ,ZZ)
-- see
changeBase
-- change integer base
changeBase(ZZ,ZZ)
-- see
changeBase
-- change integer base
check(ZZ,Package)
-- see
check
-- perform tests of a package
check(ZZ,String)
-- see
check
-- perform tests of a package
code(ZZ)
-- see
code
-- display source code
CoherentSheaf == ZZ
(missing documentation)
CoherentSheaf ^ ZZ
-- direct sum
SheafOfRings ^ ZZ
-- see
CoherentSheaf ^ ZZ
-- direct sum
CoherentSheaf ^** ZZ
-- tensor power
CoherentSheaf ZZ
-- canonical twist of a coherent sheaf
SheafOfRings ZZ
-- see
CoherentSheaf ZZ
-- canonical twist of a coherent sheaf
columnAdd(MutableMatrix,ZZ,Number,ZZ)
-- see
columnAdd
-- add a multiple of one column to another
columnAdd(MutableMatrix,ZZ,RingElement,ZZ)
-- see
columnAdd
-- add a multiple of one column to another
columnMult(MutableMatrix,ZZ,Number)
-- see
columnMult
-- multiply a column by a ring element
columnMult(MutableMatrix,ZZ,RingElement)
-- see
columnMult
-- multiply a column by a ring element
columnPermute(MutableMatrix,ZZ,List)
-- see
columnPermute
-- permute some columns
columnSwap(MutableMatrix,ZZ,ZZ)
-- see
columnSwap
-- interchange columns
compareExchange(AtomicInt,ZZ,ZZ)
-- see
compareExchange
-- compares and possibly exchanges the value of an atomic integer
compositions(ZZ,ZZ)
-- see
compositions
-- list the compositions of an integer
compositions(ZZ)
(missing documentation)
concatenate(ZZ)
-- see
concatenate
-- join strings
conwayPolynomial(ZZ)
-- see
conwayPolynomial
-- provide a Conway polynomial
conwayPolynomial(ZZ,ZZ)
-- see
conwayPolynomial
-- provide a Conway polynomial
cotangentSheaf(ZZ,ProjectiveVariety)
-- exterior powers of the cotangent sheaf of a projective variety
debug(ZZ)
(missing documentation)
degreesMonoid(ZZ)
-- see
degreesRing(List)
-- the ring or monoid of degrees
degreesRing(ZZ)
-- see
degreesRing(List)
-- the ring or monoid of degrees
diagonalMatrix(Ring,ZZ,ZZ,List)
-- make a diagonal matrix from a list
diagonalMatrix(RingFamily,ZZ,ZZ,List)
-- see
diagonalMatrix(Ring,ZZ,ZZ,List)
-- make a diagonal matrix from a list
diagonalMatrix(ZZ,ZZ,List)
-- see
diagonalMatrix(Ring,ZZ,ZZ,List)
-- make a diagonal matrix from a list
diff(ProjectiveHilbertPolynomial,ZZ)
divideByVariable(Matrix,RingElement,ZZ)
-- see
divideByVariable
-- divide all columns by a (power of a) variable
drop(BasicList,ZZ)
-- see
drop
-- drop some elements from a list or sequence.
