Prefer symbols for VarNames over strings (#1804)

docs/src/fraction.md

@@ -62,7 +62,7 @@ resulting parent objects to coerce various elements into the fraction field.
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(ZZ, "x")
+julia> R, x = polynomial_ring(ZZ, :x)
 (Univariate polynomial ring in x over integers, x)
 
 julia> S = fraction_field(R)
@@ -93,7 +93,7 @@ FactoredFractionField(R::Ring; cached::Bool = true)
 **Examples**
 
 ```jldoctest
-julia> R, (x, y) = polynomial_ring(ZZ, ["x", "y"])
+julia> R, (x, y) = polynomial_ring(ZZ, [:x, :y])
 (Multivariate polynomial ring in 2 variables over integers, AbstractAlgebra.Generic.MPoly{BigInt}[x, y])
 
 julia> S = FactoredFractionField(R)
@@ -137,7 +137,7 @@ fraction field without constructing the fraction field parent first.
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(QQ, "x")
+julia> R, x = polynomial_ring(QQ, :x)
 (Univariate polynomial ring in x over rationals, x)
 
 julia> S = fraction_field(R)
@@ -185,7 +185,7 @@ characteristic is not known an exception is raised.
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(QQ, "x")
+julia> R, x = polynomial_ring(QQ, :x)
 (Univariate polynomial ring in x over rationals, x)
 
 julia> S = fraction_field(R)
@@ -242,7 +242,7 @@ denominator(a::FracElem)
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(QQ, "x")
+julia> R, x = polynomial_ring(QQ, :x)
 (Univariate polynomial ring in x over rationals, x)
 
 julia> S = fraction_field(R)
@@ -286,7 +286,7 @@ gcd{T <: RingElem}(::FracElem{T}, ::FracElem{T})
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(QQ, "x")
+julia> R, x = polynomial_ring(QQ, :x)
 (Univariate polynomial ring in x over rationals, x)
 
 julia> f = (x + 1)//(x^3 + 3x + 1)
@@ -313,7 +313,7 @@ Base.sqrt(::FracElem{T}) where {T <: RingElem}
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(QQ, "x")
+julia> R, x = polynomial_ring(QQ, :x)
 (Univariate polynomial ring in x over rationals, x)
 
 julia> S = fraction_field(R)
@@ -346,7 +346,7 @@ valuation{T <: RingElem}(::FracElem{T}, ::T)
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(ZZ, "x")
+julia> R, x = polynomial_ring(ZZ, :x)
 (Univariate polynomial ring in x over integers, x)
 
 julia> f = (x + 1)//(x^3 + 3x + 1)
@@ -381,7 +381,7 @@ Rationals
 julia> f = rand(K, -10:10)
 -1//3
 
-julia> R, x = polynomial_ring(ZZ, "x")
+julia> R, x = polynomial_ring(ZZ, :x)
 (Univariate polynomial ring in x over integers, x)
 
 julia> S = fraction_field(R)

docs/src/free_associative_algebra.md

@@ -52,7 +52,7 @@ the parent object `S` from being cached.
 **Examples**
 
 ```jldoctest
-julia> R, (x, y) = free_associative_algebra(ZZ, ["x", "y"])
+julia> R, (x, y) = free_associative_algebra(ZZ, [:x, :y])
 (Free associative algebra on 2 indeterminates over integers, AbstractAlgebra.Generic.FreeAssociativeAlgebraElem{BigInt}[x, y])
 
 julia> (x + y + 1)^2
@@ -73,7 +73,7 @@ with coefficients and monomial words and not exponent vectors.
 **Examples**
 
 ```jldoctest
-julia> R, (x, y, z) = free_associative_algebra(ZZ, ["x", "y", "z"])
+julia> R, (x, y, z) = free_associative_algebra(ZZ, [:x, :y, :z])
 (Free associative algebra on 3 indeterminates over integers, AbstractAlgebra.Generic.FreeAssociativeAlgebraElem{BigInt}[x, y, z])
 
 julia> B = MPolyBuildCtx(R)
@@ -141,7 +141,7 @@ exponent_word(a::Generic.FreeAssociativeAlgebraElem{T}, i::Int) where T <: RingE
 **Examples**
 
