Fix some docs typos (#1803)

Author: lgoettgens

docs/src/manual/number_fields/fields.md

@@ -20,8 +20,8 @@ number_field(::DocuDummy2)
 ```
 
 !!! tip
-    Many of the constructors have arguments of type `Symbol` or
-    `AbstractString`.  If used, they define the appearance in printing, and
+    Many of the constructors have arguments of type `VarName`.
+    If used, they define the appearance in printing, and
     printing only.  The named parameter `check` can be `true` or `false`, the
     default being `true`.  This parameter controls whether the polynomials
     defining the number field are tested for irreducibility or not. Given that

docs/src/manual/number_fields/intro.md

@@ -4,7 +4,7 @@ CurrentModule = Hecke
 
 # [Introduction](@id NumberFieldsLink)
 
-By definition, mathematically a number field is just a finite extension of the rational $\mathbf{Q}$.
+By definition, mathematically a number field is just a finite extension of the rationals $\mathbf{Q}$.
 In Hecke, a number field $L$ is recursively defined as being the field of rational numbers $\mathbf{Q}$ or
 a finite extension of a number field $K$. In the second case, the extension
 can be defined in the one of the following two ways:

src/NumField/Field.jl

@@ -104,7 +104,7 @@ is_simple(a::NumField)
 
 @doc doc"""
     number_field(f::Poly{NumFieldElem}, s::VarName;
-                cached::Bool = false, check::Bool = false) -> NumField, NumFieldElem
+                cached::Bool = false, check::Bool = true) -> NumField, NumFieldElem
 
 Given an irreducible polynomial $f \in K[x]$ over some number field $K$, this
 function creates the simple number field $L = K[x]/(f)$ and returns $(L, b)$,
@@ -135,7 +135,7 @@ number_field(::DocuDummy)
 
 @doc (@doc _doc_stub_nf)
 number_field(f::PolyRingElem{<: NumFieldElem}, s::VarName;
-            cached::Bool = false, check::Bool = false)
+            cached::Bool = false, check::Bool = true)
 
 ################################################################################
 #

src/NumField/SimpleNumField/Field.jl

@@ -204,7 +204,7 @@ is_isomorphic_with_map(::SimpleNumField, ::SimpleNumField)
     is_linearly_disjoint(K::SimpleNumField, L::SimpleNumField) -> Bool
 
 Given two number fields $K$ and $L$ with the same base field $k$, this function
-returns whether $K$ and $L$ are linear disjoint over $k$.
+returns whether $K$ and $L$ are linearly disjoint over $k$.
 """
 is_linearly_disjoint(K::SimpleNumField, L::SimpleNumField)