exchange(AtomicInt,ZZ)
-- see
exchange
-- exchange the value of an atomic integer
Ext^ZZ(CoherentSheaf,CoherentSheaf)
-- global Ext
Ext^ZZ(CoherentSheaf,SheafOfRings)
-- see
Ext^ZZ(CoherentSheaf,CoherentSheaf)
-- global Ext
Ext^ZZ(SheafOfRings,CoherentSheaf)
-- see
Ext^ZZ(CoherentSheaf,CoherentSheaf)
-- global Ext
Ext^ZZ(SheafOfRings,SheafOfRings)
-- see
Ext^ZZ(CoherentSheaf,CoherentSheaf)
-- global Ext
Ext^ZZ(CoherentSheaf,SheafMap)
(missing documentation)
Ext^ZZ(CoherentSheaf,SumOfTwists)
-- global Ext
Ext^ZZ(SheafOfRings,SumOfTwists)
-- see
Ext^ZZ(CoherentSheaf,SumOfTwists)
-- global Ext
Ext^ZZ(Matrix,Ideal)
-- see
Ext^ZZ(Matrix,Module)
-- map between Ext modules
Ext^ZZ(Matrix,Module)
-- map between Ext modules
Ext^ZZ(Matrix,Ring)
-- see
Ext^ZZ(Matrix,Module)
-- map between Ext modules
Ext^ZZ(Ideal,Matrix)
-- see
Ext^ZZ(Module,Matrix)
-- map between Ext modules
Ext^ZZ(Module,Matrix)
-- map between Ext modules
Ext^ZZ(Ideal,Ideal)
-- see
Ext^ZZ(Module,Module)
-- Ext module
Ext^ZZ(Ideal,Module)
-- see
Ext^ZZ(Module,Module)
-- Ext module
Ext^ZZ(Ideal,Ring)
-- see
Ext^ZZ(Module,Module)
-- Ext module
Ext^ZZ(Module,Ideal)
-- see
Ext^ZZ(Module,Module)
-- Ext module
Ext^ZZ(Module,Module)
-- Ext module
Ext^ZZ(Module,Ring)
-- see
Ext^ZZ(Module,Module)
-- Ext module
Ext^ZZ(Ring,Ideal)
(missing documentation)
Ext^ZZ(Ring,Matrix)
(missing documentation)
Ext^ZZ(Ring,Module)
(missing documentation)
Ext^ZZ(Ring,Ring)
(missing documentation)
exteriorPower(ZZ,CoherentSheaf)
exteriorPower(ZZ,Matrix)
-- exterior power of a matrix
exteriorPower(ZZ,Module)
-- exterior power of a module
factor(ZZ)
-- see
factor(RingElement)
-- factor a ring element
Fano(ZZ,Ideal)
-- Fano scheme
Fano(ZZ,Ideal,Ring)
-- Fano scheme
fileMode(ZZ,File)
-- set file mode
fileMode(ZZ,String)
-- set file mode
fillMatrix(MutableMatrix,ZZ)
-- see
fillMatrix
-- fill a mutable matrix with random numbers
fittingIdeal(ZZ,Module)
-- see
fittingIdeal
-- Fitting ideal of a module
fittingIdeal(ZZ,Matrix)
(missing documentation)
gcd(QQ,ZZ)
-- see
gcd
-- greatest common divisor
gcd(RingElement,ZZ)
-- see
gcd
-- greatest common divisor
gcd(ZZ,QQ)
-- see
gcd
-- greatest common divisor
gcd(ZZ,RingElement)
-- see
gcd
-- greatest common divisor
gcdCoefficients(ZZ,ZZ)
-- see
gcdCoefficients
-- gcd with coefficients
Ideal _ ZZ
-- see
generators of ideals and modules
Matrix _ ZZ
-- see
generators of ideals and modules
Module _ ZZ
-- see
generators of ideals and modules
MonomialIdeal _ ZZ
-- see
generators of ideals and modules
genericMatrix(Ring,RingElement,ZZ,ZZ)
-- see
genericMatrix
-- make a generic matrix of variables
genericMatrix(Ring,ZZ,ZZ)
-- see
genericMatrix
-- make a generic matrix of variables
genericSkewMatrix(Ring,RingElement,ZZ)
-- see
genericSkewMatrix
-- make a generic skew symmetric matrix of variables
genericSkewMatrix(Ring,ZZ)
-- see
genericSkewMatrix
-- make a generic skew symmetric matrix of variables
genericSymmetricMatrix(Ring,RingElement,ZZ)
-- see
genericSymmetricMatrix
-- make a generic symmetric matrix
genericSymmetricMatrix(Ring,ZZ)
-- see
genericSymmetricMatrix
-- make a generic symmetric matrix
getPrimeWithRootOfUnity(ZZ,ZZ)
-- see
getPrimeWithRootOfUnity
-- find a prime p with a primitive n-th root of unity r in ZZ/p
GF(ZZ)
-- see
GF
-- make a finite field
GF(ZZ,ZZ)
-- see
GF
-- make a finite field
