Golden ratio/Convergence: Difference between revisions

=={{header|Maxima}}==

<syntaxhighlight lang="maxima">

iterate(phi) := 1 + (1 / phi)$

phi0: 1$

phi1: iterate(phi0)$

for n: 1 step 1 while abs(phi1 - phi0) > 1e-5 do

block(phi0: phi1, phi1: iterate(phi0), iterations: n + 1)$

display (float(phi1))$

display (iterations)$

display (float(phi1 - (0.5 * (1 + sqrt(5)))))$</syntaxhighlight>

{{out}}

<pre>$ maxima -b golden_ratio_convergence.mac

Maxima 5.46.0 https://maxima.sourceforge.io

using Lisp SBCL 2.3.4

Distributed under the GNU Public License. See the file COPYING.

Dedicated to the memory of William Schelter.

The function bug_report() provides bug reporting information.

(%i1) batch("golden_ratio_convergence.mac")

read and interpret /long-boring-pathname/golden_ratio_convergence.mac

(%i2) iterate(phi):=1+1/phi

(%i3) phi0:1

(%i4) phi1:iterate(phi0)

(%i5) for n while abs(phi1-phi0) > 1.0e-5 do

block(phi0:phi1,phi1:iterate(phi0),iterations:n+1)

(%i6) display(float(phi1))

987

float(---) = 1.618032786885246

610

(%i7) display(iterations)

iterations = 14

(%i8) display(float(phi1-0.5*(1+sqrt(5))))

987

float(--- - 0.5 (sqrt(5) + 1)) = - 1.201864648914253e-6

610

(%o9) /long-boring-pathname/golden_ratio_convergence.mac

</pre>