from notebook_preamble import J, V, define
-b ± sqrt(b^2 - 4 * a * c)
--------------------------------
2 * a$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
This math translates to Joy code in a straightforward manner. We are going to use named variables to keep track of the arguments, then write a definition without them.
-b¶b negsqrt(b^2 - 4 * a * c)¶b sqr 4 a c * * - sqrt/2a¶a 2 * /±¶There is a function pm that accepts two values on the stack and replaces them with their sum and difference.
pm == [+] [-] cleave popddb neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
We use app2 to compute both roots by using a quoted program [2a /] built with cons.
Working backwards we use dip and dipd to extract the code from the variables:
b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b [neg] dupdip sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b a c [[neg] dupdip sqr 4] dipd * * - sqrt pm a 2 * [/] cons app2
b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
The three arguments are to the left, so we can "chop off" everything to the right and say it's the definition of the quadratic function:
define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
Let's try it out:
J('3 1 1 quadratic')
If you look at the Joy evaluation trace you can see that the first few lines are the dip and dipd combinators building the main program by incorporating the values on the stack. Then that program runs and you get the results. This is pretty typical of Joy code.
V('-5 1 4 quadratic')