Re: Re: Automatic expansion of Log[a^n] for a,n explicit positive integers?
- To: mathgroup at smc.vnet.net
- Subject: [mg28243] Re: [mg28229] Re: [mg28180] Automatic expansion of Log[a^n] for a,n explicit positive integers?
- From: Harald Anlauf <anlauf at hep.tu-darmstadt.de>
- Date: Fri, 6 Apr 2001 01:52:51 -0400 (EDT)
- References: <Pine.LNX.4.21.0104051007450.27588-100000@shell.faradic.net>
- Sender: owner-wri-mathgroup at wolfram.com
>>>>> "Chris" == Chris Johnson <cjohnson at shell.faradic.net> writes:
Chris> You could use this function:
Chris> lg[z_?IntegerQ] := Plus @@ Apply[#2 Log[#1] &, FactorInteger[z], 2]
Chris> I tried to incorporate this into the definition of Log by:
Chris> Unprotect[Log];
Chris> Log[z_?IntegerQ] := Plus @@ Apply[#2Log[#1] &, FactorInteger[z], 2];
Chris> Protect[Log];
Chris> But I get a recursion error. I hope someone else might be able to suggest
Chris> a way to avoid this. Putting Hold around the Log in the pure function
Chris> leaves the Hold in the output. I hoped I could first define
Chris> Log[z_?PrimeQ] := Log[z]
Chris> to catch the Prime case, but this also leads to recursion.
You were very close, indeed!
Mianlai Zhou <lailai at carmen.nikhef.nl> wrote me that he solved this problem
by:
Unprotect[Log]
Log[n_Integer?Positive /; !PrimeQ[n]] :=
Plus @@ (#2 Log[#1] & @@@ FactorInteger[n])
Protect[Log]
I haven't checked the performance degradation that this might involve, tho.
Cheers,
-Harald