vector/arithmetic: Add _{v,m}product_

Products of vectors and matrices respectively.  It's surprising that this
was unneeded until now based on the requirements of the projects we have
done thusfar---dot products and other features have been sufficient.

* vector/arithmetic.xml (_vproduct_, _mproduct_): New templates.
  (_vproduct, _mproduct): New functions.

core/vector/arithmetic.xml

@@ -26,9 +26,11 @@
   <import package="../base" />
   <import package="../numeric/common" />
   <import package="../numeric/minmax" />
+  <import package="list" />
 
 
 
+  <section title="Vectors">
     <!-- for the time being, the vectors must be of the same length, or the first
          vector must be the longer (otherwise the values will not properly add)
     -->
@@ -71,5 +73,104 @@
         <c:sum of="@of@" />
       </rate>
     </template>
+
+
+    \ref{_vproduct_} produces the product of two vectors:
+      $V_k = A_k B_k$.
+
+    <template name="_vproduct_"
+              desc="Vector product">
+      <param name="@vector_a@" desc="First vector" />
+      <param name="@vector_b@" desc="Second vector" />
+
+
+      <c:apply name="_vproduct"
+               vector_a="@vector_a@"
+               vector_b="@vector_b@" />
+    </template>
+
+
+    \ref{_vproduct} is its helper function for recursion.
+
+    <function name="_vproduct"
+              desc="Vector product">
+      <param name="vector_a" type="float" set="vector"
+             desc="First vector" />
+      <param name="vector_b" type="float" set="vector"
+             desc="Second vector" />
+      <param name="k" type="integer"
+             desc="Current index" />
+
+
+      <t:cons-until-empty set="vector_a" index="k" car="value_a">
+        <c:product>
+          <c:value-of name="value_a" />
+
+          <!-- TODO: TAME bug where index variables always compile to args -->
+          <c:value-of name="vector_b">
+            <c:index>
+              <c:value-of name="k" />
+            </c:index>
+          </c:value-of>
+        </c:product>
+      </t:cons-until-empty>
+    </function>
+  </section>
+
+
+
+  <section title="Matrices">
+    \ref{_mproduct_} produces the product of two matrices:
+      $M_{ij} = A_{ij} B_{ij}$.
+
+    <template name="_mproduct_"
+              desc="Matrix product">
+      <param name="@matrix_a@" desc="First matrix" />
+      <param name="@matrix_b@" desc="Second matrix" />
+
+
+      <c:apply name="_mproduct"
+               matrix_a="@matrix_a@"
+               matrix_b="@matrix_b@"
+               k="ZERO" />
+    </template>
+
+
+    \ref{_mproduct} is its helper function for recursion.
+    \ref{_vproduct_} is used to reduce the problem to the product of
+      and array of~vectors.
+
+    <function name="_mproduct"
+              desc="Matrix product">
+
+      <param name="matrix_a" type="float" set="matrix"
+             desc="First matrix" />
+      <param name="matrix_b" type="float" set="matrix"
+             desc="Second matrix" />
+      <param name="k" type="integer"
+             desc="Current index" />
+
+
+      <t:cons-until-empty set="matrix_a" index="k" car="vector_a">
+        <c:let>
+          <c:values>
+            <c:value name="vector_b" type="float" set="vector"
+                     desc="Second vector">
+              <c:value-of name="matrix_b">
+                <c:index>
+                  <c:debug-to-console>
+                    <c:value-of name="k" />
+                  </c:debug-to-console>
+                </c:index>
+              </c:value-of>
+            </c:value>
+          </c:values>
+
+          <t:vproduct vector_a="vector_a"
+                      vector_b="vector_b" />
+        </c:let>
+      </t:cons-until-empty>
+    </function>
+  </section>
 </package>