Unified interface for constructors containing variable names (#1360)

Nemocas · Nov 22, 2023 · 562f826 · 562f826
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diff --git a/docs/src/constructors.md b/docs/src/constructors.md
@@ -44,7 +44,7 @@ For example, to create a parent object for univariate polynomials over the integ
 we use the `polynomial_ring` parent object constructor.
 
 ```julia
-R, x = polynomial_ring(ZZ, "x")
+R, x = polynomial_ring(ZZ, :x)
 f = x^3 + 3x + 1
 g = R(12)
 ```
@@ -57,19 +57,36 @@ $12$ to an element of the polynomial ring $\mathbb{Z}[x]$.
 For convenience, we provide a list of all the parent object constructors in
 AbstractAlgebra.jl and explain what mathematical domains they represent.
 
-| Mathematics                      | AbstractAlgebra.jl constructor              |
-|----------------------------------|---------------------------------------------|
-| $R = \mathbb{Z}$                 | `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)`                   |
-| $S = R[x]$                       | `S, x = polynomial_ring(R, "x")`            |
-| $S = R[x, y]$                    | `S, (x, y) = polynomial_ring(R, ["x", "y"])`|
-| $S = R[[x]]$ (to precision $n$)  | `S, x = power_series_ring(R, n, "x")`       |
-| $S = R((x))$ (to precision $n$)  | `S, x = laurent_series_ring(R, n, "x")`     |
-| $S = K((x))$ (to precision $n$)  | `S, x = laurent_series_field(K, n, "x")`    |
-| $S = \mathrm{Frac}_R$            | `S = fraction_field(R)`                     |
-| $S = R/(f)$                      | `S = residue_ring(R, f)`                    |
-| $S = R/(f)$ (with $(f)$ maximal) | `S = residue_field(R, f)`                   |
-| $S = \mathrm{Mat}_{m\times n}(R)$| `S = matrix_space(R, m, n)`                 |
-| $S = \mathbb{Q}[x]/(f)$          | `S, a = number_field(f, "a")`               |
+| Mathematics                          | AbstractAlgebra.jl constructor                        |
+|:-------------------------------------|:------------------------------------------------------|
+| $R = \mathbb{Z}$                     | `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)`                             |
+| $S = R[x]$                           | `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])`   |
+| $S = K(x)$                           | `S, x = rational_function_field(K, :x)`               |
+| $S = K(x, y)$                        | `S, (x, y) = rational_function_field(K, [:x, :y])`    |
+| $S = R[[x]]$ (to precision $n$)      | `S, x = power_series_ring(R, n, :x)`                  |
+| $S = R[[x, y]]$ (to precision $n$)   | `S, (x, y) = power_series_ring(R, n, [:x, :y])`       |
+| $S = R((x))$ (to precision $n$)      | `S, x = laurent_series_ring(R, n, :x)`                |
+| $S = K((x))$ (to precision $n$)      | `S, x = laurent_series_field(K, n, :x)`               |
+| $S = R((x, y))$ (to precision $n$)   | `S, (x, y) = laurent_polynomial_ring(R, n, [:x, :y])` |
+| Puiseux series ring to precision $n$ | `S, x = PuiseuxSeriesRing(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)`                             |
+| $S = \mathrm{Mat}_{m\times n}(R)$    | `S = matrix_space(R, m, n)`                           |
+| $S = \mathbb{Q}[x]/(f)$              | `S, a = number_field(f, :a)`                          |
+
+## Parent objects with variable names
+
+The multivariate parent object constructors (`polynomial_ring`, `power_series_ring`, `free_associative_algebra`, `laurent_polynomial_ring`, and `rational_function_field`) share a common interface for specifying the variable names, which is provided by `@varnames_interface`.
+
+```@docs
+AbstractAlgebra.@varnames_interface
+AbstractAlgebra.variable_names
+AbstractAlgebra.reshape_to_varnames
+```
diff --git a/docs/src/mpoly_interface.md b/docs/src/mpoly_interface.md
@@ -79,17 +79,10 @@ and floating point types.
 
 To construct a multivariate polynomial ring, there is the following constructor.
 
