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feat: add residue ring/field maps #1559

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feat: add residue ring/field maps #1559

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1 change: 0 additions & 1 deletion docs/make.jl
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Expand Up @@ -46,7 +46,6 @@ makedocs(
"function_field.md",
"finfield.md",
"real.md",
"numberfield.md",
],
"Groups" => [
"perm.md",
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7 changes: 3 additions & 4 deletions docs/src/constructors.md
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Expand Up @@ -62,7 +62,7 @@ AbstractAlgebra.jl and explain what mathematical domains they represent.
| $R = \mathbb{Z}$ | `R = ZZ` |
| $R = \mathbb{Q}$ | `R = QQ` |
| $R = \mathbb{F}_{p}$ | `R = GF(p)` |
| $R = \mathbb{Z}/n\mathbb{Z}$ | `R = residue_ring(ZZ, n)` |
| $R = \mathbb{Z}/n\mathbb{Z}$ | `R, = residue_ring(ZZ, n)` |
| $S = R[x]$ | `S, x = polynomial_ring(R, :x)` |
| $S = R[x, y]$ | `S, (x, y) = polynomial_ring(R, [:x, :y])` |
| $S = R\langle x, y\rangle$ | `S, (x, y) = free_associative_algebra(R, [:x, :y])` |
Expand All @@ -77,10 +77,9 @@ AbstractAlgebra.jl and explain what mathematical domains they represent.
| Puiseux series field to precision $n$| `S, x = puiseux_series_field(R, n, :x)` |
| $S = K(x)(y)/(f)$ | `S, y = function_field(f, :y)` with $f\in K(x)[t]$ |
| $S = \mathrm{Frac}_R$ | `S = fraction_field(R)` |
| $S = R/(f)$ | `S = residue_ring(R, f)` |
| $S = R/(f)$ (with $(f)$ maximal) | `S = residue_field(R, f)` |
| $S = R/(f)$ | `S, = residue_ring(R, f)` |
| $S = R/(f)$ (with $(f)$ maximal) | `S, = residue_field(R, f)` |
| $S = \mathrm{Mat}_{m\times n}(R)$ | `S = matrix_space(R, m, n)` |
| $S = \mathbb{Q}[x]/(f)$ | `S, a = number_field(f, :a)` |

## Parent objects with variable names

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2 changes: 1 addition & 1 deletion docs/src/index.md
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Expand Up @@ -75,7 +75,7 @@ R = GF(7)

S, y = polynomial_ring(R, "y")

T = residue_ring(S, y^3 + 3y + 1)
T, = residue_ring(S, y^3 + 3y + 1)

U, z = polynomial_ring(T, "z")

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15 changes: 5 additions & 10 deletions docs/src/matrix.md
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Expand Up @@ -827,8 +827,7 @@ fflu{T <: RingElem}(::MatElem{T}, ::SymmetricGroup)
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> K, a = number_field(x^3 + 3x + 1, "a")
(Residue field of univariate polynomial ring modulo x^3 + 3*x + 1, x)
julia> K, = residue_field(R, x^3 + 3x + 1); a = K(x);

julia> S = matrix_space(K, 3, 3)
Matrix space of 3 rows and 3 columns
Expand Down Expand Up @@ -865,8 +864,7 @@ is_rref{T <: FieldElem}(::MatElem{T})
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> K, a = number_field(x^3 + 3x + 1, "a")
(Residue field of univariate polynomial ring modulo x^3 + 3*x + 1, x)
julia> K, = residue_field(R, x^3 + 3x + 1); a = K(x);

julia> S = matrix_space(K, 3, 3)
Matrix space of 3 rows and 3 columns
Expand Down Expand Up @@ -995,8 +993,7 @@ can_solve_left_reduced_triu{T <: RingElement}(::MatElem{T}, ::MatElem{T})
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> K, a = number_field(x^3 + 3x + 1, "a")
(Residue field of univariate polynomial ring modulo x^3 + 3*x + 1, x)
julia> K, = residue_field(R, x^3 + 3x + 1); a = K(x);

