#11457: Witt Vectors
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Reporter: tdupu | Owner: roed
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.11
Component: padics | Resolution:
Keywords: witt vectors, padic, rings | Merged in:
Authors: Taylor Dupuy, David Roe | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Comment (by darij):
Hi Taylor,
> 1) Implementing a division by p^n function. This is just a morphism of
modules from p^{n} R to R/ann(p^{n} ) .
>
> 2) Implementing a lifting function. If R has the form A/p^n A then we
would like a function which takes elements of A to elements in A/p^{n+1} A
.
I don't think any of these would help compute Witt vector addition over an
arbitrary commutative ring. When you take ghost components over a ring in
which p is a zero-divisor, you lose information; you can't gain it back by
lifting as far as I know.
What I meant by "big Witt vectors" are Witt vectors that are not p-typical
(Section 9 of Hazewinkel). We should be able to use some of the extensive
symmetric functions implementation we have in Sage (including Witt
coordinates since #14775). While I'd love to play around with Witt-
Burnside, too, I don't know enough about this generalization to implement
it well (though I can learn).
When you say "specifying a particular p", does p mean the polynomial or
the prime? It might be interesting to do it on a generic polynomial,
though I wasn't thinking of that; having addition, negation and
multiplication would already be a wonderful start.
Best regards,\\
Darij
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Ticket URL: <http://trac.sagemath.org/ticket/11457#comment:14>
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