-```julia
-polynomial_ring(R::Ring, s::Vector{<:VarName}; ordering=:lex, cached::Bool=true)
+```@docs; canonical=false
+polynomial_ring(R::Ring, s::Vector{Symbol})
 ```
 
-Return a tuple, `S, vars` consisting of a polynomial ring $S$ and an array of
-generators (variables) which print according to the strings in the supplied
-vector $s$. The ordering can at present be `:lex`, `:deglex` or `:degrevlex`.
-By default, the polynomial ring is cached, and creating a polynomial ring with
-the same data will return the same ring object $S$. If this caching is not
-desired, it can be switched off by setting `cached=false`.
-
 Polynomials in a given ring can be constructed using the generators and basic
 polynomial arithmetic. However, this is inefficient and the following build
 context is provided for building polynomials term-by-term. It assumes the

diff --git a/docs/src/mpolynomial.md b/docs/src/mpolynomial.md
@@ -46,12 +46,14 @@ and the polynomial ring types belong to the abstract type `MPolyRing{T}`.
 ## Polynomial ring constructors
 
 In order to construct multivariate polynomials in AbstractAlgebra.jl, one must first
-construct the polynomial ring itself. This is accomplished with one of the following
+construct the polynomial ring itself. This is accomplished with the following
 constructors.
 
 ```@docs
-polynomial_ring(R::Ring, S::Vector{VarName}; cached::Bool = true, ordering::Symbol=:lex)
-polynomial_ring(R::Ring, n::Int, s::VarName; cached::Bool = false, ordering::Symbol = :lex)
+polynomial_ring(::Ring, ::Vector{Symbol})
+polynomial_ring(::Ring, ::Vararg)
+polynomial_ring(::Ring, ::Int)
+@polynomial_ring
 ```
 
 Like for univariate polynomials, a shorthand constructor is

diff --git a/docs/src/polynomial.md b/docs/src/polynomial.md
@@ -48,8 +48,8 @@ can accept any AbstractAlgebra polynomial type.
 In order to construct polynomials in AbstractAlgebra.jl, one must first construct the
 polynomial ring itself. This is accomplished with the following constructor.
 
-```@docs
-polynomial_ring(R::Ring, s::VarName; cached::Bool = true)
+```@docs; canonical=false
+polynomial_ring(R::NCRing, s::VarName; cached::Bool = true)
 ```
 
 A shorthand version of this function is provided: given a base ring `R`, we abbreviate

diff --git a/src/AbsMSeries.jl b/src/AbsMSeries.jl
@@ -214,42 +214,3 @@ when it was created.
 function rand(S::MSeriesRing, term_range, v...)
    rand(GLOBAL_RNG, S, term_range, v...)
 end
-
-###############################################################################
-#
-#   power_series_ring constructor
-#
-###############################################################################
-
-function power_series_ring(R::Ring, weights::Vector{Int}, prec::Int,
-      s::Vector{Symbol}; cached::Bool=true, model=:capped_absolute)
-   return Generic.power_series_ring(R, weights, prec, s; cached=cached, model=model)
-end
-
-function power_series_ring(R::Ring, prec::Vector{Int},
-      s::Vector{Symbol}; cached::Bool=true, model=:capped_absolute)
-   return Generic.power_series_ring(R, prec, s; cached=cached, model=model)
-end
-
-function power_series_ring(R::Ring, prec::Vector{Int},
-      s::AbstractVector{<:VarName}; cached::Bool=true, model=:capped_absolute)
-   sym = [Symbol(v) for v in s]
-   return power_series_ring(R, prec, sym; cached=cached, model=model)
-end
-
-function power_series_ring(R::Ring, weights::Vector{Int}, prec::Int,
-   s::AbstractVector{<:VarName}; cached::Bool=true, model=:capped_absolute)
-   sym = [Symbol(v) for v in s]
-   return power_series_ring(R, weights, prec, sym; cached=cached, model=model)
-end
-
-function power_series_ring(R::Ring, prec::Int,
-      s::Vector{Symbol}; cached::Bool=true, model=:capped_absolute)
-   return Generic.power_series_ring(R, prec, s; cached=cached, model=model)
-end
-
-function power_series_ring(R::Ring, prec::Int,
-      s::AbstractVector{<:VarName}; cached::Bool=true, model=:capped_absolute)
-   sym = [Symbol(v) for v in s]
-   return power_series_ring(R, prec, sym; cached=cached, model=model)
-end
diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
@@ -767,8 +767,12 @@ export _checkbounds
 export @alias
 export @attr
 export @attributes
+export @free_associative_algebra
+export @laurent_polynomial_ring
 export @perm_str
 export @polynomial_ring
+export @power_series_ring
+export @rational_function_field
 export abs_series
 export abs_series_type
 export AbsPowerSeriesRing
@@ -1229,11 +1233,22 @@ export Generic
 
 ###############################################################################
 #
-#   Polynomial Ring S, x = R["x"] syntax
+#   misc
+#
+###############################################################################
+
+include("misc/ProductIterator.jl")
+include("misc/Evaluate.jl")
+include("misc/VarNames.jl")
+
+###############################################################################
+#
+#   Polynomial Ring S, x = R[:x] syntax
 #
 ###############################################################################
 
 getindex(R::NCRing, s::VarName) = polynomial_ring(R, s)
+# `R[:x, :y]` returns `S, [x, y]` instead of `S, x, y`
 getindex(R::NCRing, s::VarName, ss::VarName...) =
    polynomial_ring(R, [Symbol(x) for x in (s, ss...)])
 
