log10, was: bug report, or am I doing something wrong?

It seems pretty obvious that defining log10(x) as log(x)/log(10) solves most 
of the
problems, and in fact that is what the commercial macsyma does.

Oh, consider  the simplification problem of  log10(x)- log(x)/log(10).  How 
do
you know that is zero?  One term must be simplified to the other.

It might be worthwhile to point out to readers of this newsgroup,
and maybe Luke's friends at school,  that Maxima doesn't really
like to use division.  x/y  internally is much more like

x * (y)^(-1).

Why?
Because redundant operations cause problems.  Introducing log10 is a
bad idea for that reason.

This is not an "absolute truth" ... it is a judgment call.
Whether sec(x) should immediately be converted to 1/cos(x), or kept around
for a while in that form is puzzle. Trigsimp() has to decide.
RJF




----- Original Message ----- 
From: "Robert Dodier" <robert.dodier at gmail.com>
To: <macrakis at alum.mit.edu>
Cc: "Luke Sharkey" <99LSharkey at ormskirk.lancs.sch.uk>; 
<maxima at math.utexas.edu>
Sent: Monday, February 13, 2006 8:03 AM
Subject: Re: [Maxima] log10, was: bug report, or am I doing something wrong?


> hello stavros,
>
>> Understood, but that means you lose all of Maxima's "knowledge" about
>> logs.  You would presumably want log10(a*b) to simplify to
>> log10(a)+log10(b), etc., which would mean duplicating the log
>> simplifier.  You would want logcontract, integrate, limit, realpart,
>> etc. to operate on log10.  You would want comparison to know that
>> log10(x)<log(x) when x>1, etc. etc.
>
> yeah. well, it could happen with sufficient effort, but
> i'm not willing to invest the weeks or months necessary,
> so it won't happen any year soon ...
>
> best
> robert
>
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