julia> S = matrix_space(K, 3, 3)
Matrix space of 3 rows and 3 columns
Expand Down Expand Up @@ -1120,8 +1117,7 @@ is_invertible{T <: RingElement}(::MatrixElem{T})
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> K, a = number_field(x^3 + 3x + 1, "a")
(Residue field of univariate polynomial ring modulo x^3 + 3*x + 1, x)
julia> K, = residue_field(R, x^3 + 3x + 1); a = K(x);

julia> S = matrix_space(K, 3, 3)
Matrix space of 3 rows and 3 columns
Expand Down Expand Up @@ -1211,8 +1207,7 @@ is_hessenberg{T <: RingElem}(::MatElem{T})
**Examples**

```jldoctest
julia> R = residue_ring(ZZ, 7)
Residue ring of integers modulo 7
julia> R, = residue_ring(ZZ, 7);

julia> S = matrix_space(R, 4, 4)
Matrix space of 4 rows and 4 columns
Expand Down
54 changes: 0 additions & 54 deletions docs/src/numberfield.md
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9 changes: 3 additions & 6 deletions docs/src/polynomial.md
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Expand Up @@ -298,8 +298,7 @@ gcdinv(f::PolyRingElem, g::PolyRingElem)
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> S = residue_ring(R, x^3 + 3x + 1)
Residue ring of univariate polynomial ring modulo x^3 + 3*x + 1
julia> S, = residue_ring(R, x^3 + 3x + 1);

julia> T, y = polynomial_ring(S, "y")
(Univariate polynomial ring in y over residue ring, y)
Expand Down Expand Up @@ -464,8 +463,7 @@ julia> S, y = polynomial_ring(R, "y")
julia> T, z = polynomial_ring(QQ, "z")
(Univariate polynomial ring in z over rationals, z)

julia> U = residue_ring(ZZ, 17)
Residue ring of integers modulo 17
julia> U, = residue_ring(ZZ, 17);

julia> V, w = polynomial_ring(U, "w")
(Univariate polynomial ring in w over residue ring, w)
Expand Down Expand Up @@ -859,8 +857,7 @@ julia> S, y = polynomial_ring(R, "y")
julia> T, z = polynomial_ring(QQ, "z")
(Univariate polynomial ring in z over rationals, z)

julia> U = residue_ring(T, z^3 + 3z + 1)
Residue ring of univariate polynomial ring modulo z^3 + 3*z + 1
julia> U, = residue_ring(T, z^3 + 3z + 1);

julia> V, w = polynomial_ring(U, "w")
(Univariate polynomial ring in w over residue ring, w)
Expand Down
23 changes: 8 additions & 15 deletions docs/src/residue.md
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Expand Up @@ -46,8 +46,9 @@ residue_field(R::Ring, m::RingElem; cached::Bool = true)
```

Given a base ring `R` and residue $m$ contained in this ring, return the parent object
of the residue ring $R/(m)$. By default the parent object `S` will depend only on `R`
and `m` and will be cached. Setting the optional argument `cached` to `false` will
of the residue ring $R/(m)$ together with the canonical projection. By default
the parent object `S` will depend only on `R` and `m` and will be cached.
Setting the optional argument `cached` to `false` will
prevent the parent object `S` from being cached.

