Hey all,
So, I'm making progress on p-adics and power series, though slowly. A
couple of questions about unifying the terminology.
1. There are numerous possibilities for talking about the various
types of precision (eg precision, relative precision, modulus,
big_oh...). There are two concepts that we need to label with these
terms: the precision of the unit part and the ideal of the ring that
we're working modulo. For example, 3^3+3^5+O(3^7) would have
precisions 4 and 7. I have been using the terms "precision" for the
first part and "modulus" for the second, but I'm not convinced that
this is the right choice because the term "precision" is fairly well
entrenched in the power series world as the second. So if "precision"
is the second, perhaps we can use "relative precision" for the first.
What do people think?
2. A second issue arises with extension fields. In a tower of fields
(or rings), we want to have functions that return the field immediately
below the current one, as well as the field at the bottom of the tower.
We were considering using "ground field" and "base field" ("ground
ring" and "base ring"), but base ring is used in power series to mean
the coefficient ring. How about "ground field" and "rock bottom field"
("ground ring" and "rock bottom ring")? Also, should the function
names in the field and ring cases differ or should we call them both
ring extensions?
3. There are a couple of functions in the current implementations of
p-adics and power series that I don't think make all that much sense to
be there, given their nonexact nature (also because I'm making power
series immutable). In particular, I would like to delete
additive_order, multiplicative_order, is_zero from padics and
__setitem__ from power series.
David
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