From fde2a2e1e40c1ffcc7bc51df1ac5cdd134623a12 Mon Sep 17 00:00:00 2001
From: Tibor Gruen <tibor.gruen@gmail.com>
Date: Mon, 17 Aug 2020 14:29:31 +0200
Subject: [PATCH] made an example to recreate nat trans between nine and six

---
 examples/NaturalTransformation.g | 51 ++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 examples/NaturalTransformation.g

diff --git a/examples/NaturalTransformation.g b/examples/NaturalTransformation.g
new file mode 100644
index 0000000..b1704bf
--- /dev/null
+++ b/examples/NaturalTransformation.g
@@ -0,0 +1,51 @@
+Read("CategoryOfRepresentations.g");
+
+e11 := 1;; e12 := 1;; e13 := 0;; e42 := 1;; e43 := 1;;
+
+eMat := [
+[e11, e12, e13],
+[0, e11, e12],
+[0, 0, e11],
+[0, e42, e43],
+[0, 0, e42]
+];
+#! [ [ 1, 1, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ]
+
+f11 := 1;; f12 := 0;; f13 := 1;; f33 := 0;; f43 := 1;;
+fMat := [
+[f11, f12, f13],
+[0, f11, f13],
+[0, 0, f33],
+[0, 0, f43]
+];
+#! [ [ 1, 0, 1 ], [ 0, 1, 1 ], [ 0, 0, 0 ], [ 0, 0, 1 ] ]
+
+e12 := 1;; e13 := 0;; e42 := 1;; e43 := 1;;
+f12 := 0;; f13 := -e12;; f43 := e12-e42;;
+
+eMat := [
+[0, e12, e13],
+[0, 0, e12],
+[0, 0, 0],
+[0, e42, e43],
+[0, 0, e42]
+];
+
+fMat := [
+[0, f12, -e12],
+[0, 0, -e12],
+[0, 0, 0],
+[0, 0, e12-e42]
+];
+
+eta := [
+VectorSpaceMorphism(
+nine(kq.1), HomalgMatrix(eMat, GF3), six(kq.1) ),
+VectorSpaceMorphism(
+nine(kq.2), HomalgMatrix(fMat, GF3), six(kq.2) ) ];
+ninetosix := AsMorphismInHomCategory( nine, eta, six );
+
+IsObject( nine );
+#! true
+IsMorphism( ninetosix );
+# Error
\ No newline at end of file