Hmm. I've also had trouble interpreting what assume() affects, and I'm
glad to hear that I'm not the only one.  What Robert says here helps a
lot, but is there anything written anywhere else that goes into a bit
more detail?  I'm sure there's more to it than a missing filter on the
output of solve.  e.g., that doesn't explain Neal's other example:

> sage: assume(x == 1)
> sage: bool(x == 1)
> False

I do a bunch of writing down equations, stating assumptions, and
trying to prove inequalities.  Understanding what assume() does and
does not do could make my job a lot easier!

--Doug

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