Grassmannian(ZZ,ZZ)
-- the Grassmannian of linear subspaces of a vector space
Grassmannian(ZZ,ZZ,PolynomialRing)
-- see
Grassmannian(ZZ,ZZ)
-- the Grassmannian of linear subspaces of a vector space
HH^ZZ ChainComplex
-- cohomology of a chain complex
HH^ZZ ChainComplexMap
-- cohomology of a chain complex map
HH^ZZ Module
-- local cohomology of a module
HH^ZZ SheafMap
(missing documentation)
HH^ZZ SheafOfRings
-- cohomology of a sheaf of rings on a projective variety
HH^ZZ SumOfTwists
-- coherent sheaf cohomology module
HH^ZZ(AffineVariety,CoherentSheaf)
(missing documentation)
HH^ZZ CoherentSheaf
-- see
HH^ZZ(ProjectiveVariety,CoherentSheaf)
-- cohomology of a coherent sheaf on a projective variety
HH^ZZ(ProjectiveVariety,CoherentSheaf)
-- cohomology of a coherent sheaf on a projective variety
HH^ZZ(ProjectiveVariety,SheafMap)
(missing documentation)
HH^ZZ(ProjectiveVariety,SumOfTwists)
(missing documentation)
HH^ZZ(Variety,SheafOfRings)
(missing documentation)
HH_ZZ ChainComplex
-- homology of a chain complex
HH_ZZ ChainComplexMap
-- homology of a chain complex map
HH_ZZ Sequence
(missing documentation)
hilbertFunction(ZZ,Ideal)
-- see
hilbertFunction
-- the Hilbert function
hilbertFunction(ZZ,Module)
-- see
hilbertFunction
-- the Hilbert function
hilbertFunction(ZZ,Ring)
-- see
hilbertFunction
-- the Hilbert function
hooks(ZZ)
-- see
hooks
-- list hooks attached to a key
icPIdeal(RingElement,RingElement,ZZ)
-- see
icPIdeal
-- compute the integral closure in prime characteristic of a principal ideal
Ideal * ZZ
(missing documentation)
Ideal ^ ZZ
-- power of an ideal
MonomialIdeal ^ ZZ
-- see
Ideal ^ ZZ
-- power of an ideal
insert(ZZ,Thing,VisibleList)
-- see
insert
-- copy a list, inserting an element
integralClosure(Ideal,RingElement,ZZ)
-- integral closure of an ideal in an affine domain
integralClosure(Ideal,ZZ)
-- see
integralClosure(Ideal,RingElement,ZZ)
-- integral closure of an ideal in an affine domain
interval(QQ,ZZ)
-- see
interval
-- construct an interval
interval(RR,ZZ)
-- see
interval
-- construct an interval
interval(ZZ)
-- see
interval
-- construct an interval
interval(ZZ,QQ)
-- see
interval
-- construct an interval
interval(ZZ,RR)
-- see
interval
-- construct an interval
interval(ZZ,ZZ)
-- see
interval
-- construct an interval
inverseSystem(ZZ,Ideal)
-- see
inverseSystem
-- Inverse systems with equivariance
inverseSystem(ZZ,Matrix)
-- see
inverseSystem
-- Inverse systems with equivariance
isLiftable(SheafMap,ZZ)
(missing documentation)
isMember(ZZ,RRi)
-- see
isMember(QQ,RRi)
-- membership test in an interval
isPrime(ZZ)
-- see
isPrime
-- whether a integer or polynomial is prime
isPseudoprime(ZZ)
-- whether an integer is probably prime
isReal(ZZ)
-- see
isReal
-- whether a number is real
isUnit(ZZ)
-- see
isUnit
-- whether a ring element is a unit
kill(ZZ)
-- kill a process
koszul(ZZ,Matrix)
-- a differential in a Koszul complex
lcm(QQ,ZZ)
-- see
lcm
-- least common multiple
lcm(RingElement,ZZ)
-- see
lcm
-- least common multiple
lcm(ZZ,QQ)
-- see
lcm
-- least common multiple
lcm(ZZ,RingElement)
-- see
lcm
-- least common multiple
lcm(ZZ,ZZ)
-- see
lcm
-- least common multiple
leadTerm(ZZ,Ideal)
-- get the ideal of lead polynomials
leadTerm(ZZ,Matrix)
-- get the matrix of lead polynomials of each column
leadTerm(ZZ,RingElement)
