More slide stuff

src/teaching/cse-562/2021sp/index.erb

@@ -17,6 +17,8 @@ schedule:
       slides: slide/2021-02-09-RA-Basics-and-Spark.html
   - date: "Feb. 11"
     topic: "Relational Algebra Equivalence Rules"
+    materials:
+      slides: slide/2021-02-11-RA-Equivs.html
   - date: "Feb. 16"
     topic: "Algorithms, Checkpoint 1"
     due: "Checkpoint 0"

src/teaching/cse-562/2021sp/slide/2021-02-11-RA-Equivs.erb

@@ -341,6 +341,7 @@ textbook: "Ch. 16.2"
   </section>
 
   <section>
+    $$\sigma_{c}(\pi_{A}(R)) \Rightarrow \pi_{A}(\sigma_{c}(R))$$
     <pre><code class="scala">
   plan.transform {
     case Filter(condition, Project(columns, child)) => 
@@ -376,9 +377,10 @@ textbook: "Ch. 16.2"
 
   <section>
     <h3>Spark</h3>
-
+    
+    $$\sigma_c(R \cup S) \Rightarrow (\sigma_c(R)) \cup (\sigma_c(R))$$
     <pre><code class="scala">
-  plan.transform {
+  plan.transformDown {
     case Filter(condition, Union(children)) => 
       Union(
         children.map { child =>