Make Antic accept symbols and chars (Nemocas#1202)

Author: albinahlback

src/antic/nf_elem.jl

@@ -1224,22 +1224,22 @@ rand(K::AnticNumberField, r) = rand(Random.GLOBAL_RNG, K, r)
 ###############################################################################
 
 @doc Markdown.doc"""
-    NumberField(f::fmpq_poly, s::AbstractString; cached::Bool = true, check::Bool = true)
+    NumberField(f::fmpq_poly, s::Union{AbstractString, Char, Symbol};
+                cached::Bool = true, check::Bool = true)
 
 Return a tuple $R, x$ consisting of the parent object $R$ and generator $x$
 of the number field $\mathbb{Q}[x]/(f)$ where $f$ is the supplied polynomial.
 The supplied string `s` specifies how the generator of the number field
 should be printed.
 """
-function NumberField(f::fmpq_poly, s::AbstractString; cached::Bool = true, check::Bool = true)
-   S = Symbol(s)
-   parent_obj = AnticNumberField(f, S, cached, check)
+function NumberField(f::fmpq_poly, s::Union{AbstractString, Char, Symbol}; cached::Bool = true, check::Bool = true)
+   parent_obj = AnticNumberField(f, Symbol(s), cached, check)
 
    return parent_obj, gen(parent_obj)
 end
 
 @doc Markdown.doc"""
-    CyclotomicField(n::Int, s::AbstractString, t = "\$"; cached = true)
+    CyclotomicField(n::Int, s::Union{AbstractString, Char, Symbol} = "z_$n", t = "_\$"; cached = true)
 
 Return a tuple $R, x$ consisting of the parent object $R$ and generator $x$
 of the $n$-th cyclotomic field, $\mathbb{Q}(\zeta_n)$. The supplied string
@@ -1248,11 +1248,11 @@ provided, the string `t` specifies how the generator of the polynomial ring
 from which the number field is constructed, should be printed. If it is not
 supplied, a default dollar sign will be used to represent the variable.
 """
-function CyclotomicField(n::Int, s::AbstractString = "z_$n", t = "_\$"; cached = true)
-   Zx, x = PolynomialRing(FlintZZ, string(gensym()); cached = cached)
+function CyclotomicField(n::Int, s::Union{AbstractString, Char, Symbol} = "z_$n", t = "_\$"; cached = true)
+   Zx, x = PolynomialRing(FlintZZ, gensym(); cached = cached)
    Qx, = PolynomialRing(FlintQQ, t; cached = cached)
    f = cyclotomic(n, x)
-   C, g = NumberField(Qx(f), s; cached = cached, check = false)
+   C, g = NumberField(Qx(f), Symbol(s); cached = cached, check = false)
    set_special(C, :show => show_cyclo, :cyclo => n)
    return C, g
 end
@@ -1264,7 +1264,7 @@ end
 
 
 @doc Markdown.doc"""
-    CyclotomicRealSubfield(n::Int, s::AbstractString, t = "\$"; cached = true)
+    CyclotomicRealSubfield(n::Int, s::Union{AbstractString, Char, Symbol} = "(z_$n + 1/z_$n)", t = "\$"; cached = true)
 
 Return a tuple $R, x$ consisting of the parent object $R$ and generator $x$
 of the totally real subfield of the $n$-th cyclotomic field,
@@ -1274,11 +1274,11 @@ the generator of the polynomial ring from which the number field is
 constructed, should be printed. If it is not supplied, a default dollar sign
 will be used to represent the variable.
 """
-function CyclotomicRealSubfield(n::Int, s::AbstractString = "(z_$n + 1/z_$n)", t = "\$"; cached = true)
-   Zx, x = PolynomialRing(FlintZZ, string(gensym()); cached = cached)
+function CyclotomicRealSubfield(n::Int, s::Union{AbstractString, Char, Symbol} = "(z_$n + 1/z_$n)", t = "\$"; cached = true)
+   Zx, x = PolynomialRing(FlintZZ, gensym(); cached = cached)
    Qx, = PolynomialRing(FlintQQ, t; cached = cached)
    f = cos_minpoly(n, x)
-   R, a =  NumberField(Qx(f), s; cached = cached, check = false)
+   R, a =  NumberField(Qx(f), Symbol(s); cached = cached, check = false)
    set_special(R, :show => show_maxreal, :maxreal => n)
    return R, a
 end