-- get the lead polynomials using part of the monomial order
CC << ZZ
-- see
left shift
RR << ZZ
-- see
left shift
RRi << ZZ
-- see
left shift
ZZ << ZZ
-- see
left shift
lift(CC,type of ZZ)
-- see
lift
-- lift to another ring
lift(Ideal,type of ZZ)
-- see
lift
-- lift to another ring
lift(Matrix,type of CC_*,type of ZZ)
-- see
lift
-- lift to another ring
lift(Matrix,type of QQ,type of ZZ)
-- see
lift
-- lift to another ring
lift(Matrix,type of RR_*,type of ZZ)
-- see
lift
-- lift to another ring
lift(Matrix,type of RRi_*,type of ZZ)
-- see
lift
-- lift to another ring
lift(Matrix,type of ZZ,type of ZZ)
-- see
lift
-- lift to another ring
lift(QQ,type of ZZ)
-- see
lift
-- lift to another ring
lift(RR,type of ZZ)
-- see
lift
-- lift to another ring
lift(RRi,type of ZZ)
-- see
lift
-- lift to another ring
lift(ZZ,type of ZZ)
-- see
lift
-- lift to another ring
lngamma(ZZ)
-- see
lngamma
-- logarithm of the Gamma function
locate(ZZ)
-- see
locate
-- locate source code
map(CoherentSheaf,CoherentSheaf,Matrix,ZZ)
(missing documentation)
map(Module,Module,ZZ)
-- see
map(Module,Module,RingElement)
-- construct the map induced by multiplication by a ring element on the generators
map(Module,ZZ,ZZ)
-- see
map(Module,Module,RingElement)
-- construct the map induced by multiplication by a ring element on the generators
map(Module,ZZ,Function)
-- create a matrix from a free module by specifying a function that gives each entry
map(Module,ZZ,List)
-- create a matrix by giving a sparse or dense list of entries
Matrix ^ ZZ
-- power
minors(ZZ,Matrix)
-- ideal generated by minors
Module * ZZ
(missing documentation)
Module ^ ZZ
-- direct sum
Module ^** ZZ
-- tensor power
MonoidElement * ZZ
(missing documentation)
MonoidElement == ZZ
(missing documentation)
MonoidElement ^ ZZ
(missing documentation)
mutableIdentity(Ring,ZZ)
-- make a mutable identity matrix
mutableIdentity(RingFamily,ZZ)
-- see
mutableIdentity(Ring,ZZ)
-- make a mutable identity matrix
MutableMatrix * ZZ
(missing documentation)
MutableMatrix ^ ZZ
(missing documentation)
mutableMatrix(Ring,ZZ,ZZ)
-- make a mutable matrix filled with zeroes
mutableMatrix(RingFamily,ZZ,ZZ)
-- see
mutableMatrix(Ring,ZZ,ZZ)
-- make a mutable matrix filled with zeroes
Net ^ ZZ
-- raise a net or string
String ^ ZZ
-- see
Net ^ ZZ
-- raise a net or string
String | ZZ
-- see
Net | Net
-- join strings or nets
ZZ | String
-- see
Net | Net
-- join strings or nets
new AtomicInt from ZZ
-- initialize an atomic integer
new ZZ from AtomicInt
-- load an atomic integer
numeric(ZZ,CC)
-- see
numeric
-- convert to floating point
numeric(ZZ,Constant)
-- see
numeric
-- convert to floating point
numeric(ZZ,InfiniteNumber)
-- see
numeric
-- convert to floating point
numeric(ZZ,Matrix)
-- see
numeric
-- convert to floating point
numeric(ZZ,Number)
-- see
numeric
-- convert to floating point
numeric(ZZ,RRi)
-- see
numeric
-- convert to floating point
numeric(ZZ,Vector)
-- see
numeric
-- convert to floating point
numeric(ZZ,VisibleList)
-- see
numeric
-- convert to floating point
numericInterval(ZZ,Constant)
-- see
numericInterval
-- converts to an interval
options(ZZ)
-- see
options(Command)
-- get optional arguments and default values of functions and methods
pack(BasicList,ZZ)
-- see
pack
-- pack elements of a list or string into several shorter lists or strings
pack(String,ZZ)
