Notebooks in Sphinx?
Converting the notebooks to ReST with nbconvert, then using sphinx on the .rst files gives a pretty decent effect, except that the title levels are off a little. I need to look into hosting for the notebooks, maybe on MS Azure. In the meantime, I prefer the HTML made by Sphinx to the HTML made by nbconvert directly. It has index and cross refs and the code blocks scroll horizontally which is crucial for wide Joy traces. And Garamond. God bless Garamond. For the Sphinx docs I'm going to edit the notebook ReST files by hand, diverging from the originals.
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`Quadratic formula <https://en.wikipedia.org/wiki/Quadratic_formula>`__
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=======================================================================
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.. code:: ipython2
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from notebook_preamble import J, V, define
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Cf.
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`jp-quadratic.html <http://www.kevinalbrecht.com/code/joy-mirror/jp-quadratic.html>`__
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::
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-b +/- sqrt(b^2 - 4 * a * c)
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-----------------------------
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2 * a
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:math:`\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}`
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Write a straightforward program with variable names.
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====================================================
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::
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b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
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Check it.
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~~~~~~~~~
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::
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b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
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-b b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
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-b b^2 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
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-b b^2 4ac - sqrt [+] [-] cleave a 2 * [truediv] cons app2
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-b b^2-4ac sqrt [+] [-] cleave a 2 * [truediv] cons app2
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-b sqrt(b^2-4ac) [+] [-] cleave a 2 * [truediv] cons app2
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-b -b+sqrt(b^2-4ac) -b-sqrt(b^2-4ac) a 2 * [truediv] cons app2
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-b -b+sqrt(b^2-4ac) -b-sqrt(b^2-4ac) 2a [truediv] cons app2
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-b -b+sqrt(b^2-4ac) -b-sqrt(b^2-4ac) [2a truediv] app2
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-b -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a
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Codicil
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~~~~~~~
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::
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-b -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a roll< pop
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-b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a -b pop
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-b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a
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Derive a definition.
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====================
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::
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b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2 roll< pop
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b [neg] dupdip sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2 roll< pop
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b a c [[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2 roll< pop
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b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truediv] cons app2 roll< pop
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b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truediv] cons app2 roll< pop
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.. code:: ipython2
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define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truediv] cons app2 roll< pop')
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.. code:: ipython2
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J('3 1 1 quadratic')
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.. parsed-literal::
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-0.3819660112501051 -2.618033988749895
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Simplify
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~~~~~~~~
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We can define a ``pm`` plus-or-minus function:
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.. code:: ipython2
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define('pm == [+] [-] cleave popdd')
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Then ``quadratic`` becomes:
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.. code:: ipython2
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define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [truediv] cons app2')
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.. code:: ipython2
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J('3 1 1 quadratic')
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.. parsed-literal::
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-0.3819660112501051 -2.618033988749895
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Define a "native" ``pm`` function.
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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The definition of ``pm`` above is pretty elegant, but the implementation
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takes a lot of steps relative to what it's accomplishing. Since we are
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likely to use ``pm`` more than once in the future, let's write a
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primitive in Python and add it to the dictionary.
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.. code:: ipython2
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from joy.library import SimpleFunctionWrapper
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from notebook_preamble import D
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@SimpleFunctionWrapper
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def pm(stack):
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a, (b, stack) = stack
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p, m, = b + a, b - a
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return m, (p, stack)
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D['pm'] = pm
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The resulting trace is short enough to fit on a page.
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.. code:: ipython2
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V('3 1 1 quadratic')
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.. parsed-literal::
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. 3 1 1 quadratic
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3 . 1 1 quadratic
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3 1 . 1 quadratic
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3 1 1 . quadratic
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3 1 1 . over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [truediv] cons app2
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3 1 1 1 . [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [truediv] cons app2
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3 1 1 1 [[[neg] dupdip sqr 4] dipd * * - sqrt pm] . dip 2 * [truediv] cons app2
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3 1 1 . [[neg] dupdip sqr 4] dipd * * - sqrt pm 1 2 * [truediv] cons app2
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3 1 1 [[neg] dupdip sqr 4] . dipd * * - sqrt pm 1 2 * [truediv] cons app2
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3 . [neg] dupdip sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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3 [neg] . dupdip sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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3 . neg 3 sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 . 3 sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 3 . sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 3 . dup mul 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 3 3 . mul 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 9 . 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 9 4 . 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 9 4 1 . 1 * * - sqrt pm 1 2 * [truediv] cons app2
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-3 9 4 1 1 . * * - sqrt pm 1 2 * [truediv] cons app2
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-3 9 4 1 . * - sqrt pm 1 2 * [truediv] cons app2
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-3 9 4 . - sqrt pm 1 2 * [truediv] cons app2
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-3 5 . sqrt pm 1 2 * [truediv] cons app2
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-3 2.23606797749979 . pm 1 2 * [truediv] cons app2
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-0.7639320225002102 -5.23606797749979 . 1 2 * [truediv] cons app2
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-0.7639320225002102 -5.23606797749979 1 . 2 * [truediv] cons app2
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-0.7639320225002102 -5.23606797749979 1 2 . * [truediv] cons app2
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-0.7639320225002102 -5.23606797749979 2 . [truediv] cons app2
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-0.7639320225002102 -5.23606797749979 2 [truediv] . cons app2
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-0.7639320225002102 -5.23606797749979 [2 truediv] . app2
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[-0.7639320225002102] [2 truediv] . infra first [-5.23606797749979] [2 truediv] infra first
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-0.7639320225002102 . 2 truediv [] swaack first [-5.23606797749979] [2 truediv] infra first
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-0.7639320225002102 2 . truediv [] swaack first [-5.23606797749979] [2 truediv] infra first
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-0.3819660112501051 . [] swaack first [-5.23606797749979] [2 truediv] infra first
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-0.3819660112501051 [] . swaack first [-5.23606797749979] [2 truediv] infra first
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[-0.3819660112501051] . first [-5.23606797749979] [2 truediv] infra first
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-0.3819660112501051 . [-5.23606797749979] [2 truediv] infra first
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-0.3819660112501051 [-5.23606797749979] . [2 truediv] infra first
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-0.3819660112501051 [-5.23606797749979] [2 truediv] . infra first
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-5.23606797749979 . 2 truediv [-0.3819660112501051] swaack first
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-5.23606797749979 2 . truediv [-0.3819660112501051] swaack first
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-2.618033988749895 . [-0.3819660112501051] swaack first
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-2.618033988749895 [-0.3819660112501051] . swaack first
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-0.3819660112501051 [-2.618033988749895] . first
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-0.3819660112501051 -2.618033988749895 .
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