Creation of Modules
Module(O, n) : RngOrd, RngIntElt -> ModOrd
Module(O) : RngOrd -> ModOrd, Map
Module(I) : RngOrdFracIdl -> ModOrd, Map
Module(S) : SeqEnum[Tup] -> ModOrd, Map
Module(S) : SeqEnum[RngOrdFracIdl] -> ModOrd
Module(S) : SeqEnum[ModRngElt] -> ModOrd, Map, ModMatRngElt
Example ModOrd_create (H65E1)
sub<M | m> : ModOrd, SeqEnum[ModOrdElt] -> ModOrd, Map
quo<M | S> : ModOrd, ModOrd -> ModOrd, Map
Example ModOrd_sub-quo (H65E2)
Elementary Functions
BaseRing(M) : ModOrd -> Rng
Degree(M) : ModOrd -> RngIntElt
Ngens(M) : ModOrd -> RngIntElt
M . i : ModOrd, RngIntElt -> ModTupRngElt
Determinant(M) : ModOrd -> RngOrdIdl
Dimension(M) : ModOrd -> RngIntElt
Operations on Modules
M eq N : ModOrd, ModOrd -> BoolElt
x in M : Any, ModOrd -> BoolElt
M1 meet M2 : ModOrd, ModOrd -> ModOrd
M subset N : ModOrd, ModOrd -> BoolElt
Arithmetic with Modules
I * M : RngOrdIdl, ModOrd -> ModOrd
M1 * M2 : ModOrd, ModOrd -> ModOrd
M1 + M2 : ModOrd, ModOrd -> ModOrd
u * I : ModOrdElt, RngOrdIdl -> ModOrd
Basis of a Module
Basis(M) : ModOrd -> SeqEnum
PseudoBasis(M) : ModOrd -> SeqEnum
Other Functions on Modules
[Future release] Dual(M) : ModOrd -> ModOrd
ElementaryDivisors(M, N) : ModOrd, ModOrd -> SeqEnum
Reduce(M) : ModOrd -> ModOrd, Map
[Future release] Steiniz(M) : ModOrd -> RngOrdIdl
Homomorphisms between Modules
hom<M -> N | T> : ModOrd, ModOrd, Map -> Map
Hom(M, N) : ModOrd, ModOrd -> ModOrd, Map
IsSubmodule(M, N) : ModOrd, ModOrd -> BoolElt, Map
Morphism(M, N) : ModOrd, ModOrd -> Map
Example ModOrd_hom (H65E3)
Creation of Elements
M ! v : ModOrd, SeqEnum -> ModOrdElt
Example ModOrd_coerce-quo (H65E4)
Arithmetic with Elements
x + y : ModOrdElt, ModOrdElt -> ModOrdElt
x - y : ModOrdElt, ModOrdElt -> ModOrdElt
u * c : ModOrdElt, RngElt -> ModOrdElt
u / c : ModOrdElt, RngElt -> ModOrdElt
I * u : RngOrdIdl, ModOrdElt -> ModOrd
Other Functions on Elements
x eq y : ModOrdElt, ModOrdElt -> Bool