@@ -1264,15 +1279,6 @@ Base.typed_vcat(R::NCRing, args...) = _matrix(R, vcat(args...))
 _matrix(R::NCRing, a::AbstractVector) = matrix(R, length(a), isempty(a) ? 0 : 1, a)
 _matrix(R::NCRing, a::AbstractMatrix) = matrix(R, a)
 
-###############################################################################
-#
-#   misc
-#
-###############################################################################
-
-include("misc/ProductIterator.jl")
-include("misc/Evaluate.jl")
-
 ###############################################################################
 #
 #   Load error objects

diff --git a/src/FreeAssAlgebra.jl b/src/FreeAssAlgebra.jl
@@ -255,47 +255,3 @@ end
 function rand(S::FreeAssAlgebra, term_range, exp_bound, v...)
    rand(GLOBAL_RNG, S, term_range, exp_bound, v...)
 end
-
-###############################################################################
-#
-#   free_associative_algebra constructor
-#
-###############################################################################
-
-function free_associative_algebra(
-   R::Ring,
-   s::AbstractVector{<:VarName};
-   cached::Bool = true)
-
-   S = [Symbol(v) for v in s]
-   return Generic.free_associative_algebra(R, S, cached=cached)
-end
-
-function free_associative_algebra(
-   R::Ring,
-   s::Vector{Symbol};
-   cached::Bool = true)
-
-   return Generic.free_associative_algebra(R, s, cached=cached)
-end
-
-function free_associative_algebra(
-   R::Ring,
-   n::Int,
-   s::VarName;
-   cached::Bool = false)
-
-   S = [Symbol(s, i) for i in 1:n]
-   return Generic.free_associative_algebra(R, S; cached=cached)
-end
-
-function free_associative_algebra(
-   R::Ring,
-   n::Int,
-   s::Symbol=:x;
-   cached::Bool = false)
-
-   S = [Symbol(s, i) for i in 1:n]
-   return Generic.free_associative_algebra(R, S; cached=cached)
-end
-
diff --git a/src/LaurentMPoly.jl b/src/LaurentMPoly.jl
@@ -143,24 +143,18 @@ end
 ###############################################################################
 
 @doc raw"""
-    laurent_polynomial_ring(R::Ring, s::Vector{T}; cached::Bool = true) where T <: VarName
-
-Given a base ring `R` and an array of strings `s` specifying how the
-generators (variables) should be printed, return a tuple `T, (x1, x2, ...)`
-representing the new ring $T = R[x1, 1/x1, x2, 1/x2, ...]$ and the generators
-$x1, x2, ...$ of the  ring. By default the parent object `T` will
-depend only on `R` and `x1, x2, ...` and will be cached. Setting the optional
-argument `cached` to `false` will prevent the parent object `T` from being
-cached.
-"""
-function laurent_polynomial_ring(R::Ring, s::AbstractVector{<:VarName}; cached::Bool = true)
-   return Generic.laurent_polynomial_ring(R, [Symbol(v) for v in s], cached=cached)
-end
+    laurent_polynomial_ring(R::Ring, varnames...; cached::Bool = true)
 
-function laurent_polynomial_ring(R::Ring, s::Vector{Symbol}; cached::Bool = true)
-   return Generic.laurent_polynomial_ring(R, s; cached=cached)
-end
+Given a base ring `R` and variable names `varnames...`, say `:x, :y, :z`, return
+a tuple `S, x, y, z` representing the new ring $S = R[x, 1/x, y, 1/y, z, 1/z]$
+and the generators $x, y, z$ of the ring.
 
-function laurent_polynomial_ring(R::Ring, n::Int, s::VarName=:x; cached::Bool = false)
-   return Generic.laurent_polynomial_ring(R, [Symbol(s, i) for i=1:n]; cached=cached)
-end
+By default (`cached=true`), the output `S` will be cached, i.e. if
+`laurent_polynomial_ring ` is invoked again with the same arguments, the same
+(*identical*) ring is returned. Setting `cached` to `false` ensures a distinct
+new ring is returned, and will also prevent it from being cached.
+
+For information about the many ways to specify `varnames...` refer to [`polynomial_ring`](@ref) or the
+specification in [`AbstractAlgebra.@varnames_interface`](@ref).
+"""
+laurent_polynomial_ring(R::Ring, s::Vector{Symbol})