Module -- the class of all modules

Description

See modules for an overview of modules in Macaulay2. See modules in Macaulay2 for a tutorial overview of modules.

Modules in Macaulay2 are implemented as subquotient modules. Submodules and quotients of free modules are perhaps the most common and important modules, and subquotients form the smallest class of modules that naturally includes these cases.

Common ways to make a module:

Ring ^ ZZ -- make a free module
Ring ^ List -- make a free module
cokernel(Matrix) -- cokernel of a map of modules, graded modules, or chaincomplexes
image(Matrix) -- image of a map
kernel(Matrix) -- kernel of a matrix

Common ways to get information about modules:

ring Module
numgens(Module) -- number of generators of a module
degrees(Module) -- degrees of generators
generators(Module) -- the generator matrix of a module
relations(Module) -- the defining relations
isFreeModule -- whether something is a free module
isHomogeneous(Module) -- whether something is homogeneous (graded)

Numerical information about a module:

codim(Module) -- codimension of the support of a module
dim(Module) -- compute the Krull dimension
rank(Module) -- compute the rank

Submodules, quotients, and subquotient modules:

ambient(Module) -- ambient free module
cover(Module) -- get the covering free module
super(Module) -- get the ambient module
Module / Module -- quotient module
subquotient(Matrix,Matrix) -- make a subquotient module
isSubset(Module,Module) -- whether one object is a subset of another

Common operations on modules:

Module + Module -- sum of submodules
Module == Module -- equality
Module ++ Module -- direct sum of modules
Module ^ List -- projection onto summand
Module ** Module -- tensor product of modules
Module ^** ZZ -- tensor power
Module _ List -- map from free module to some generators

Minimalization:

mingens(Module) -- minimal generator matrix
trim(Module) -- minimize generators and relations
minimalPresentation(Module) -- minimal presentation of a module

Graded modules:

basis -- basis or generating set of all or part of a ring, ideal or module
truncate(ZZ,Module) -- truncation of the graded ring, ideal or module at a specified degree or set of degrees
degree(Module)
genera(Module)
hilbertSeries(Module) -- compute the Hilbert series of the module
hilbertFunction(ZZ,Module) -- the Hilbert function
poincare(Module) -- assemble degrees of a ring, module, or ideal into a polynomial
regularity(Module) -- compute the Castelnuovo-Mumford regularity

Annihilators, quotients and Gröbner bases:

gb(Module) -- compute a Gröbner basis
Ideal : Ideal -- ideal or submodule quotient
annihilator(Module) -- the annihilator ideal
saturate(Module,Ideal) -- saturation of ideal or submodule

Common homological computations:

resolution(Module) -- compute a free resolution of a module
pdim(Module) -- calculate the projective dimension of a module
Hom -- module of homomorphisms
homomorphism(Matrix) -- get the homomorphism from element of Hom
Ext^ZZ(Module,Module) -- Ext module
Tor_ZZ(Module,Module) -- compute a Tor module
HH^ZZ Module -- local cohomology of a module
homology(Matrix,Matrix) -- homology of a pair of maps
fittingIdeal(ZZ,Module) -- Fitting ideal of a module

Multilinear algebra:

exteriorPower(ZZ,Module) -- exterior power of a module

Functions and methods returning a module :

