#26195 closed enhancement (fixed)
Tate algebras
Reported by:  caruso  Owned by:  

Priority:  major  Milestone:  sage8.5 
Component:  padics  Keywords:  
Cc:  TristanVaccon, ghThibautVerron, caruso, roed  Merged in:  
Authors:  Xavier Caruso, Thibaut Verron  Reviewers:  David Roe 
Report Upstream:  N/A  Work issues:  
Branch:  4982c7e (Commits, GitHub, GitLab)  Commit:  
Dependencies:  #26479, #26575  Stopgaps: 
Description (last modified by )
This ticket implements Tate algebras over complete discrete valuation rings/fields, together with Gröbner bases for ideals in these algebras.
See the documentation of sage.rings.tate_algebra
for details.
Change History (90)
comment:1 Changed 4 years ago by
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comment:2 Changed 4 years ago by
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comment:3 Changed 4 years ago by
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05cf041  Restriction + small fix in inverse_of_unit

comment:6 Changed 4 years ago by
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5d0e354  Fix bugs in quo_rem

comment:7 Changed 4 years ago by
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comment:8 Changed 4 years ago by
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7800393  Revert changes to .dirlocals.el

comment:12 Changed 4 years ago by
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2383ba0  Fixed tests

comment:13 Changed 4 years ago by
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comment:14 Changed 4 years ago by
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comment:15 Changed 4 years ago by
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8446736  Bug fixed in TateAlgebraTerms & more functionalities for ideals

comment:16 Changed 4 years ago by
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comment:17 Changed 4 years ago by
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comment:18 Changed 4 years ago by
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fd3bf7b  Some improvements in Buchberger algorithm

comment:19 Changed 4 years ago by
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bfddf6e  Rewrite in cython

comment:20 Changed 4 years ago by
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bc7c763  Better (?) choice of ordering of Spolynomials

comment:21 Changed 4 years ago by
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comment:22 Changed 4 years ago by
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comment:23 Changed 4 years ago by
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b00b8e0  Use directly the cython class PolyDict

comment:24 Changed 4 years ago by
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100cbb7  Fix bug in creation of elements in Tate algebras

comment:25 Changed 4 years ago by
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comment:27 Changed 4 years ago by
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0f6391a  f.residue() now returns a polynomial over the residue field

comment:28 Changed 4 years ago by
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comment:29 Changed 4 years ago by
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a5b9d36  Partial documentation of Tate algebra term elements

comment:30 Changed 4 years ago by
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comment:31 Changed 4 years ago by
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7c2ac0b  Implement a factory

comment:33 Changed 4 years ago by
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comment:34 Changed 4 years ago by
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2a4044c  Documentation for Tate terms

comment:35 Changed 4 years ago by
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d10fca9  Doctest for TateAlgebraElement __init__

comment:37 Changed 4 years ago by
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comment:39 Changed 4 years ago by
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0576cde  Shorten doctests

comment:40 Changed 4 years ago by
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53c7ed3  Typo

comment:41 Changed 4 years ago by
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fa9b86b  Merge branch 'develop' into t/26195/tate_algebras

comment:42 Changed 4 years ago by
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comment:43 Changed 4 years ago by
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ef8799f  Partial documentation for the Tate algebra monoid class

comment:44 Changed 4 years ago by
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comment:45 Changed 4 years ago by
 Cc roed added
I cc roed because, David, you might know the answer at the following question.
In this ticket, we have implemented two parents, the first one for the Tate algebra itself and the second one for the monoid of terms of the Tate Algebra. Here is a basic example:
sage: A.<x,y> = TateAlgebra(Zp(2)); A Tate Algebra in x (val >= 0), y (val >= 0) over 2adic Field with capped relative precision 20 sage: T = A.monoid_of_terms(); T Monoid of terms in x (val >= 0), y (val >= 0) over 2adic Field with capped relative precision 20
We now want to add a method for recovering A
(the Tate algebra) from T
(the monoid of terms). However a method algebra
already exists: it is inherited from sage.categories.sets_cat.Sets
and provides a very general construction of an algebra over an arbitrary set.
We believe that this general construction is not very relevant in our setting and that T.algebra()
should instead output A
. So our question is: is it allowed/appropriate to override the method algebra
(keeping in mind that it comes from the category machinery)?
In any case, we will create a method tate_algebra
but we think that having algebra
at the same time (with a different behavior) could be confusing.
comment:46 Changed 4 years ago by
Yes, you are allowed (maybe even encouraged) to override algebra
, and in this case, you should because you have a specialized implementation of the algebra.
Also, I want to just point out a common idiom that we've used is to define the monoid of monomials, then use CombinatorialFreeModule
and the category of AlgebrasWithBasis
to construct the corresponding algebra by implementing product_on_basis
. Although this has been known to have some issues with overhead due to the number of indirections (which can be mitigated by directly implementing the multiplication in the element class), and this might not work for what you need.
comment:47 Changed 4 years ago by
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comment:49 Changed 4 years ago by
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52b9ad1  Documentation of Buchberger's function

comment:50 Changed 4 years ago by
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comment:51 Changed 4 years ago by
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408512d  Normalize output of groebner_basis

comment:53 Changed 4 years ago by
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 Status changed from new to needs_review
comment:54 Changed 4 years ago by
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65e7edb  Add doctest to the method dotprod

comment:55 Changed 4 years ago by
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4966e04  Uncapitalize error messages

comment:56 Changed 4 years ago by
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0c8f801  Small fixes after patchbot's review

