Sage cannot simplify sums of logarithms

[sagetrac-whuss]

Currently there is no direct way in Sage to apply the transformation:

log(x) + log(y) -> log(x*y)

The attached patch fixes this by inserting a call to logcontract()
in the definition of simplify_radical.

Now the following works:

sage: f = log(sqrt(2) - 1) + log(sqrt(2) + 1)
sage: f.simplify_full()
0

But I'm not sure if this is the right place for this.

CC: @sagetrac-fmaltey

Component: calculus

Keywords: logarithm

Author: Robert Mařík

Reviewer: Karl-Dieter Crisman

Merged: sage-4.3.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7334

[sagetrac-whuss]

Attachment: trac-7334-logcontract.patch.gz

[kcrisman]

comment:2

Hey, I love this idea! And the code seems fine on the face of it.

But probably it makes the most sense to make it separately available as a simplification, i.e. make a new method .simplify_log() or something. Exposing as many of these as possible is good for the (many) users who keep one wanting some, but not all simplifications, which I think is something people really like about Maxima (from reading their lists).

Anyway, then you could just call this wherever you think is best in the definition of .simplify_full(), which certainly should have this included. And one would want a (perhaps slightly complicated) example added to simplify_full() which shows that it's used correctly there as well.

[robert-marik]

comment:3

I also think that it is better to keep the function logcontract separately from simplify_full() since sometimes the contraction of logarithms is not what user wants. Consider please also option which allows to set logconfcoef as described in Maxima. This allows to contract expressions like log(x)+1/2log(8) into log(xsqrt(8)).

[robert-marik]

comment:4

Replying to @kcrisman:

Anyway, then you could just call this wherever you think is best in the definition of .simplify_full(), which certainly should have this included.

Do not do it please. The user knows if he/she wants to contract logarithms or not and then he/she can run the coresponding method. If you include this as an automatical simplification in simplify_full, consider the following

• domain of log(1-x)+log(1+x) is different from domain of log(1-x^2)

• you should add a function which expands logarithms

Thanks
Robert

[robert-marik]

comment:5

Attached new patch, apply only this patch.

Options which controls if simplify expressions like 1/2*log(x) or not has been introduced.

simplify_log now does not use radcan, it calls only logcontract in Maxima session. However, there are many aliases for radcan:
radical_simplify, simplify_radical, exp_simplify, simplify_exp