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@@ -10,9 +10,9 @@ Cf.
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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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-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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@@ -28,21 +28,21 @@ a definition without them.
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::
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b neg
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b neg
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``sqrt(b^2 - 4 * a * c)``
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~~~~~~~~~~~~~~~~~~~~~~~~~
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::
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b sqr 4 a c * * - sqrt
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b sqr 4 a c * * - sqrt
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``/2a``
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~~~~~~~
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::
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a 2 * /
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a 2 * /
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``±``
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~~~~~
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@@ -52,14 +52,14 @@ replaces them with their sum and difference.
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::
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pm == [+] [-] cleave popdd
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pm == [+] [-] cleave popdd
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Putting Them Together
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~~~~~~~~~~~~~~~~~~~~~
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::
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b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
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b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
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We use ``app2`` to compute both roots by using a quoted program
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``[2a /]`` built with ``cons``.
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@@ -72,20 +72,20 @@ the variables:
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::
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b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
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b [neg] dupdip sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
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b a c [[neg] dupdip sqr 4] dipd * * - sqrt pm a 2 * [/] cons app2
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b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
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b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
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b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
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b [neg] dupdip sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
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b a c [[neg] dupdip sqr 4] dipd * * - sqrt pm a 2 * [/] cons app2
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b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
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b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
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The three arguments are to the left, so we can "chop off" everything to
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the right and say it's the definition of the ``quadratic`` function:
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The three arguments are to the left, so we can “chop off” everything to
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the right and say it’s the definition of the ``quadratic`` function:
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.. code:: ipython2
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define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
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Let's try it out:
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Let’s try it out:
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.. code:: ipython2
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