-- see
pack
-- pack elements of a list or string into several shorter lists or strings
pack(ZZ,BasicList)
-- see
pack
-- pack elements of a list or string into several shorter lists or strings
pack(ZZ,String)
-- see
pack
-- pack elements of a list or string into several shorter lists or strings
pad(Net,ZZ)
-- see
pad
-- pad a string or net with spaces
pad(String,ZZ)
-- see
pad
-- pad a string or net with spaces
pad(ZZ,Net)
-- see
pad
-- pad a string or net with spaces
pad(ZZ,String)
-- see
pad
-- pad a string or net with spaces
part(InfiniteNumber,ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(InfiniteNumber,ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(Nothing,ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(Nothing,ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,InfiniteNumber,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,InfiniteNumber,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,Nothing,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,Nothing,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(InfiniteNumber,ZZ,Number)
(missing documentation)
part(ZZ,InfiniteNumber,Number)
(missing documentation)
part(ZZ,Number)
(missing documentation)
part(ZZ,ZZ,Number)
(missing documentation)
Partition _ ZZ
-- get element
partitions(ZZ)
-- see
partitions
-- list the partitions of an integer
partitions(ZZ,ZZ)
-- see
partitions
-- list the partitions of an integer
peek'(ZZ,Thing)
-- see
peek'
-- examine contents of an object
permanents(ZZ,Matrix)
-- see
permanents
-- ideal generated by square permanents of a matrix
permutations(ZZ)
-- see
permutations
-- produce all permutations of a list
pfaffians(ZZ,Matrix)
-- see
pfaffians
-- ideal generated by Pfaffians
RingMap ^ ZZ
-- see
powers
product(ZZ,Function)
-- product of consecutive values of a function
projectiveHilbertPolynomial(ZZ)
-- see
projectiveHilbertPolynomial
-- Hilbert polynomial of projective space
projectiveHilbertPolynomial(ZZ,ZZ)
-- see
projectiveHilbertPolynomial
-- Hilbert polynomial of projective space
ProjectiveHilbertPolynomial ZZ
-- value of polynomial
quotientRemainder(ZZ,ZZ)
-- see
quotientRemainder(RingElement,RingElement)
-- quotient and remainder
random(ZZ,Ideal)
-- get a random homogeneous element from a graded ideal
random(ZZ,Ring)
-- get a random homogeneous element from a graded ring
randomMutableMatrix(ZZ,ZZ,RR,ZZ)
-- a random mutable matrix of integers
read(File,ZZ)
-- read from a file
regex(String,ZZ,String)
-- see
regex
-- evaluate a regular expression search
regex(String,ZZ,ZZ,String)
-- see
regex
-- evaluate a regular expression search
regSeqInIdeal(Ideal,ZZ)
-- see
regSeqInIdeal
-- a regular sequence contained in an ideal
regSeqInIdeal(Ideal,ZZ,ZZ,ZZ)
-- see
regSeqInIdeal
-- a regular sequence contained in an ideal
remove(MutableList,ZZ)
-- see
remove
-- remove an entry from a mutable hash table, list, or database
replace(ZZ,Thing,VisibleList)
-- copy a list, replacing an element
CC >> ZZ
-- see
right shift
RR >> ZZ
-- see
right shift
RRi >> ZZ
-- see
right shift
ZZ >> ZZ
-- see
right shift
Ring / ZZ
-- see
Ring / Ideal
-- make a quotient ring
Ring ^ ZZ
-- make a free module
RingFamily ^ ZZ
-- see
Ring ^ ZZ
-- make a free module
Ring _ ZZ
-- get a ring variable by index
RingElement ^ ZZ
-- power
rotate(ZZ,VisibleList)
-- rotate a list