Ideal * Module -- see * -- a binary operator, usually used for multiplication
MonomialIdeal * Module -- see * -- a binary operator, usually used for multiplication
RingElement * Module -- see * -- a binary operator, usually used for multiplication
ambient(Module) -- ambient free module
ChainComplex ^ ZZ -- access member, cohomological degree
ChainComplex _ ZZ -- component
GradedModule _ ZZ -- see ChainComplex _ ZZ -- component
coimage(Matrix) -- see coimage -- coimage of a map
cokernel(Matrix) -- see cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
cokernel(RingElement) -- see cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
comodule(Ideal) -- see comodule -- submodule to quotient module
comodule(Module) -- see comodule -- submodule to quotient module
quotient(Ideal) -- see comodule -- submodule to quotient module
quotient(Module) -- see comodule -- submodule to quotient module
cover(Module) -- get the covering free module
dual(Module) -- dual module
Ext(Ideal,Ideal) -- see Ext(Module,Module) -- total Ext module
Ext(Ideal,Module) -- see Ext(Module,Module) -- total Ext module
Ext(Ideal,Ring) -- see Ext(Module,Module) -- total Ext module
Ext(Module,Ideal) -- see Ext(Module,Module) -- total Ext module
Ext(Module,Module) -- total Ext module
Ext(Module,Ring) -- see Ext(Module,Module) -- total Ext module
Ext(Ring,Ideal) (missing documentation)
Ext(Ring,Module) (missing documentation)
Ext(Ring,Ring) (missing documentation)
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,SumOfTwists) -- global Ext
Ext^ZZ(SheafOfRings,SumOfTwists) -- see Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
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,Module) (missing documentation)
Ext^ZZ(Ring,Ring) (missing documentation)
exteriorPower(ZZ,Module) -- exterior power of a module
HH^ZZ ChainComplex -- cohomology of a chain complex
HH^ZZ Module -- local cohomology of a module
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,SumOfTwists) (missing documentation)
HH^ZZ(Variety,SheafOfRings) (missing documentation)
HH_ZZ ChainComplex -- homology of a chain complex
Hom(Ideal,Ideal) -- see Hom -- module of homomorphisms
Hom(Ideal,Module) -- see Hom -- module of homomorphisms
Hom(Ideal,Ring) -- see Hom -- module of homomorphisms
Hom(Module,Ideal) -- see Hom -- module of homomorphisms
Hom(Module,Module) -- see Hom -- module of homomorphisms
Hom(Module,Ring) -- see Hom -- module of homomorphisms
Hom(Ring,Ideal) -- see Hom -- module of homomorphisms
Hom(Ring,Module) -- see Hom -- module of homomorphisms
Hom(Ring,Ring) -- see Hom -- module of homomorphisms
Hom(CoherentSheaf,CoherentSheaf) -- global Hom
Hom(CoherentSheaf,SheafOfRings) -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
Hom(SheafOfRings,CoherentSheaf) -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
Hom(SheafOfRings,SheafOfRings) -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
homogenize(Module,RingElement) -- see homogenize -- homogenize with respect to a variable
homogenize(Module,RingElement,List) -- see homogenize -- homogenize with respect to a variable
homology(Matrix,Matrix) -- homology of a pair of maps
Ideal / Ideal -- quotient module
image(Matrix) -- see image -- image of a map
image(RingElement) -- see image -- image of a map
intersect(Module) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersect(Module,Module) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
kernel(Matrix) -- kernel of a matrix
kernel(RingElement) -- see kernel(Matrix) -- kernel of a matrix
kernelOfLocalization(Module,Ideal) -- see kernelOfLocalization -- the kernel of the localization map
lift(Module,type of InexactNumber') (missing documentation)
lift(Module,type of Number) (missing documentation)
lift(Module,type of RingElement) (missing documentation)
minimalPresentation(Module) -- minimal presentation of a module
prune(Module) -- see minimalPresentation(Module) -- minimal presentation of a module
Module * RingElement (missing documentation)
Module ** Ring -- tensor product
Ring ** Module -- see Module ** Ring -- tensor product
Module + Module -- sum of submodules
Module ++ Module -- direct sum of modules
Module / Ideal -- see Module / Module -- quotient module
Module / List -- see Module / Module -- quotient module
Module / Module -- quotient module
Module / RingElement -- see Module / Module -- quotient module
Module / Sequence -- see Module / Module -- quotient module
Module / Vector -- see Module / Module -- quotient module
Module ^ ZZ -- direct sum
Module ^** ZZ -- tensor power
module(CoherentSheaf) -- get the module defining a coherent sheaf
module(Ideal) (missing documentation)
module(Ring) -- make or get a module
module(SheafOfRings)
pullback(Matrix,Matrix) (missing documentation)
pushForward(RingMap,Module)
pushout(Matrix,Matrix) (missing documentation)
Module : Ideal -- see quotient(Module,Module) -- ideal or submodule quotient
Module : RingElement -- see quotient(Module,Module) -- ideal or submodule quotient
quotient(Module,Ideal) -- see quotient(Module,Module) -- ideal or submodule quotient
quotient(Module,RingElement) -- see quotient(Module,Module) -- ideal or submodule quotient
removeLowestDimension(Module) -- see removeLowestDimension -- remove components of lowest dimension
Ring ^ List -- make a free module
RingFamily ^ List -- see Ring ^ List -- make a free module
Ring ^ ZZ -- make a free module
RingFamily ^ ZZ -- see Ring ^ ZZ -- make a free module
RingMap Module -- see RingMap RingElement -- apply a ring map
saturate(Module) -- see saturate -- saturation of ideal or submodule
saturate(Module,Ideal) -- see saturate -- saturation of ideal or submodule
saturate(Module,RingElement) -- see saturate -- saturation of ideal or submodule
saturate(Vector) -- see saturate -- saturation of ideal or submodule
saturate(Vector,Ideal) -- see saturate -- saturation of ideal or submodule
saturate(Vector,RingElement) -- see saturate -- saturation of ideal or submodule
subquotient -- make a subquotient module
substitute(Module,List) -- see substitute -- substituting values for variables
substitute(Module,Matrix) -- see substitute -- substituting values for variables
substitute(Module,Ring) -- see substitute -- substituting values for variables
substitute(Module,RingFamily) -- see substitute -- substituting values for variables
sum(ChainComplex) -- direct sum of the components of a chain complex
super(Module) -- see super -- get the ambient module
symmetricPower(ZZ,Module) -- see symmetricPower -- symmetric power
Module ** Module -- see tensor(Module,Module) -- tensor product of modules
tensor(Module,Module) -- tensor product of modules
RingMap ** Module -- see tensor(RingMap,Matrix) -- tensor product via a ring map
tensor(RingMap,Module) -- see tensor(RingMap,Matrix) -- tensor product via a ring map
topComponents(Module) -- see topComponents -- compute top dimensional component of an ideal or module
topComponents(Module,ZZ) (missing documentation)
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,Module) (missing documentation)
Tor_ZZ(Ring,Ring) (missing documentation)
trim(Module) -- see trim -- minimize generators and relations
truncate(List,Module) -- truncation of the graded ring, ideal or module at a specified degree or set of degrees

