On 2013-05-15, Bill Eaton <wpeaton4 at gmail.com> wrote:
> It would be really handy if I could teach Maxima the various properties of
> logarithms and inverse logarithms. My interest is base 10, but it seems that
> it would be fairly generic for other integer bases.
That's a useful & interesting idea, but it isn't easy in Maxima. One
would have to create simplification rules for all properties of
interest, perhaps observing the same flags as for the built-in log.
It is likely that some interesting properties of built-in log are
implicit in the way that it is treated by functions such as 'solve' or
'integrate'. The only way to get base-10 log to inherit those (short of
reimplementing all the functions of interest) is to convert from base-10
log to natural log, apply the function, and try to convert back
afterwards.
The claim about the natural log being more fundamental and therefore
preferable is mistaken -- for one thing, Maxima has already quite a
collection of conveniences and shortcuts. More fundamentally,
mathematics is just logic applied to some collection of assumptions.
Maxima would be more powerful if it could be less invested in any
given assumptions, and more flexible about introducing new ones which
are suitable for a particular problem domain. As it stands, it's
somewhat messy to extend or retract Maxima's mathematical knowledge.
That is a bug, not a feature.
best
Robert Dodier