#2972 Wrong limits involving logs

[kcrisman]

According to https://groups.google.com/forum/#!topic/sage-support/5nhGpXPyCwk :

Other examples of wrong limits with logarithm in exponent in Sage:
lim((((27(log(n,3))))/n3),n=infinity) returns 0 (Wolfram Alpha and Maple return 1).
lim((((27(log(n,3)+1)))/n3),n=infinity) returns 0 (Wolfram Alpha and Maple return 27).
lim(((27(log(n,3)+1)-1)/26+n-log(n,3)-1)/n3,n=infinity) returns 0 (Wolfram Alpha and Maple return 27/26).
Using SageMathVersion6.7, ReleaseDate:2015−05−17.

(%i3) limit( 27^(log(n)/log(3))/n^3, n, inf);
(%o3)                                  0
(%i4) limit( 27^(log(n)/log(3)+1)/n^3, n, inf);
(%o4)                                  0
(%i5) limit( ((27^(log(n)/log(3)+1)-1)/26+n-log(n)/log(3)-1)/n^3,n,inf);
(%o5)                                  0

So hopefully somehow Maxima can be "told" about certain identities about logs, at least in limits.

[Robert Dodier]

Dunno what's the cause of the errors, but, for the record, gruntz returns the same results as cited for WA & Maple.

[Dan Gildea]

Fixed in commit [461825113f3c66b7cea6b0a14d2e2f79d6da2f0b]

call radcan to handle expressions like 3*log(3)/log(27).
Incorrect result was caused by sign(log(27)-3*log(3)) => neg -- too
much confidence in result of bfloat in sign code.

[kcrisman]

Awesome! Thank you. (Though downstream not everyone is enthusiastic about radcan, hopefully nothing surprising will come up.)