round(ZZ)
-- see
round
-- round a number
round(ZZ,RR)
-- see
round
-- round a number
rowAdd(MutableMatrix,ZZ,Number,ZZ)
-- see
rowAdd
-- add a multiple of one row to another
rowAdd(MutableMatrix,ZZ,RingElement,ZZ)
-- see
rowAdd
-- add a multiple of one row to another
rowMult(MutableMatrix,ZZ,Number)
-- see
rowMult
-- multiply a row by a ring element
rowMult(MutableMatrix,ZZ,RingElement)
-- see
rowMult
-- multiply a row by a ring element
rowPermute(MutableMatrix,ZZ,List)
-- see
rowPermute
-- permute some rows
rowSwap(MutableMatrix,ZZ,ZZ)
-- see
rowSwap
-- interchange rows
scan(ZZ,Function)
-- see
scan
-- apply a function to each element in a list or sequence
Schubert(ZZ,ZZ,VisibleList)
-- find the Plücker ideal of a Schubert variety
select(ZZ,BasicList,Function)
-- select a limited number of elements from a list
select(ZZ,Function)
-- select integers
select(ZZ,HashTable,Function)
-- select a limited number of pairs from a hash table
selectInSubring(ZZ,Matrix)
-- see
selectInSubring
-- select columns in a subring
separate(String,ZZ,String)
-- see
separate
-- split a string into substrings using a regular expression
setRandomSeed(ZZ)
-- see
setRandomSeed
-- set starting point for random number generator
sheafExt^ZZ(CoherentSheaf,CoherentSheaf)
-- see
sheafExt
-- sheaf Ext of coherent sheaves
sheafExt^ZZ(CoherentSheaf,SheafOfRings)
-- see
sheafExt
-- sheaf Ext of coherent sheaves
sheafExt^ZZ(SheafOfRings,CoherentSheaf)
-- see
sheafExt
-- sheaf Ext of coherent sheaves
sheafExt^ZZ(SheafOfRings,SheafOfRings)
-- see
sheafExt
-- sheaf Ext of coherent sheaves
SheafMap == ZZ
(missing documentation)
SheafMap ^ ZZ
(missing documentation)
SheafMap ZZ
(missing documentation)
sheafMap(Matrix,ZZ)
(missing documentation)
simpleDocFrob(ZZ,Matrix)
-- see
simpleDocFrob
-- a sample documentation node
someTerms(RingElement,ZZ,ZZ)
-- see
someTerms
-- select some terms of a polynomial
store(AtomicInt,ZZ)
-- see
store
-- store the value of an atomic integer
String _ ZZ
-- get element from string
submatrixByDegrees(Matrix,ZZ,ZZ)
-- see
submatrixByDegrees
-- submatrix consisting of rows and columns in an interval or box of degrees
subsets(List,ZZ)
-- see
subsets
-- produce the subsets of a set or list
subsets(Sequence,ZZ)
-- see
subsets
-- produce the subsets of a set or list
subsets(Set,ZZ)
-- see
subsets
-- produce the subsets of a set or list
subsets(ZZ)
-- see
subsets
-- produce the subsets of a set or list
subsets(ZZ,ZZ)
-- see
subsets
-- produce the subsets of a set or list
substitute(Matrix,ZZ)
-- see
substitute
-- substituting values for variables
substring(String,ZZ)
-- see
substring
-- extract part of a string
substring(String,ZZ,ZZ)
-- see
substring
-- extract part of a string
substring(ZZ,String)
-- see
substring
-- extract part of a string
substring(ZZ,ZZ,String)
-- see
substring
-- extract part of a string
sum(ZZ,Function)
-- sum consecutive values of a function
switch(ZZ,ZZ,VisibleList)
-- see
switch
-- copy a list, switching two elements
symmetricPower(ZZ,Matrix)
-- see
symmetricPower
-- symmetric power
symmetricPower(ZZ,Module)
-- see
symmetricPower
-- symmetric power
symmetricPower(ZZ,CoherentSheaf)
(missing documentation)
take(BasicList,ZZ)
-- see
take
-- Take some elements from a list or sequence.
take(Thing,ZZ)
-- see
take
-- Take some elements from a list or sequence.
