>In what situations would algexact:true lead %solve to actually yield worse-looking solutions? (If ever.)
Globally setting algexact to true is fairly safe, I think. I considered making algexct true at the top-level to_poly_solve
functions, but for reasons I cannot completely recall, I decided not to do it. Likley I found a few cases that worked better
with algexact false.
(%i1) ?? algexact;
-- Option variable: algexact
Default value: `false'
`algexact' affects the behavior of `algsys' as follows:
If `algexact' is `true', `algsys' always calls `solve' and then
uses `realroots' on `solve''s failures.
If `algexact' is `false', `solve' is called only if the eliminant
was not univariate, or if it was a quadratic or biquadratic.
Thus `algexact: true' does not guarantee only exact solutions,
just that `algsys' will first try as hard as it can to give exact
solutions, and only yield approximations when all else fails.