First examples of trace.

NumberFields/NumberFields.m2

@@ -4,7 +4,8 @@ newPackage(
         Date => "June 1, 2024",
     	Authors => {{}},
     	Headline => "number fields",
-	PackageImports => {}
+	PackageImports => {}, 
+	PackageExports => {"PushForward"}
 	)
 
 export{
@@ -47,4 +48,5 @@ numberFieldExtension(RingMap) := opts -> phi1 -> (
 
 end
 
-loadPackage ("NumberFields", Reload=>true)
+loadPackage ("NumberFields", Reload=>true)
+

NumberFields/trace.m2

@@ -0,0 +1,18 @@
+loadPackage ("NumberFields", Reload=>true)
+
+R = QQ[]
+S = QQ[x]/(x^6+x^5+x^4+x^3+x^2+x+1)
+S = QQ[x]/(x^3-2)
+S = QQ[x,y]/(x^3-2, y^2+y+1)
+
+phi = map(S, R)
+myList = pushFwd phi
+elementOverR = myList#2
+
+myMatrix = elementOverR(x^2)
+
+A = map(S^1, S^1, {{x^3}}) -- ^1 turns a ring into a rank-one module, ^2 turns it into a rank-two module, etc.
+pushFwd(map(S^1, S^1, {{x^2}}))
+trace pushFwd(map(S^1, S^1, {{1_S}}))
+
+degree(myList#0)