Methods that use a module :

Ideal == Module -- see == -- equality
Module == Ideal -- see == -- equality
Module == Module -- see == -- equality
Module == ZZ -- see == -- equality
ZZ == Module -- see == -- equality
adjoint'(Matrix,Module,Module) -- see adjoint -- the tensor-Hom adjunction maps
adjoint(Matrix,Module,Module) -- see adjoint -- the tensor-Hom adjunction maps
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
annihilator(Module) -- see annihilator -- the annihilator ideal
associatedPrimes(Module) -- see associatedPrimes -- find associated primes
basis(InfiniteNumber,InfiniteNumber,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(InfiniteNumber,List,Module) -- 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(List,InfiniteNumber,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,List,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
basis(List,Module) -- 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(Module) -- 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,List,Module) -- 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,ZZ,Module) -- see basis -- basis or generating set of all or part of a ring, ideal or module
betti(Module) -- see betti -- display or modify a Betti diagram
ChainComplex ** Module -- see ChainComplex ** ChainComplex -- tensor product
Module ** ChainComplex -- see ChainComplex ** ChainComplex -- tensor product
Module ** ChainComplexMap -- see ChainComplex ** ChainComplexMap -- tensor product
ChainComplexMap ** Module -- see ChainComplexMap ** ChainComplex -- tensor product
checkDegrees(Module,Module) -- see checkDegrees -- compares the degrees of generators of two modules
codim(Module) -- codimension of the support of a module
components(Module) -- see components -- list the components of a direct sum
compose(Module,Module,Module) -- see compose -- composition as a pairing on Hom-modules
coverMap(Module) -- the surjective map from a free module to a module corresponding to the generators
degree(Module)
degrees(Module) -- see degrees(Ring) -- degrees of generators
describe(Module) -- see describe -- real description
dim(Module) -- compute the Krull dimension
directSum(Module) -- see directSum -- direct sum of modules or maps
euler(Module)
eulers(Module) -- see eulers(CoherentSheaf)
expectedReesIdeal(Module) -- see expectedReesIdeal -- symmetric algebra ideal plus jacobian dual
Ext^ZZ(Matrix,Module) -- map between Ext modules
Ext^ZZ(Module,Matrix) -- map between Ext modules
factor(Module) -- factor a ZZ-module
fittingIdeal(ZZ,Module) -- see fittingIdeal -- Fitting ideal of a module
flip(Module,Module) -- see flip -- isomorphism map of commutativity of tensor product
formation(Module) -- see formation -- recover the methods used to make a module
gb(Module) -- see gb -- compute a Gröbner basis
gbRemove(Module) -- see gbRemove -- remove Gröbner basis
gbSnapshot(Module) -- see gbSnapshot -- the Gröbner basis matrix as so far computed
genera(Module) -- see genera(CoherentSheaf)
generator(Module) -- see generator -- provide a single generator
Module _ ZZ -- see generators of ideals and modules
generators(Module) -- the generator matrix of a module
genus(Module) -- see genus(CoherentSheaf)
gradedModule(Module) -- see gradedModule -- make a graded module
GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product
Module ** GradedModule -- see GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product
groebnerBasis(Module) -- see groebnerBasis -- Gröbner basis, as a matrix
hilbertFunction(List,Module) -- see hilbertFunction -- the Hilbert function
hilbertFunction(Module) -- see hilbertFunction -- the Hilbert function
hilbertFunction(ZZ,Module) -- see hilbertFunction -- the Hilbert function
hilbertPolynomial(Module) -- compute the Hilbert polynomial of the module
hilbertSeries(Module) -- compute the Hilbert series of the module
Hom(ChainComplex,Module) -- see Hom(Module,ChainComplex) -- the Hom functor
Hom(ChainComplexMap,Module) -- see Hom(Module,ChainComplex) -- the Hom functor
