```@meta CurrentModule = Hecke

## Creation

```@docs
Order(::AnticNumberField, ::Array{nf_elem, 1})
Order(::AnticNumberField, ::FakeFmpqMat)
Order(::NfOrdFracIdl)
EquationOrder(::AnticNumberField)
MaximalOrder(::AnticNumberField)
MaximalOrder(::NfOrd)

Example

```@repl using Hecke; # hide Qx, x = PolynomialRing(FlintQQ, "x"); K, a = NumberField(x^2 - 2, "a"); O = EquationOrder(K)

## Basic properties

```@docs
parent(::NfOrd)
isequation_order(::NfOrd)
signature(::NfOrd)
nf(::NfOrd)
degree(::NfOrd)
basis(::NfOrd)
basis(::NfOrd, ::AnticNumberField)
basis_mat(::NfOrd)
basis_mat_inv(::NfOrd)
discriminant(::NfOrd)
gen_index(O::NfOrd)
index(O::NfOrd)
isindex_divisor(::NfOrd, ::fmpz)
minkowski_mat(::NfOrd, ::Int)
in(::nf_elem, ::NfOrd)
den(::nf_elem, ::NfOrd)
norm_change_const(::NfOrd)
trace_matrix(::NfOrd)
+(::NfOrd, ::NfOrd)
poverorder(::NfOrd, ::fmpz)
pmaximal_overorder(::NfOrd, ::fmpz)

Elements

Creation

```@docs (O::NfOrd)(::nf_elem)

### Basic properties

```@docs
parent(::NfOrdElem)
elem_in_nf(::NfOrdElem)
elem_in_basis(::NfOrdElem)
discriminant(::Array{NfOrdElem, 1})
==(::NfOrdElem, ::NfOrdElem)
zero(::NfOrd)
one(::NfOrd)
iszero(::NfOrdElem)
isone(::NfOrdElem)

Arithmetic

```@docs -(::NfOrdElem) +(::NfOrdElem, ::NfOrdElem) -(::NfOrdElem, ::NfOrdElem) *(::NfOrdElem, ::NfOrdElem) ^(::NfOrdElem, ::Int) mod(::NfOrdElem, ::Int) powermod(::NfOrdElem, ::fmpz, ::Int)

### Miscallenous

```@docs
representation_mat(::NfOrdElem)
representation_mat(::NfOrdElem, ::AnticNumberField)
trace(::NfOrdElem)
norm(::NfOrdElem)
rand(::NfOrd, ::Int)
minkowski_map(::NfOrdElem, ::Int)
conjugates_arb(::NfOrdElem, ::Int)
conjugates_arb_log(::NfOrdElem, ::Int)
t2(::NfOrdElem, ::Int)

Ideals

Creation

```@docs ideal(::NfOrd, ::Int) ideal(::NfOrd, ::fmpz) ideal(::NfOrd, ::fmpz_mat) ideal(::NfOrd, ::NfOrdElem) ring_of_multipliers(::NfOrdIdl) *(::NfOrd, ::NfOrdElem)

### Arithmetic

```@docs
==(::NfOrdIdl, ::NfOrdIdl)
+(::NfOrdIdl, ::NfOrdIdl)
*(::NfOrdIdl, ::NfOrdIdl)
lcm(::NfOrdIdl, ::NfOrdIdl)

Miscaellenous

```@docs order(::NfOrdIdl) basis(::NfOrdIdl) basis_mat(::NfOrdIdl) basis_mat_inv(::NfOrdIdl) minimum(::NfOrdIdl) norm(::NfOrdIdl) in(::NfOrdElem, ::NfOrdIdl) idempotents(::NfOrdIdl, ::NfOrdIdl) mod(::NfOrdElem, ::NfOrdIdl) pradical(::NfOrd, p::fmpz)

## Fractional ideals

### Creation

```@docs
frac_ideal(::NfOrd, ::fmpz_mat)
frac_ideal(::NfOrd, ::fmpz_mat, ::fmpz)
frac_ideal(::NfOrd, ::FakeFmpqMat)
frac_ideal(::NfOrd, ::NfOrdIdl)
frac_ideal(::NfOrd, ::NfOrdIdl, ::fmpz)
frac_ideal(::NfOrd, ::nf_elem)
frac_ideal(::NfOrd, ::NfOrdElem)

Arithmetic

```@docs ==(::NfOrdFracIdl, ::NfOrdFracIdl)

### Miscaellenous

```@docs
order(::NfOrdFracIdl)
basis_mat(::NfOrdFracIdl)
basis_mat_inv(::NfOrdFracIdl)
basis(::NfOrdFracIdl)
norm(::NfOrdFracIdl)