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