Monoid ^** ZZ
-- see
tensor(Monoid,Monoid)
-- tensor product of monoids
Ring ^** ZZ
-- see
tensor(Monoid,Monoid)
-- tensor product of monoids
tests(ZZ,Package)
-- see
tests
-- locate a package's tests
tests(ZZ,String)
-- see
tests
-- locate a package's tests
toCC(ZZ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,CC)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ,QQ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ,RR)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ,ZZ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,RR)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,RR,QQ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,RR,RR)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,RR,ZZ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,ZZ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,ZZ,QQ)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,ZZ,RR)
-- see
toCC
-- convert to high-precision complex number
toCC(ZZ,ZZ,ZZ)
-- see
toCC
-- convert to high-precision complex number
toDual(ZZ,Ideal)
-- see
toDual
-- finds the inverse system to an ideal up to a given degree
toDual(ZZ,Matrix)
-- see
toDual
-- finds the inverse system to an ideal up to a given degree
topComponents(Module,ZZ)
(missing documentation)
Tor_ZZ(Ideal,Matrix)
(missing documentation)
Tor_ZZ(Matrix,Ideal)
(missing documentation)
Tor_ZZ(Matrix,Module)
Tor_ZZ(Matrix,Ring)
(missing documentation)
Tor_ZZ(Module,Matrix)
Tor_ZZ(Ideal,Ideal)
-- see
Tor_ZZ(Module,Module)
-- compute a Tor module
Tor_ZZ(Ideal,Module)
-- see
Tor_ZZ(Module,Module)
-- compute a Tor module
Tor_ZZ(Ideal,Ring)
-- see
Tor_ZZ(Module,Module)
-- compute a Tor module
Tor_ZZ(Module,Ideal)
-- see
Tor_ZZ(Module,Module)
-- compute a Tor module
Tor_ZZ(Module,Module)
-- compute a Tor module
Tor_ZZ(Module,Ring)
-- see
Tor_ZZ(Module,Module)
-- compute a Tor module
Tor_ZZ(Ring,Ideal)
(missing documentation)
Tor_ZZ(Ring,Matrix)
(missing documentation)
Tor_ZZ(Ring,Module)
(missing documentation)
Tor_ZZ(Ring,Ring)
(missing documentation)
truncate(BettiTally,InfiniteNumber,ZZ)
(missing documentation)
truncate(BettiTally,ZZ,InfiniteNumber)
(missing documentation)
truncate(BettiTally,ZZ,ZZ)
(missing documentation)
truncate(ZZ,Matrix)
-- see
truncate(List,Matrix)
-- truncation of a map of free modules
truncate(ZZ,Ideal)
-- see
truncate(List,Module)
-- truncation of the graded ring, ideal or module at a specified degree or set of degrees
truncate(ZZ,Module)
-- see
truncate(List,Module)
-- truncation of the graded ring, ideal or module at a specified degree or set of degrees
truncate(ZZ,Ring)
-- see
truncate(List,Module)
-- truncation of the graded ring, ideal or module at a specified degree or set of degrees
truncateOutput(ZZ)
-- see
truncateOutput
uniquePermutations(ZZ)
-- see
uniquePermutations
-- produce all unique permutations of a list
vars(ZZ)
-- see
vars(List)
-- a sequence of variables
VirtualTally == ZZ
(missing documentation)
VirtualTally ? ZZ
(missing documentation)
VirtualTally ^** ZZ
-- Cartesian power of sets and tallies
VisibleList _ ZZ
-- get element from list
wedgeProduct(ZZ,ZZ,Module)
-- the exterior multiplication map
ZZ * MonoidElement
(missing documentation)
ZZ * MutableMatrix
(missing documentation)
ZZ .. ZZ
-- sequences of consecutive integers
ZZ ..< ZZ
-- sequences of consecutive integers
ZZ : Thing
-- repeat an item
ZZ == CoherentSheaf
(missing documentation)
ZZ == MonoidElement
(missing documentation)
ZZ == SheafMap
(missing documentation)
ZZ == VirtualTally
(missing documentation)
ZZ ? VirtualTally
(missing documentation)
ZZ _ Module
-- integers or zero element
ZZ | ZZ
-- logical or
ZZ ~
-- logical not
Fixed objects of class
ZZ
:
maxAllowableThreads
-- the maximum possible number of simultaneously running tasks
maxExponent
minExponent
printingTimeLimit
For the programmer
The object
ZZ
is
a
ring
, with ancestor classes
Number
<
Thing
.