Cleaning up docs.

docs/Quadratic.rst

@@ -18,15 +18,21 @@ Cf.
 :math:`\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}`
 
 Write a straightforward program with variable names.
-====================================================
+----------------------------------------------------
 
 ::
 
     b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
 
+We use ``cleave`` to compute the sum and difference and then ``app2`` to
+finish computing both roots using a quoted program ``[2a truediv]``
+built with ``cons``.
+
 Check it.
 ~~~~~~~~~
 
+Evaluating by hand:
+
 ::
 
      b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
@@ -41,7 +47,11 @@ Check it.
     -b -b+sqrt(b^2-4ac)    -b-sqrt(b^2-4ac)    [2a truediv]         app2
     -b -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a
 
-Codicil
+(Eventually we’ll be able to use e.g. Sympy versions of the Joy commands
+to do this sort of thing symbolically. This is part of what is meant by
+a “categorical” language.)
+
+Cleanup
 ~~~~~~~
 
 ::
@@ -51,7 +61,7 @@ Codicil
        -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a
 
 Derive a definition.
-====================
+--------------------
 
 ::
 
@@ -76,13 +86,13 @@ Derive a definition.
 
 
 Simplify
-~~~~~~~~
+--------
 
 We can define a ``pm`` plus-or-minus function:
 
-.. code:: ipython2
+::
 
-    define('pm == [+] [-] cleave popdd')
+    pm == [+] [-] cleave popdd
 
 Then ``quadratic`` becomes:
 
@@ -106,22 +116,15 @@ Define a "native" ``pm`` function.
 The definition of ``pm`` above is pretty elegant, but the implementation
 takes a lot of steps relative to what it's accomplishing. Since we are
 likely to use ``pm`` more than once in the future, let's write a
-primitive in Python and add it to the dictionary.
+primitive in Python and add it to the dictionary. (This has been done
+already.)
 
 .. code:: ipython2
 
-    from joy.library import SimpleFunctionWrapper
-    from notebook_preamble import D
-    
-    
-    @SimpleFunctionWrapper
     def pm(stack):
         a, (b, stack) = stack
         p, m, = b + a, b - a
         return m, (p, stack)
-    
-    
-    D['pm'] = pm
 
 The resulting trace is short enough to fit on a page.