I have a maxima script that generates terms where after logcontract is run I get an expression with many terms of the type
log((A^n)/(B^n))
where both A and B are non trivial expressions
how can I get maxima to rearrange this into n*log(A/B) so that I can then perform a variable substitution and factor in terms of log(A/B) ?
I explicitly need it in the form log(A/B) and not log(A)-log(B)
A and B may be assumed positive.
OK, take two. Here's another approach via pattern matching.
(%i1) matchdeclare ([aa, bb, nn], all);
(%o1) done
(%i2) defrule (mylogrule, log((bb^nn)/(aa^nn)), nn*log(bb/aa));
nn
bb bb
(%o2) mylogrule : log(----) -> log(--) nn
nn aa
aa
(%i3) log(A^4/B^4);
4
A
(%o3) log(--)
4
B
(%i4) apply1 (%o3, mylogrule);
A
(%o4) 4 log(-)
B
(%i5) log(A^k/B^k);
k
A
(%o5) log(--)
k
B
(%i6) apply1 (%o5, mylogrule);
A
(%o6) log(-) k
B
Note that apply1 finds log(...) expressions and applies the rule even in complex expressions (not just expressions where the top-level operator is log).
I wrote the rule as log(bb^nn/aa^nn) because log(aa^nn/bb^nn) comes out as -nn*log(bb/aa) ... which isn't wrong but it's inconvenient. Probably has to do with the order in which arguments are matched; I didn't investigate.
I find the following combination of logexpand (with the super option) and logcontract seems to do the job.
(%i1) log((A^n)/(B^n)), logexpand=super;
(%o1) log(A) n - log(B) n
(%i2) %, logcontract;
A
(%o2) log(-) n
B