[FRIAM] Euler's Identity in 3

[Marcus Daniels]

Or,

$ ginsh
ginsh - GiNaC Interactive Shell (GiNaC V1.7.11)
  __,  _______  Copyright (C) 1999-2020 Johannes Gutenberg University Mainz,
 (__) *       | Germany.  This is free software with ABSOLUTELY NO WARRANTY.
  ._) i N a C | You are welcome to redistribute it under certain conditions.
<-------------' For details type `warranty;'.

Type ?? for a list of help topics.
> exp(Pi*I);
-1
>

-----Original Message-----
From: Friam <friam-bounces at redfish.com> On Behalf Of u?l? ???
Sent: Tuesday, March 9, 2021 12:55 PM
To: FriAM <friam at redfish.com>
Subject: [FRIAM] Euler's Identity in 3

So, I'm trying to learn Rust. And in thinking about the ontological status of mathematical representations of waves (https://arxiv.org/abs/2101.10873), I figured I'd validate Euler's identity:

fn main() {
  let e = num::complex::Complex::new(std::f32::consts::E,0.);
  let e2ip = e.powc(num::complex::Complex::new(0.,std::f32::consts::PI));
  let i = num::complex::Complex::new(0.,1.);
  println!("ln(e^iπ) = {}",e2ip.ln());
  println!("ln(-1) = {}", i.powi(2).ln()); } $ cargo run
ln(e^iπ) = 0+3.1415925i
ln(-1) = 0+3.141592653589793i

I don't have any idea if that's a reasonable way to do that, since I'm ignorant of Rust. But it's interesting to contrast it with R and Sage:

$ Rscript -e "log(exp(1)^((0+1i)*pi));log((0+1i)^2)"
[1] 0+3.141593i
[1] 0+3.141593i

sage: numerical_approx(ln(e^(i*pi)));numerical_approx(ln(i^2))
3.14159265358979*I
3.14159265358979*I

The precision difference between the 2 results in Rust is interesting. It's the same if I use powf() instead of powi(). Any clues? Or should I simply RTFM?

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