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-- also includes: vector
-- TODO: (module, Ideal)
document {
Key => module,
Headline => "make or get a module"
}
document { Key => (module, Ring),
Usage => "module R",
Inputs => {"R"},
Outputs => {{"the free module of rank 1 over the ring R"}},
EXAMPLE lines ///
ZZ
module ZZ
///}
document { Key => (module, Vector),
Headline => "the module of a vector",
Usage => "module v",
Inputs => {"v"},
Outputs => {{"the module that contains the vector ", TT "v"}},
"The class of ", TT "v", " is also equal to the module of ", TT "v", ".",
EXAMPLE lines ///
F = ZZ^4
v = F_2
module v
class v
///}
document { Key => (module, SheafOfRings),
SeeAlso => { Variety, OO },
Usage => "module F",
Inputs => { "F" },
Outputs => { { "the module corresponding to ", TT "F" }},
EXAMPLE lines ///
R = QQ[x..z]
X = Proj R
OO_X^6
module oo
///
}
document {
Key => {relations,(relations, Module)},
Headline => "the defining relations",
TT "relations M", " -- produce the relations defining a module M.",
PARA{},
"The relations are represented as a matrix, and if not stored
in the module under M.relations, the matrix is understood to be
empty.",
PARA{},
SeeAlso => {"generators","subquotient"}}
document {
Key => {vector,(vector,List),(vector,Matrix)},
Headline => "make a vector",
TT "vector {a,b,c,...}", " -- produces an element of a free module from a list.",
PARA{},
"The elements a,b,c,... must be elements of the same ring, or be
convertible to elements of the same ring."}
document {
Key => {super,(super, GradedModule),(super, CoherentSheaf),(super, Matrix),(super, Module),(super,Vector)},
Headline => "get the ambient module",
TT "super M", " -- yields the module that the module ", TT "M", " is a submodule of.",
BR{},
TT "super f", " -- if ", TT "f", " is a map whose target is a submodule
of ", TT "M", ", yields the composite of ", TT "f", " with the inclusion into ", TT "M", ".",
PARA{},
SeeAlso => { "cover", "ambient" }}
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