Hom(Module,ChainComplex) -- the Hom functor
Hom(Module,ChainComplexMap) -- see Hom(Module,ChainComplex) -- the Hom functor
Hom(Matrix,Module) -- see Hom(Module,Matrix) -- induced map on Hom
Hom(Module,Matrix) -- induced map on Hom
ideal(Module) -- converts a module to an ideal
inducedMap(Module,Module) -- compute the map induced by the identity
inducedMap(Module,Module,Matrix) -- compute the induced map
inducedMap(Module,Nothing,Matrix) -- see inducedMap(Module,Module,Matrix) -- compute the induced map
inducedMap(Nothing,Module,Matrix) -- see inducedMap(Module,Module,Matrix) -- compute the induced map
inducesWellDefinedMap(Module,Module,Matrix) -- see inducesWellDefinedMap -- whether a map is well defined
inducesWellDefinedMap(Module,Nothing,Matrix) -- see inducesWellDefinedMap -- whether a map is well defined
inducesWellDefinedMap(Nothing,Module,Matrix) -- see inducesWellDefinedMap -- whether a map is well defined
installHilbertFunction(Module,RingElement) (missing documentation)
isDirectSum(Module) -- see isDirectSum -- whether something is a direct sum
isFreeModule(Module) -- see isFreeModule -- whether something is a free module
isHomogeneous(Module) -- see isHomogeneous -- whether something is homogeneous (graded)
isIdeal(Module) -- see isIdeal -- whether something is an ideal
isIsomorphic(Module,Module) -- see isIsomorphic -- Probabilistic test for isomorphism of modules
isLinearType(Module) -- see isLinearType -- Determine whether module has linear type
isLinearType(Module,RingElement) -- see isLinearType -- Determine whether module has linear type
isModule(Module) -- see isModule -- whether something is a module
isPrimary(Module,Module) -- see isPrimary -- determine whether a submodule is primary
isQuotientModule(Module) -- see isQuotientModule -- whether something is evidently a quotient of a free module
isReduction(Module,Module) -- see isReduction -- Determine whether an ideal is a reduction
isReduction(Module,Module,RingElement) -- see isReduction -- Determine whether an ideal is a reduction
isSubmodule(Module) -- see isSubmodule -- whether a module is evidently a submodule of a free module
isSubquotient(Module,Module) -- check whether a module is a subquotient of another
isSubset(Ideal,Module) -- see isSubset(Module,Module) -- whether one object is a subset of another
isSubset(Module,Ideal) -- see isSubset(Module,Module) -- whether one object is a subset of another
isSubset(Module,Module) -- whether one object is a subset of another
isSupportedInZeroLocus(Ideal,Module) -- see isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
length(Module) -- Computes the length of a module
lift(Module,type of InexactNumber) (missing documentation)
map(Module) -- identity map
map(Module,Module,Function) -- create a matrix by specifying a function that gives each entry
map(Module,Module,List) -- create a matrix by giving a sparse or dense list of entries
map(Module,Module,Matrix) -- create the matrix induced on generators by a given matrix
map(Module,Module,Number) -- see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
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,Module,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,RingMap,Matrix) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,RingMap) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,List) -- create a matrix by giving a doubly nested list of ring elements
map(Module,Nothing,Matrix) -- recast a matrix to have a new target, and a free module as source
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 % Module -- see methods for normal forms and remainder -- normal form of ring elements and matrices
mingens(Module) -- minimal generator matrix
minimalBetti(Module) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
Module * ZZ (missing documentation)
GradedModule ++ Module -- see Module ++ Module -- direct sum of modules
Module ++ GradedModule -- see Module ++ Module -- direct sum of modules
Module ^ Array -- projection onto summand
Module ^ List -- projection onto summand