The `residue_field` constructor does the same thing as the `residue_ring` constructor,
Expand All @@ -71,8 +72,7 @@ resulting parent objects to coerce various elements into the residue ring.
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> S = residue_ring(R, x^3 + 3x + 1)
Residue ring of univariate polynomial ring modulo x^3 + 3*x + 1
julia> S, = residue_ring(R, x^3 + 3x + 1);

julia> f = S()
0
Expand Down Expand Up @@ -174,8 +174,7 @@ modulus(::ResElem)
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> S = residue_ring(R, x^3 + 3x + 1)
Residue ring of univariate polynomial ring modulo x^3 + 3*x + 1
julia> S, = residue_ring(R, x^3 + 3x + 1);

julia> f = S(x + 1)
x + 1
Expand Down Expand Up @@ -229,8 +228,7 @@ Base.inv(::ResElem)
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> S = residue_ring(R, x^3 + 3x + 1)
Residue ring of univariate polynomial ring modulo x^3 + 3*x + 1
julia> S, = residue_ring(R, x^3 + 3x + 1);

julia> f = S(x + 1)
x + 1
Expand All @@ -252,8 +250,7 @@ gcd{T <: RingElem}(::ResElem{T}, ::ResElem{T})
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> S = residue_ring(R, x^3 + 3x + 1)
Residue ring of univariate polynomial ring modulo x^3 + 3*x + 1
julia> S, = residue_ring(R, x^3 + 3x + 1);

julia> f = S(x + 1)
x + 1
Expand Down Expand Up @@ -304,18 +301,14 @@ rand(R::ResidueRing, v...)
**Examples**

```jldoctest; setup = :(import Random; Random.seed!(42))
julia> R = residue_ring(ZZ, 7)
Residue ring of integers modulo 7
julia> R, = residue_ring(ZZ, 7);

julia> f = rand(R, 0:6)
4

julia> S, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> U = residue_field(S, x^3 + 3x + 1)
Residue field of univariate polynomial ring modulo x^3 + 3*x + 1

julia> g = rand(S, 2:2, -10:10)
-1//4*x^2 - 2//7*x + 1
```
3 changes: 1 addition & 2 deletions docs/src/total_fraction.md
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Expand Up @@ -265,8 +265,7 @@ rand(R::TotFracRing, v...)
**Examples**

```jldoctest; setup = :(import Random; Random.seed!(42))
julia> R = residue_ring(ZZ, 12)
Residue ring of integers modulo 12
julia> R, = residue_ring(ZZ, 12);
julia> K = total_ring_of_fractions(R)
Total ring of fractions of Residue ring of integers modulo 12
Expand Down
2 changes: 1 addition & 1 deletion docs/src/types.md
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Expand Up @@ -34,7 +34,7 @@ corresponding to the ring $\mathbb{Z}/7\mathbb{Z}$. We then create a new element
of this ring by calling the parent object `R`.

