Merge branch 'master' into lg/rename-number-of

Nemocas · Jan 23, 2024 · bff0247 · bff0247
2 parents ce4e503 + 5a441df
commit bff0247
Show file tree

Hide file tree

Showing 36 changed files with 405 additions and 477 deletions.
diff --git a/docs/make.jl b/docs/make.jl
@@ -46,7 +46,6 @@ makedocs(
                  "function_field.md",
                  "finfield.md",
                  "real.md",
-                 "numberfield.md",
              ],
              "Groups" => [
                  "perm.md",

diff --git a/docs/src/constructors.md b/docs/src/constructors.md
@@ -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])`   |
@@ -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
 

diff --git a/docs/src/index.md b/docs/src/index.md
@@ -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")
 

diff --git a/docs/src/matrix.md b/docs/src/matrix.md
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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

diff --git a/docs/src/numberfield.md b/docs/src/numberfield.md
diff --git a/docs/src/polynomial.md b/docs/src/polynomial.md
@@ -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)
@@ -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)
@@ -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)

diff --git a/docs/src/residue.md b/docs/src/residue.md
@@ -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,
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
 ```
diff --git a/docs/src/total_fraction.md b/docs/src/total_fraction.md
@@ -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

diff --git a/docs/src/types.md b/docs/src/types.md
@@ -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)
 ```
 

diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
@@ -16,7 +16,7 @@ using Test # for "interface-conformance" functions
 
 # 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,
@@ -677,6 +677,8 @@ 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
@@ -737,7 +739,6 @@ 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
@@ -883,6 +884,8 @@ export divhigh
 export divides
 export domain
 export downscale
+export EuclideanRingResidueField
+export EuclideanRingResidueRing
 export elem_type
 export enable_cache!
 export evaluate
@@ -1071,7 +1074,6 @@ export normal_form
 export normalise
 export nullspace
 export num_coeff
-export number_field
 export O
 export one
 export order

diff --git a/src/Aliases.jl b/src/Aliases.jl
@@ -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

diff --git a/src/Generic.jl b/src/Generic.jl
@@ -266,8 +266,6 @@ include("generic/Residue.jl")
 
 include("generic/ResidueField.jl")
 
-include("generic/NumberField.jl")
-
 include("generic/Poly.jl")
 
 include("generic/NCPoly.jl")

diff --git a/src/Matrix.jl b/src/Matrix.jl
@@ -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}
@@ -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}
@@ -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
@@ -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