Creation of Modules
Module(O, n) : RngOrd, RngIntElt -> ModDed
Module(O) : RngOrd -> ModDed, Map
Module(I) : RngOrdFracIdl -> ModDed, Map
Module(S) : SeqEnum[Tup] -> ModDed, Map
Module(S) : SeqEnum[RngOrdFracIdl] -> ModDed
Module(S) : SeqEnum[ModElt] -> ModDed, Map
Example ModDed_create (H58E1)
sub<M | m> : ModDed, SeqEnum[ModDedElt] -> ModDed, Map
quo<M | S> : ModDed, ModDed -> ModDed, Map
Example ModDed_sub-quo (H58E2)
Elementary Functions
BaseRing(M) : ModDed -> Rng
Degree(M) : ModDed -> RngIntElt
Ngens(M) : ModDed -> RngIntElt
M . i : ModDed, RngIntElt -> ModTupRngElt
Determinant(M) : ModDed -> RngOrdIdl
Dimension(M) : ModDed -> RngIntElt
Example ModDed_elementary (H58E3)
Predicates on Modules
M eq N : ModDed, ModDed -> BoolElt
x in M : Any, ModDed -> BoolElt
M subset N : ModDed, ModDed -> BoolElt
Arithmetic with Modules
I * M : RngOrdIdl, ModDed -> ModDed
M1 + M2 : ModDed, ModDed -> ModDed
u * I : ModDedElt, RngOrdIdl -> ModDed
Example ModDed_ops_arith (H58E4)
Basis of a Module
Basis(M) : ModDed -> SeqEnum
PseudoBasis(M) : ModDed -> SeqEnum
Other Functions on Modules
M1 meet M2 : ModDed, ModDed -> ModDed
Dual(M) : ModDed -> ModDed
ElementaryDivisors(M, N) : ModDed, ModDed -> SeqEnum
SteinitzClass(M) : ModDed -> RngOrdIdl
SteinitzForm(M) : ModDed -> ModDed
Example ModDed_basis-other (H58E5)
Homomorphisms between Modules
hom<M -> N | T> : ModDed, ModDed, Map -> Map
Hom(M, N) : ModDed, ModDed -> ModDed, Map
IsSubmodule(M, N) : ModDed, ModDed -> BoolElt, Map
Morphism(M, N) : ModDed, ModDed -> Map
Example ModDed_hom (H58E6)
Creation of Elements
M ! v : ModDed, SeqEnum -> ModDedElt
Example ModDed_coerce-quo (H58E7)
Arithmetic with Elements
x + y : ModDedElt, ModDedElt -> ModDedElt
x - y : ModDedElt, ModDedElt -> ModDedElt
u * c : ModDedElt, RngElt -> ModDedElt
u / c : ModDedElt, RngElt -> ModDedElt
I * u : RngOrdIdl, ModDedElt -> ModDed
Other Functions on Elements
x eq y : ModDedElt, ModDedElt -> Bool
ElementToSequence(a) : ModDedElt -> SeqEnum