 ```jldoctest
-julia> R, (x, y, z) = free_associative_algebra(ZZ, ["x", "y", "z"])
+julia> R, (x, y, z) = free_associative_algebra(ZZ, [:x, :y, :z])
 (Free associative algebra on 3 indeterminates over integers, AbstractAlgebra.Generic.FreeAssociativeAlgebraElem{BigInt}[x, y, z])
 
 julia> map(total_degree, (R(0), R(1), -x^2*y^2*z^2*x + z*y))
@@ -190,7 +190,7 @@ exponent_words(a::FreeAssociativeAlgebraElem{T}) where T <: RingElement
 **Examples**
 
 ```jldoctest
-julia> R, (a, b, c) = free_associative_algebra(ZZ, ["a", "b", "c"])
+julia> R, (a, b, c) = free_associative_algebra(ZZ, [:a, :b, :c])
 (Free associative algebra on 3 indeterminates over integers, AbstractAlgebra.Generic.FreeAssociativeAlgebraElem{BigInt}[a, b, c])
 
 julia> collect(terms(3*b*a*c - b + c + 2))
@@ -245,8 +245,9 @@ The implementation uses a non-commutative version of the Buchberger algorithm as
 **Examples**
 
 ```jldoctest; setup = :(using AbstractAlgebra)
-julia> R, (x, y, u, v, t, s) = free_associative_algebra(GF(2), ["x", "y", "u", "v", "t", "s"])
-(Free associative algebra on 6 indeterminates over finite field F_2, AbstractAlgebra.Generic.FreeAssociativeAlgebraElem{AbstractAlgebra.GFElem{Int64}}[x, y, u, v, t, s])
+julia> R = @free_associative_algebra(GF(2), [:x, :y, :u, :v, :t, :s])
+Free associative algebra on 6 indeterminates x, y, u, v, ..., s
+  over finite field F_2
 
 julia> g = Generic.groebner_basis([u*(x*y)^3 + u*(x*y)^2 + u + v, (y*x)^3*t + (y*x)^2*t + t + s])
 5-element Vector{AbstractAlgebra.Generic.FreeAssociativeAlgebraElem{AbstractAlgebra.GFElem{Int64}}}:
@@ -260,7 +261,7 @@ julia> g = Generic.groebner_basis([u*(x*y)^3 + u*(x*y)^2 + u + v, (y*x)^3*t + (y
 In order to check whether a given element of the algebra is in the ideal generated by a Groebner 
 basis `g`, one can compute its normal form.
 ```jldoctest; setup = :(using AbstractAlgebra)
-julia> R, (x, y, u, v, t, s) = free_associative_algebra(GF(2), ["x", "y", "u", "v", "t", "s"]);
+julia> R = @free_associative_algebra(GF(2), [:x, :y, :u, :v, :t, :s]);
 
 julia> g = Generic.groebner_basis([u*(x*y)^3 + u*(x*y)^2 + u + v, (y*x)^3*t + (y*x)^2*t + t + s]);
 

docs/src/function_field.md

@@ -50,7 +50,7 @@ resulting parent objects to coerce various elements into the function field.
 **Examples**
 
 ```jldoctest
-julia> S, x = rational_function_field(QQ, "x")
+julia> S, x = rational_function_field(QQ, :x)
 (Rational function field over rationals, x)
 
 julia> f = S()
@@ -68,7 +68,7 @@ x + 1
 julia> m = S(numerator(x + 1, false), numerator(x + 2, false))
 (x + 1)//(x + 2)
 
-julia> R, (x, y) = rational_function_field(QQ, ["x", "y"])
+julia> R, (x, y) = rational_function_field(QQ, [:x, :y])
 (Rational function field over rationals, AbstractAlgebra.Generic.RationalFunctionFieldElem{Rational{BigInt}, AbstractAlgebra.Generic.MPoly{Rational{BigInt}}}[x, y])
 
 julia> (x + y)//y^2
@@ -85,7 +85,7 @@ We give some examples of such functionality.
 **Examples**
 
 ```jldoctest
-julia> S, x = rational_function_field(QQ, "x")
+julia> S, x = rational_function_field(QQ, :x)
 (Rational function field over rationals, x)
 
 julia> f = S(x + 1)
@@ -147,7 +147,7 @@ gcd(::Generic.RationalFunctionFieldElem{T, U}, ::Generic.RationalFunctionFieldEl
 **Examples**
 