```julia
R = residue_ring(ZZ, 7)
R, = residue_ring(ZZ, 7)
a = R(3)
```

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8 changes: 5 additions & 3 deletions src/AbstractAlgebra.jl
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Expand Up @@ -19,7 +19,7 @@ import GroupsCore: gens, ngens, order, mul!, istrivial

# A list of all symbols external packages should not import from AbstractAlgebra
const import_exclude = [:import_exclude, :QQ, :ZZ,
:RealField, :number_field, :NumberField, :GF,
:RealField, :GF,
:AbstractAlgebra,
:inv, :log, :exp, :sqrt, :div, :divrem,
:numerator, :denominator,
Expand Down Expand Up @@ -655,6 +655,8 @@ import .Generic: dense_matrix_type
import .Generic: dim
import .Generic: disable_cache!
import .Generic: downscale
import .Generic: EuclideanRingResidueField
import .Generic: EuclideanRingResidueRing
import .Generic: enable_cache!
import .Generic: exp_gcd
import .Generic: exponent
Expand Down Expand Up @@ -716,7 +718,6 @@ import .Generic: norm
import .Generic: normal_form
import .Generic: normalise
import .Generic: num_coeff
import .Generic: number_field
import .Generic: one
import .Generic: order
import .Generic: ordering
Expand Down Expand Up @@ -861,6 +862,8 @@ export divhigh
export divides
export domain
export downscale
export EuclideanRingResidueField
export EuclideanRingResidueRing
export elem_type
export enable_cache!
export evaluate
Expand Down Expand Up @@ -1047,7 +1050,6 @@ export normalise
export nrows
export nullspace
export num_coeff
export number_field
export nvars
export O
export one
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1 change: 0 additions & 1 deletion src/Aliases.jl
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Expand Up @@ -54,7 +54,6 @@ Base.@deprecate_binding LaurentPolynomialRing laurent_polynomial_ring
Base.@deprecate_binding LaurentSeriesRing laurent_series_ring
Base.@deprecate_binding LaurentSeriesField laurent_series_field
Base.@deprecate_binding FractionField fraction_field
Base.@deprecate_binding NumberField number_field

Base.@deprecate_binding FunctionField function_field
Base.@deprecate_binding RationalFunctionField rational_function_field
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2 changes: 0 additions & 2 deletions src/Generic.jl
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Expand Up @@ -265,8 +265,6 @@ include("generic/Residue.jl")

include("generic/ResidueField.jl")

include("generic/NumberField.jl")

include("generic/Poly.jl")

include("generic/NCPoly.jl")
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39 changes: 6 additions & 33 deletions src/Matrix.jl
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Expand Up @@ -2226,21 +2226,10 @@ Return the determinant of the matrix $M$. We assume $M$ is square.
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> K, a = number_field(x^3 + 3x + 1, "a")
(Residue field of univariate polynomial ring modulo x^3 + 3*x + 1, x)

julia> S = matrix_space(K, 3, 3)
Matrix space of 3 rows and 3 columns
over residue field of univariate polynomial ring modulo x^3 + 3*x + 1

julia> A = S([K(0) 2a + 3 a^2 + 1; a^2 - 2 a - 1 2a; a^2 + 3a + 1 2a K(1)])
[ 0 2*x + 3 x^2 + 1]
[ x^2 - 2 x - 1 2*x]
[x^2 + 3*x + 1 2*x 1]
julia> A = R[x 1; 1 x^2];

julia> d = det(A)
11*x^2 - 30*x - 5

x^3 - 1
```
"""
function det(M::MatrixElem{T}) where {T <: RingElement}
Expand Down Expand Up @@ -2599,24 +2588,10 @@ Return the rank of the matrix $M$.
# Examples

```jldoctest; setup = :(using AbstractAlgebra)
julia> R, x = polynomial_ring(QQ, "x")
(Univariate polynomial ring in x over rationals, x)

julia> K, a = number_field(x^3 + 3x + 1, "a")
(Residue field of univariate polynomial ring modulo x^3 + 3*x + 1, x)

julia> S = matrix_space(K, 3, 3)
Matrix space of 3 rows and 3 columns
over residue field of univariate polynomial ring modulo x^3 + 3*x + 1

julia> A = S([K(0) 2a + 3 a^2 + 1; a^2 - 2 a - 1 2a; a^2 + 3a + 1 2a K(1)])
[ 0 2*x + 3 x^2 + 1]
[ x^2 - 2 x - 1 2*x]
[x^2 + 3*x + 1 2*x 1]
julia> A = QQ[1 2; 3 4];

julia> d = rank(A)
3

2
```
"""
function rank(M::MatrixElem{T}) where {T <: RingElement}
Expand Down Expand Up @@ -4469,8 +4444,7 @@ the resulting polynomial is an element of it.
# Examples

```jldoctest; setup = :(using AbstractAlgebra)
julia> R = residue_ring(ZZ, 7)
Residue ring of integers modulo 7
julia> R, = residue_ring(ZZ, 7);

julia> S = matrix_space(R, 4, 4)
Matrix space of 4 rows and 4 columns
Expand Down Expand Up @@ -6276,8 +6250,7 @@ preserves the minimal and characteristic polynomials of a matrix.
# Examples

```jldoctest; setup = :(using AbstractAlgebra)
julia> R = residue_ring(ZZ, 7)
Residue ring of integers modulo 7
julia> R, = residue_ring(ZZ, 7);

julia> S = matrix_space(R, 4, 4)
Matrix space of 4 rows and 4 columns
Expand Down
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