#11457: Witt Vectors
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Reporter: tdupu | Owner: roed
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.7
Component: padics | Resolution:
Keywords: witt vectors, padic, rings | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Taylor Dupuy, David Roe | Merged in:
Dependencies: | Stopgaps:
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Comment (by darij):
There are at least two serious issues with this implementation of Witt
vectors:
1) The Frobenius map on the Witt vectors doesn't just take the p-th power
of every coordinate. This is only true if p = 0 in the base ring.
2) The definition of Witt vector addition and multiplication through the
ghost components don't work over a ring where p isn't invertible (or at
least a non-zero divisor). This is why every time this definition is used
to actually define the Witt vectors, it is accompanied by a functoriality
condition.
I fear that fixing the issues requires rewriting the methods from scratch.
I am also wondering whether anything speaks against implementing Witt
vectors for general nests as well (including the nest of all positive
integers, leading to "big Witt vectors").
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11457#comment:8>
Sage <http://www.sagemath.org>
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