Re: Simplifying Units in Ezunits Package

Hello everyone,

Your message, Michael, is very interesting. Thank you for sharing it. I’m
also reading the posts in the thread “ezunits fundamental_units quite slow”
with great interest, and I’m curious to see the outcome.

I came across an example where a single "apply1(expr, rfoo)" wasn't enough.
The denominator of this equation requires more than one iteration to be
fully simplified:

(%i6)   I_1: 0.1 `nA;
        I_2: 0.5 `mA;
        I_3: 0.4 `nA;
        R_1: 2 `kOhm;
        V_1: 0.2 `kOhm*nA;
        expr: I_1/((I_2 + I_3)*R_1 + V_1);

(expr)  0.1 ` nA/((0.5 ` mA+0.4 ` nA)*(2 ` kOhm)+0.2 ` kOhm*nA)

(%i7)   apply1(expr, rfoo);
(%o7)   0.1 ` nA/(0.2 ` kOhm*nA+0.0010000008 ` A*kOhm)

(%i8)  apply1(%, rfoo) ``1/GOhm;
(%o8)   0.0999999000001 ` 1/GOhm

To simplify this process, I wrote a very short function that calls
"apply1(expr, rfoo)" in a loop until the next result matches the previous
one, assuming this is the simplest expression possible.
Maybe someone will find it useful:

simplify_units(expr) :=
    block ([previous, current : expr],
        previous = false,
        while not (current = previous) do (
            previous : current,
            current : apply1(current, rfoo)),
        current)$

This could surely be improved. Perhaps it would be worth adding the maximum
possible number of iterations.

I also measured the execution time of the methods of simplifying the
example expression from the beginning of the mail. All of them succeeded.
- Function "to_si()" provided by Serge: 5.35 s
- Function "simplify_units()" which calls Robert's original "apply1(expr,
rfoo)" function: 4 s
- Function "simplify_units()" calling modified "apply1(expr, rfoo)"
function, where "fundamental_units" is replaced with "units" as suggested
by Michael: 3.21 s
Yes, my old laptop is slow =)

Best regards,
Mateusz

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