 ```jldoctest
-julia> R, x = rational_function_field(QQ, "x")
+julia> R, x = rational_function_field(QQ, :x)
 (Rational function field over rationals, x)
 
 julia> f = (x + 1)//(x^3 + 3x + 1)
@@ -174,7 +174,7 @@ Base.sqrt(::Generic.RationalFunctionFieldElem{T, U}) where {T <: FieldElem, U <:
 **Examples**
 
 ```jldoctest
-julia> R, x = rational_function_field(QQ, "x")
+julia> R, x = rational_function_field(QQ, :x)
 (Rational function field over rationals, x)
 
 julia> a = (21//4*x^6 - 15*x^5 + 27//14*x^4 + 9//20*x^3 + 3//7*x + 9//10)//(x + 3)
@@ -281,16 +281,16 @@ examples of such functionality.
 **Examples**
 
 ```jldoctest
-julia> R, x = rational_function_field(GF(23), "x") # characteristic p
+julia> R, x = rational_function_field(GF(23), :x) # characteristic p
 (Rational function field over finite field F_23, x)
 
-julia> U, z = R["z"]
+julia> U, z = R[:z]
 (Univariate polynomial ring in z over rational function field, z)
 
 julia> g = z^2 + 3z + 1
 z^2 + 3*z + 1
 
-julia> S, y = function_field(g, "y")
+julia> S, y = function_field(g, :y)
 (Function Field over finite field F_23 with defining polynomial y^2 + 3*y + 1, y)
 
 julia> f = (x + 1)*y + 1
@@ -357,16 +357,16 @@ num_coeff(::Generic.FunctionFieldElem, ::Int)
 **Examples**
 
 ```jldoctest
-julia> R, x = rational_function_field(QQ, "x")
+julia> R, x = rational_function_field(QQ, :x)
 (Rational function field over rationals, x)
 
-julia> U, z = R["z"]
+julia> U, z = R[:z]
 (Univariate polynomial ring in z over rational function field, z)
 
 julia> g = z^2 + 3*(x + 1)//(x + 2)*z + 1
 z^2 + (3*x + 3)//(x + 2)*z + 1
 
-julia> S, y = function_field(g, "y")
+julia> S, y = function_field(g, :y)
 (Function Field over rationals with defining polynomial (x + 2)*y^2 + (3*x + 3)*y + x + 2, y)
 
 julia> base_field(S)
@@ -420,16 +420,16 @@ norm(::Generic.FunctionFieldElem)
 ```
 
 ```jldoctest
-julia> R, x = rational_function_field(QQ, "x")
+julia> R, x = rational_function_field(QQ, :x)
 (Rational function field over rationals, x)
 
-julia> U, z = R["z"]
+julia> U, z = R[:z]
 (Univariate polynomial ring in z over rational function field, z)
 
 julia> g = z^2 + 3*(x + 1)//(x + 2)*z + 1
 z^2 + (3*x + 3)//(x + 2)*z + 1
 
-julia> S, y = function_field(g, "y")
+julia> S, y = function_field(g, :y)
 (Function Field over rationals with defining polynomial (x + 2)*y^2 + (3*x + 3)*y + x + 2, y)
 
 julia> f = (-3*x - 5//3)//(x - 2)*y + (x^3 + 1//9*x^2 + 5)//(x - 2)

docs/src/ideal.md

@@ -60,7 +60,7 @@ contain duplicates, zero entries or be empty.
 **Examples**
 
