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

This is still a silly thing to do, but if you want to replace all additions
with additions of 2 items, then
consider this..

bplus([r]):= if length(r)>2 then bplus(first(r),apply(bplus,rest(r))) else
'bplus(first(r),second(r));

subst(bplus,?mplus,  your_expression);  or some such..  I tried this and
had to do ev(%),
but other hacks should work.




On Sun, May 3, 2026 at 12:33 PM Henry Baker <[email protected]> wrote:

> OK, I looked at the Python3 code for the EML compiler, and it looks like
> it would be trivial to translate its formulae into Maxima using pattern
> matching.
>
> For example, here are some of the Python3 functions:
>
> def EML(a, b): return f"EML[{a},{b}]"
> def eml_exp(z): return EML(z, "1") # Exp[z]
> def eml_log(z): return EML("1", eml_exp(EML("1", z))) # Log[z]
> def eml_zero(): return eml_log("1") # 0 = Log[1]
> def eml_sub(a, b): return EML(eml_log(a), eml_exp(b)) # a - b
> def eml_neg(z): return eml_sub(eml_zero(), z) # -z
> def eml_add(a, b): return eml_sub(a, eml_neg(b)) # a + b
> def eml_inv(z): return eml_exp(eml_neg(eml_log(z))) # 1/z
> def eml_mul(a, b): return eml_exp(eml_add(eml_log(a), eml_log(b))) # a*b
> def eml_div(a, b): return eml_mul(a, eml_inv(b)) # a/b
> def eml_pow(a, b): return eml_exp(eml_mul(b, eml_log(a))) # a^b
> def eml_one(): return "1"
> def eml_two(): return eml_add("1", "1")
> def eml_double(z): return eml_add(z, z)
>
> Thus, in Maxima
> matchdeclare(z,all);
> tellsimp(exp(z),EML(z,1));
> tellsimp(log(z),EML(1,exp(EML(1,z))));
>
> However, such a pattern-matching compiler would have a bigger problem with
> sums and products, and an even bigger problem with converting constants --
> e.g., integers, rationals, floats.
>
> The good news: EML compiling and simplification provide a pretty decent
> workout for Maxima, and would likely make some pretty good test cases
> and/or benchmarks.
>
> -----Original Message-----
> From: Henry Baker <[email protected]>
> Sent: May 2, 2026 8:53 AM
> To: Przemek Klosowski via Maxima-discuss <
> [email protected]>
> Subject: Re: [Maxima-discuss] [EXTERNAL] Re: 1-button calculator ~ "all
> elementary fns from a single operator"
>
> OK, I downloaded the "EML compiler" from here:
>
> https://github.com/VA00/SymbolicRegressionPackage/tree/master
>
> The EML compiler requires python3 &amp; numpy (and probably other stuff
> that I might already have installed).
>
> I then did a trivial script to convert from Mathematica expressions to
> Maxima expressions.
>
> EML requires that log(0)=minf, so I defined mylog(x):=if (x=0) then minf
> else log(x), and used mylog(x) instead of log(x) in the definition of eml.
>
> However, I now require that %e^minf = 0.
>
> What is the magic in Maxima to make this happen? I did "? minf", but that
> didn't provide any help.
>
> -----Original Message-----
> From: Henry Baker
> Sent: May 1, 2026 11:23 AM
> To: Przemek Klosowski via Maxima-discuss
> Subject: Re: [Maxima-discuss] [EXTERNAL] Re: 1-button calculator ~ "all
> elementary fns from a single operator"
>
> Obviously, Google was confused.
>
> Q: If z = exp(x)-log(y), then x = log(z + log(y)) might look a tad better
> ? Is this log(z+log(y)) function universal in the same sense as eml() ?
>
> Q: if we have a 1BC expression for f(x)=y, can we then trivially compute
> x=f^-1(y) ?
>
> Q: The 1BC paper seems to want to rely on functions defined over the
> reals; I suspect that functions defined over the complex numbers might give
> additional 1BC results that might be prettier ? Perhaps the constant %pi*%i
> might work to force things into the complex plane ?
>
> Q: I've always had a fondness for asinh(x), as it is bijective onto the
> reals, and has many of the same properties/characteristics as "gradual
> underflow" floating point numbers. I'm wondering if it could be part of a
> universal 1BC function ?
>
> -----Original Message-----
> From: Przemek Klosowski via Maxima-discuss
> Sent: May 1, 2026 9:24 AM
> To:
> Subject: Re: [Maxima-discuss] [EXTERNAL] Re: 1-button calculator ~ "all
> elementary 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)
>
> (%i1) eq:'diff(y,x)=y*exp(x);
> dy x
> (%o1) ── = %e y
> dx
> (%i2) ode2(eq,y,x);
> x
> %e
> (%o2) y = %e %c
>
> what am I missing?
>
>
>
> _______________________________________________
> Maxima-discuss mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>
>
>
>
> _______________________________________________
> Maxima-discuss mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>
>
>
>
> _______________________________________________
> Maxima-discuss mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>
>
>
>
> _______________________________________________
> Maxima-discuss mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>

_______________________________________________
Maxima-discuss mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/maxima-discuss