gh-35485: New comparison mode to lazy series and better undefined check
<!-- Please provide a concise, informative and self-explanatory title.
-->
<!-- Don't put issue numbers in the title. Put it in the Description
below. -->
<!-- For example, instead of "Fixes #12345", use "Add a new method to
multiply two integers" -->
### :books: Description
<!-- Describe your changes here in detail. -->
<!-- Why is this change required? What problem does it solve? -->
<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes #12345". -->
<!-- If your change requires a documentation PR, please link it
appropriately. -->
This fixes #35071 by:
1. providing a method to streams to see if they are unitinalized
2. includes a new mode for comparisons in the lazy series ring based on
the proposal in #35429.
The new comparison mode `secure` simply returns `False` when it cannot
verify that `f == g` and makes sure that `(f == g) == not (f != g)`, and
this will become the new default. In particular, it will return `True`
for `f != g` both when it cannot show that `f == g` and when they are
genuinely different. In order to verify when the comparison is unknown,
we expose the `is_nonzero()` that only returns `True` when the series is
_known_ to be nonzero. Thus, we verify by `(f - g).is_nonzero()`.
When a finite halting precision is given, then that takes priority.
For the infinite halting precision in the "old" version (`secure =
True`), it will raise a `ValueError` when it cannot verify the result.
**NOTE:** `f.is_zero()` is still the default `not f` for speed and the
assumption these are in agreement elsewhere in Sage.
### :memo: Checklist
<!-- Put an `x` in all the boxes that apply. It should be `[x]` not `[x
]`. -->
- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation accordingly.
### :hourglass: Dependencies
<!-- List all open PRs that this PR logically depends on
- #12345: short description why this is a dependency
- #34567: ...
-->
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
URL: https://github.com/sagemath/sage/pull/35485
Reported by: Travis Scrimshaw
Reviewer(s): Martin Rubey, Travis Scrimshaw
