Re: 1-button calculator ~ "all elemen tary fns from a single operator"

BTW, Google just told me that the obvious differential equation for eml(x,y) is

dy/dx = y*exp(x)

I was hoping for something even simpler -- anyone ?, anyone ?

-----Original Message-----
From: Henry Baker <[email protected]>
Sent: Apr 30, 2026 6:05 PM
To: Barton Willis via Maxima-discuss <[email protected]>
Subject: [Maxima-discuss] 1-button calculator ~ "all elementary fns from a single operator"

Andrzej Odrzywołek 's paper "All elementary functions from a single operator" has been making the rounds:

https://arxiv.org/pdf/2603.21852

In his paper, Odrzywołek concludes that the binary function eml(x,y)=exp(x)-ln(y), together with the constant 1 (one), is universal for "elementary" functions (using the complex domain).

Here is a discussion of what is an "elementary" function:

https://en.wikipedia.org/wiki/Elementary_function

---
I noticed that Odrzywołek did NOT talk about derivatives or differential equations, yet isn't the notion of "elementary" tied rather tightly to 'elementary' differential equations (for a suitable definition of 'elementary' differential equation).

Thus, does Odrzywołek's "eml(x,y}" function have a suitable differential equation definition ?



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