 ```jldoctest
-julia> R, (x, y) = polynomial_ring(ZZ, ["x", "y"]; internal_ordering=:degrevlex)
+julia> R, (x, y) = polynomial_ring(ZZ, [:x, :y]; internal_ordering=:degrevlex)
 (Multivariate polynomial ring in 2 variables over integers, AbstractAlgebra.Generic.MPoly{BigInt}[x, y])
 
 julia> V = [3*x^2*y - 3*y^2, 9*x^2*y + 7*x*y]
@@ -92,7 +92,7 @@ gens(::Generic.Ideal{T}) where T <: RingElement
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(ZZ, "x")
+julia> R, x = polynomial_ring(ZZ, :x)
 (Univariate polynomial ring in x over integers, x)
 
 julia> V = [1 + 2x^2 + 3x^3, 5x^4 + 1, 2x - 1]
@@ -128,7 +128,7 @@ intersect(::Generic.Ideal{T}, ::Generic.Ideal{T}) where T <: RingElement
 **Examples**
 
 ```jldoctest
-julia> R, x = polynomial_ring(ZZ, "x")
+julia> R, x = polynomial_ring(ZZ, :x)
 (Univariate polynomial ring in x over integers, x)
 
 julia> V = [1 + 2x^2 + 3x^3, 5x^4 + 1, 2x - 1]
@@ -170,7 +170,7 @@ normal_form(::U, ::Generic.Ideal{U}) where {T <: RingElement, U <: Union{PolyRin
 **Examples**
 
 ```jldoctest
-julia> R, (x, y) = polynomial_ring(ZZ, ["x", "y"]; internal_ordering=:degrevlex)
+julia> R, (x, y) = polynomial_ring(ZZ, [:x, :y]; internal_ordering=:degrevlex)
 (Multivariate polynomial ring in 2 variables over integers, AbstractAlgebra.Generic.MPoly{BigInt}[x, y])
 
 julia> V = [3*x^2*y - 3*y^2, 9*x^2*y + 7*x*y]

docs/src/index.md

@@ -57,7 +57,7 @@ This example makes use of multivariate polynomials.
 ```julia
 using AbstractAlgebra
 
-R, (x, y, z) = polynomial_ring(ZZ, ["x", "y", "z"])
+R, (x, y, z) = polynomial_ring(ZZ, [:x, :y, :z])
 
 f = x + y + z + 1
 
@@ -73,11 +73,11 @@ using AbstractAlgebra
 
 R = GF(7)
 
-S, y = polynomial_ring(R, "y")
+S, y = polynomial_ring(R, :y)
 
 T, = residue_ring(S, y^3 + 3y + 1)
 
-U, z = polynomial_ring(T, "z")
+U, z = polynomial_ring(T, :z)
 
 f = (3y^2 + y + 2)*z^2 + (2*y^2 + 1)*z + 4y + 3;
 
@@ -95,7 +95,7 @@ Here is an example using matrices.
 ```julia
 using AbstractAlgebra
 
-R, x = polynomial_ring(ZZ, "x")
+R, x = polynomial_ring(ZZ, :x)
 
 S = matrix_space(R, 10, 10)
 
@@ -109,9 +109,9 @@ And here is an example with power series.
 ```julia
 using AbstractAlgebra
 
-R, x = QQ["x"]
+R, x = QQ[:x]
 
-S, t = power_series_ring(R, 30, "t")
+S, t = power_series_ring(R, 30, :t)
 
 u = t + O(t^100)
 

docs/src/laurent_mpolynomial.md

@@ -104,7 +104,7 @@ $\prod_i x_i^{n_i}$ from the normalized representation. In particular,
 this means that the output of `gcd` will not have any negative exponents.
 
 ```jldoctest
-julia> R, (x, y) = laurent_polynomial_ring(ZZ, ["x", "y"]);
+julia> R, (x, y) = laurent_polynomial_ring(ZZ, [:x, :y]);
 
 julia> canonical_unit(2*x^-5 - 3*x + 4*y^-4 + 5*y^2)
 -x^-5*y^-4

docs/src/laurent_polynomial.md

@@ -41,7 +41,7 @@ Laurent polynomials implement the ring interface, and some methods
 from the polynomial interface, for example:
 
 ```jldoctest
-julia> R, x = laurent_polynomial_ring(ZZ, "x")
+julia> R, x = laurent_polynomial_ring(ZZ, :x)
 (Univariate Laurent polynomial ring in x over integers, x)
 
 julia> var(R)