Started to add implementations of basic methods

* compositums
* degree of a number field

NumberFields/NumberFields.m2

@@ -14,6 +14,7 @@ export{
    "NumberFieldExtension",
    "numberFieldExtension",
    "isGalois",
+--   "degreeNF",
 };
 
 NumberField = new Type of Ring
@@ -33,6 +34,30 @@ numberField(RingElement) := opts -> f1 -> (
 	new NumberField from toField (R1/ideal(f1))
 )
 
+numberField(Ring) := opts -> R1 -> (
+
+
+    if not isPrime (ideal 0_R1) then error("Expected a field.");
+    if not dim R1 == 0 then error("Expected a field.");
+
+	if char R1 != 0 then error("Expected characteristic 0.");
+
+    flattenedR1 := (flattenRing(R1))#0;
+    iota := map(flattenedR1,QQ);
+    try pushFwd(iota) else error("Not finite dimensional over QQ");
+
+	new NumberField from toField (flattenedR1)
+)
+
+
+--degreeNF = method(Options => {})
+--degreeNF(NumberField) := opts -> nf -> (
+--
+--    iota := map(nf,QQ);
+--
+--    degree((pushFwd(iota))#0)
+--)
+
 NumberFieldExtension = new Type of HashTable
 
 numberFieldExtension = method(Options => {})
@@ -50,3 +75,23 @@ end
 
 loadPackage ("NumberFields", Reload=>true)
 
+--compositums = method(Options => {})
+--compusitums(NumberField,NumberField) := opts -> (K1,K2) -> (
+--    T := K1 ** K2;
+--
+--    -- compositums correspond to prime ideals
+--    II := primaryDecomposition (ideal 0_T);
+--
+--    -- quotient rings
+--    QRs := apply(II, I -> T / I);
+--
+--    -- make them number field objects?
+--    NFs := apply(QRs, qr -> numberField(qr));
+--
+--    -- calculate degrees
+--
+--    -- sort by degree
+--
+--    -- get maps from K1 & K2
+--
+--)