Using smart-phone to do complex arithmetics
Offline mode:
Nowadays, our smart-phones can do very complex mathematics offline. For example, arbitrary-precision complex-number arithmetics, numeric differentiation/integration, symbolic differentiation/integration, linear algebra, etc.
The image to the left illustrates calculating sin(sqrt(π-ⅈ)) up to 1000 digits for both the real and imaginary part.
The image in the middle illustrates numerical differentiation (the diff function), numerical integration (the quad function), symbolic integration (the sympy.integrate function), symbolic differentiation (the sympy.diff function).
The image to the right illustrates arbitrary-precision complex-number matrix functions and Eigen decomposition of a 2x2 complex matrix.
In addition to all standard maths functions such as pow, abs, exp, log, sin, cos, tan, sinh, cosh, tanh, asin, acos, atan, asinh, acosh, atanh, atan2, etc, it can even compute numerous special functions, e.g., Riemann zeta function ζ(z), gamma function Γ(z), poly-gamma function ψ(m)(z), Bessel functions Jα(z), Yα(z), Legendre functions, Elliptic functions (http://mpmath.org/doc/current/functions/elliptic.html), etc.
This is truly amazing!!!
Online mode:
Apart from doing offline arithmetic, our smart-phone can connect to server and view all running jobs wherever you are as long as you have Wifi or cellular data.
The above screenshot illustrates viewing jobs running on server while watching an MP4 video (of Project DIVA ^_^) on the smartphone
I remember that in the ancient times, mathematicians had been spending very long time calculating π up to many decimal points. For example, Ludolph van Ceulen spent a major part of his life calculating the numerical value of π. After his death, the value of π up to 35 decimal points was engraved on his tombstone in Leiden. Today, everyone can use their mobile smart-phone to compute much more complex arithmetic up to much greater precision. How big science and technology leap this is!
Declarations:
All screenshots are obtained on my Samsung Galaxy S7 using the Android App called Termux (I used the hacker's keyboard App). You can use GNURoot Debian as well.
Under Termux, you need to install packages such as python, openssh, python packages like mpmath (thanks to Fredrik Johansson), numpy, sympy.
However, to know whether the same is also achievable on an iPhone, you have to consult IOS experts-:)