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

That DE is simpler than I would have expected!

Since f(x)=x+1 can be defined by a composition of 19 instances of EML,
maybe Maxima can find a DE definition for f using it? :-)

... one reason I still strongly doubt that EML has any practical or
theoretical interest.




On Thu, Apr 30, 2026, 21:29 Henry Baker <[email protected]> wrote:

> 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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