>> Great to hear it. As noted on the ideas page, this one will require a
>> good deal of thought to be done in the application, so let's start
>> discussing.

Thanks a lot, and sorry for the late reply

>> Another thing I'd like to know is if there's literature on solving
>> algorithms, particularly solving transcendental equations, and very
>> particularly on if there are any complete algorithms out there for
>> some class of equations.

I found a old paper called "SOLVING SYMBOLIC EQUATIONS WITH PRESS"
http://www.research.ed.ac.uk/portal/files/413486/Solving_Symbolic_Equations_%20with_PRESS.pdf

>> Do we know how other computer algebra systems solve this problem?  How 
>> robust are the algorithms behind wolframalpha.com ?

I have found another paper "A Review of Symbolic Solvers"
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.44.9444&rep=rep1&type=pdf
and according to it Mathematica performs performs pretty bad.

>> An audit of the current solve code might be in order. In particular,
>> I'd like to know:
>>
>> 1. what are the different "solvers"? (if we split solve into "hints"
>> like with dsolve, these would be the different hints), and
>> 2. which are algorithmically complete (i.e., we know they will give
>> all solutions, or they can detect somehow if they may have missed
>> one)?
>>
>> And this may raise auxiliary questions, like:
>>
>> - to what degree can the different solvers be separated? For instance,
>> one solver (I'm not sure if it's actually implemented) would use
>> decompose() to solve recursively. How would such "recursive solvers"
>> look in a hints system?
>>
>> - of those that are heuristic (not algorithmically complete), can they
>> be improved?

I'm going through the solvers code and will answer these questions soon.

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