From f8490324ea30b3503da41257a6049a0f8c32b7e4 Mon Sep 17 00:00:00 2001
From: Nicholas Gaubatz <nickgaubatz@gmail.com>
Date: Sun, 2 Jun 2024 15:21:08 -0600
Subject: [PATCH] First examples of trace.

---
 NumberFields/NumberFields.m2 |  6 ++++--
 NumberFields/trace.m2        | 18 ++++++++++++++++++
 2 files changed, 22 insertions(+), 2 deletions(-)
 create mode 100644 NumberFields/trace.m2

diff --git a/NumberFields/NumberFields.m2 b/NumberFields/NumberFields.m2
index 28d7e87..d19095d 100755
--- a/NumberFields/NumberFields.m2
+++ b/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)
\ No newline at end of file
+loadPackage ("NumberFields", Reload=>true)
+
diff --git a/NumberFields/trace.m2 b/NumberFields/trace.m2
new file mode 100644
index 0000000..720711c
--- /dev/null
+++ b/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)
\ No newline at end of file