comment:57 Changed 4 years ago by
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comment:58 Changed 4 years ago by
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comment:59 Changed 4 years ago by
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7c4b4ae  Address David's comments on Zulip

comment:60 Changed 4 years ago by
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6227937  Accelerate (?) square roots and nth roots

comment:62 Changed 4 years ago by
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comment:63 Changed 4 years ago by
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5f64c3a  Small improvement

comment:64 Changed 4 years ago by
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a064d26  Add a special case in __pow__ when the exponent is a rational number

comment:65 Changed 4 years ago by
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comment:66 Changed 4 years ago by
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comment:67 Changed 4 years ago by
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comment:68 Changed 4 years ago by
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comment:69 Changed 4 years ago by
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comment:70 Changed 4 years ago by
I wanted to point out a couple of points:
 for the methods
log
andexp
, I essentially copy the code insage.rings.padics.padic_element_generic
; so I wonder if it would be a good idea to factorize this code. One solution would be to split the current classpAdicElementGeneric
into two parts (e.gpAdicElementGeneric
andpAdicNumberGeneric
), the second one inheriting from the first one, and let Tate series derive from the most general one.
 in the method
lift_to_precision
, I defined a nested functionlift_without_error
but I think it would be better to add a keyword argumentno_error
(or something like that) tolift_to_precision
(for padic number); what's your opinion?
comment:71 Changed 4 years ago by
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comment:72 Changed 4 years ago by
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comment:73 Changed 4 years ago by
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comment:74 Changed 4 years ago by
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comment:75 Changed 4 years ago by
 Dependencies changed from #26479 to #26479, #26575
comment:76 Changed 4 years ago by
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Branch pushed to git repo; I updated commit sha1. New commits:
724bc71  Allow ... at beginning of doctest output

0fa318f  No longer substitute for ... inside ....:, fix doctests

f02ffa1  Merge branch 'develop' into t/26575/ellipses

fc8df57  Replace back <ELLIPSIS_TAG> by ... in exc_msg

bad89d2  Merge branch 't/26575/ellipses' into t/26195/tate_algebras

d8c17c9  Remove parentheses and fix bigoh notation in doctests

comment:77 Changed 4 years ago by
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comment:78 Changed 4 years ago by
 Reviewers set to David Roe
 Status changed from needs_review to positive_review
Looks good!
comment:79 Changed 4 years ago by
 Milestone changed from sage8.4 to sage8.5
comment:80 Changed 4 years ago by
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 Resolution set to fixed
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comment:81 Changed 4 years ago by
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Tate algebras elements are now among the 10 files having the most failures with python3. See #26212.
EDIT: And this is also bad:
sage t long src/sage/rings/tate_algebra_ideal.pyx # 29 doctests failed
One example of failure: bad use of range:
File "sage/rings/tate_algebra_ideal.pyx", line 83, in sage.rings.tate_algebra_ideal._groebner_basis_buchberger (build/cythonized/sage/rings/tate_algebra_ideal.c:3488) indices = range(l) TypeError: Expected list, got range
Other failure: change dict while iterating over this dict:
File "sage/rings/tate_algebra_element.pyx", line 1151, in sage.rings.tate_algebra_element.TateAlgebraElement._normalize (build/cythonized/sage/rings/tate_algebra_element.c:12421) for (e,c) in self._poly.__repn.items(): RuntimeError: dictionary changed size during iteration
comment:82 Changed 4 years ago by
python3 problems are fixed in #26692, please review
comment:83 Changed 4 years ago by
Sorry about that! I didn't see any py3 failures on the patchbot, so I thought it was okay. I've got a py3 build, so I'll try to check big tickets there from now on.
comment:84 Changed 4 years ago by
This should be fixed:
[288/306] Cythonizing sage/rings/tate_algebra_element.pyx warning: sage/rings/tate_algebra_element.pyx:301:10: Compatible but nonidentical C method '_mul_' not redeclared in definition part of extension type 'TateAlgebraTerm'. This may cause incorrect vtables to be generated. warning: sage/structure/element.pxd:188:15: Previous declaration is here
comment:85 Changed 4 years ago by
Essentially, you're missing a declaration for cpdef _mul_
in tate_algebra_element.pxd
comment:86 Changed 4 years ago by
There are also some thing I consider bad style, for example
@coerce_binop def __floordiv__(self, other):
Why not use _floordiv_
from the coercion model?
There is also the inefficient
from sage.structure.richcmp import op_EQ, op_NE, op_LT, op_GT, op_LE, op_GE
which should be
from cpython.object cimport Py_LT, Py_LE, Py_EQ, Py_NE, Py_GT, Py_GE
comment:87 followup: ↓ 89 Changed 4 years ago by
And isn't _pushout_family()
really just coercion_model.common_parent()
?
comment:88 Changed 4 years ago by
This is reinventing sage.structure.richcmp.rich_to_bool
:
if op == op_LT: return c < 0 if op == op_LE: return c <= 0 if op == op_GT: return c > 0 if op == op_GE: return c >= 0
comment:89 in reply to: ↑ 87 Changed 4 years ago by
Thanks Jeroen for your useful comments!
I addressed all of them except this one:
And isn't
_pushout_family()
really justcoercion_model.common_parent()
?
because I'm not sure that _pushout_family()
and coercion_model.common_parent()
do the same job. At least if I replace the code of _pushout_family()
by:
elements = [initial] + list(elements) return coercion_model.common_parent(*elements)
I get many doctest failures.
comment:90 Changed 4 years ago by
cf ticket #26807
Branch pushed to git repo; I updated commit sha1. New commits:
First working version