Module _ Array -- inclusion from summand
Module _ List -- map from free module to some generators
Module _* (missing documentation)
Module Array -- make a chain complex from a module
module(Module) (missing documentation)
monomialIdeal(Module) -- see monomialIdeal(Ideal) -- monomial ideal of lead monomials of a Gröbner basis
multidegree(Module) -- see multidegree -- multidegree
numgens(Module) -- number of generators of a module
pdim(Module) -- calculate the projective dimension of a module
poincare(Module) -- see poincare -- assemble degrees of a ring, module, or ideal into a polynomial
preimage(Matrix,Module) -- see preimage -- preimage of a map
presentation(Module) -- presentation of a module
primaryDecomposition(Module) -- irredundant primary decomposition of a module
Module : Module -- see quotient(Module,Module) -- ideal or submodule quotient
quotient(Module,Module) -- ideal or submodule quotient
random(Module) (missing documentation)
random(Module,Module) -- make a random module map
rank(Module) -- see rank -- compute the rank
reesAlgebra(Module) -- see reesAlgebra -- Compute the defining ideal of the Rees Algebra
reesAlgebra(Module,RingElement) -- see reesAlgebra -- Compute the defining ideal of the Rees Algebra
reesIdeal(Module) -- see reesIdeal -- Compute the defining ideal of the Rees Algebra
reesIdeal(Module,RingElement) -- see reesIdeal -- Compute the defining ideal of the Rees Algebra
regularity(Module) -- see regularity -- compute the Castelnuovo-Mumford regularity
relations(Module) -- see relations -- the defining relations
reshape(Module,Module,Matrix) -- see reshape -- reshape a matrix
resolution(Module) -- compute a free resolution of a module
ring(Module) -- see ring -- get the associated ring of an object
Ring / Module -- see Ring / Ideal -- make a quotient ring
schreyerOrder(Module) -- obtain Schreyer order information
Module ~ -- see sheaf(Module) -- make a coherent sheaf
sheaf(Module) -- make a coherent sheaf
sheaf(Variety,Module) -- make a coherent sheaf
specialFiber(Module) -- see specialFiber -- Special fiber of a blowup
specialFiber(Module,RingElement) -- see specialFiber -- Special fiber of a blowup
specialFiberIdeal(Module) -- see specialFiberIdeal -- Special fiber of a blowup
specialFiberIdeal(Module,RingElement) -- see specialFiberIdeal -- Special fiber of a blowup
subquotient(Module,Matrix,Matrix) -- see subquotient -- make a subquotient module
subquotient(Module,Matrix,Nothing) -- see subquotient -- make a subquotient module
subquotient(Module,Nothing,Matrix) -- see subquotient -- make a subquotient module
subquotient(Module,Nothing,Nothing) -- see subquotient -- make a subquotient module
substitute(Module,Option) -- see substitute -- substituting values for variables
symmetricAlgebra(Module) -- see symmetricAlgebra -- the symmetric algebra of a module
symmetricAlgebraIdeal(Module) -- see symmetricAlgebraIdeal -- Ideal of the symmetric algebra of an ideal or module
Matrix ** Module -- see tensor(Matrix,Module) -- tensor product
Module ** Matrix -- see tensor(Matrix,Module) -- tensor product
tensor(Matrix,Module) -- tensor product
tensor(Module,Matrix) -- see tensor(Matrix,Module) -- tensor product
tensorAssociativity(Module,Module,Module) -- see tensorAssociativity -- associativity isomorphisms for tensor products
Tor_ZZ(Matrix,Module)
Tor_ZZ(Module,Matrix)
truncate(ZZ,Module) -- see truncate(List,Module) -- truncation of the graded ring, ideal or module at a specified degree or set of degrees
vector(Module,List) -- see vector -- make a vector
vector(Module,Matrix) -- see vector -- make a vector
vector(Module,Number) -- see vector -- make a vector
vector(Module,RingElement) -- see vector -- make a vector
versalEmbedding(Module) -- see versalEmbedding -- Compute a versal embedding
wedgeProduct(ZZ,ZZ,Module) -- the exterior multiplication map
ZZ _ Module -- integers or zero element

For the programmer

The object Module is a type, with ancestor classes ImmutableType < HashTable < Thing.