Tate algebras

[xcaruso]

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.

Depends on #26479 Depends on #26575

CC: @sagetrac-TristanVaccon @ThibautVerron @xcaruso @roed314

Component: padics

Author: Xavier Caruso, Thibaut Verron

Branch: 4982c7e

Reviewer: David Roe

Issue created by migration from https://trac.sagemath.org/ticket/26195

[xcaruso]

Branch: u/caruso/tate_algebras

[ThibautVerron]

Commit: b8a6ac3

[ThibautVerron]

Changed branch from u/caruso/tate_algebras to u/gh-ThibautVerron/TateAlgebras

[xcaruso]

Changed branch from u/gh-ThibautVerron/TateAlgebras to u/caruso/TateAlgebras

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Branch pushed to git repo; I updated commit sha1. New commits:

9ca2244

First working version

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Branch pushed to git repo; I updated commit sha1. New commits:

05cf041

Restriction + small fix in inverse_of_unit

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Changed commit from 9ca2244 to 05cf041

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5d0e354

Fix bugs in quo_rem

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Changed commit from 05cf041 to 5d0e354

[ThibautVerron]

Changed commit from 5d0e354 to 5abdb64

[ThibautVerron]

Changed branch from u/caruso/TateAlgebras to u/gh-ThibautVerron/tate_algebras

[ThibautVerron]

New commits:

fa4e37a	First docstring
5abdb64	Merge branch 'u/caruso/TateAlgebras' of git://trac.sagemath.org/sage into t/26195/TateAlgebras

[xcaruso]

Changed branch from u/gh-ThibautVerron/tate_algebras to u/caruso/tate_algebras

[ThibautVerron]

Changed branch from u/caruso/tate_algebras to u/gh-ThibautVerron/tate_algebras

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

7800393

Revert changes to .dir-locals.el

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Branch pushed to git repo; I updated commit sha1. New commits:

2383ba0

Fixed tests

[xcaruso]

Changed branch from u/gh-ThibautVerron/tate_algebras to u/caruso/tate_algebras

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Branch pushed to git repo; I updated commit sha1. New commits:

8446736

Bug fixed in TateAlgebraTerms & more functionalities for ideals

[xcaruso]

Description changed:

--- 
+++ 
@@ -1 +1,25 @@
-We propose to implement Tate algebras over complete discrete valuation rings/fields.
+This ticket implements Tate algebras over complete discrete valuation rings/fields, together with Gröbner bases for ideals in these algebras.
+
+Small demo:
+
+```
+sage: R = Zp(2, 10, print_mode='digits')
+sage: A.<x,y> = TateAlgebra(R)
+sage: f = x^2 + 2*x + x*y^3 + 4*y + y
+sage: g = y^2*x^3 + 2*x + x^2 + 2*x^4*y
+sage: I = A.ideal([f,2*g])
+sage: J = A.ideal([f,g])
+sage: I.groebner_basis()
+[(...0000000001)*x*y^3 + (...0000000001)*x^2 + (...0000000101)*y + (...00000000010)*x,
+ (...1110001010)*x^2 + (...1010000100)*y^3 + (...1100010100)*x + (...1001101000)*x^2*y^2 + (...0011101000)*y + (...1111110000)*y^2 + (...0000100000)*x^2*y + (...1100100000)*x*y^2 + (...0010100000)*x*y + O(2^10),
+ (...1111000010)*y + (...1010110100)*y^8 + (...1110011100)*y^3 + (...0100001000)*y^6 + (...0001110000)*y^7 + (...0111010000)*y^5 + (...0011100000)*y^2 + (...1001000000)*y^4 + O(2^10)]
+sage: J.groebner_basis()
+[(...0111000101)*x^2 + (...1101000010)*y^3 + (...1110001010)*x + (...0100110100)*x^2*y^2 + (...0001110100)*y + (...0111111000)*y^2 + (...0000010000)*x^2*y + (...1110010000)*x*y^2 + (...0001010000)*x*y + O(2^10),
+ (...0111100001)*y + (...0101011010)*y^8 + (...0111001110)*y^3 + (...1010000100)*y^6 + (...0000111000)*y^7 + (...0011101000)*y^5 + (...1001110000)*y^2 + (...0100100000)*y^4 + O(2^10)]
+sage: I.is_saturated()
+False
+sage: Io = I.saturate()
+sage: J.is_saturated()
+True
+sage: Io == J
+```

[xcaruso]

Description changed:

--- 
+++ 
@@ -22,4 +22,5 @@
 sage: J.is_saturated()
 True
 sage: Io == J
+True

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

fd3bf7b

Some improvements in Buchberger algorithm

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bfddf6e

Rewrite in cython

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Branch pushed to git repo; I updated commit sha1. New commits:

bc7c763

Better (?) choice of ordering of S-polynomials

[ThibautVerron]

Changed branch from u/caruso/tate_algebras to u/gh-ThibautVerron/tate_algebras

[xcaruso]

Changed branch from u/gh-ThibautVerron/tate_algebras to u/caruso/tate_algebras

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b00b8e0

Use directly the cython class PolyDict

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Changed commit from b00b8e0 to 100cbb7

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Branch pushed to git repo; I updated commit sha1. New commits:

100cbb7

Fix bug in creation of elements in Tate algebras

[ThibautVerron]

Changed branch from u/caruso/tate_algebras to u/gh-ThibautVerron/tate_algebras

[xcaruso]

Changed branch from u/gh-ThibautVerron/tate_algebras to u/caruso/tate_algebras

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 100cbb7 to 0f6391a

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Branch pushed to git repo; I updated commit sha1. New commits:

0f6391a

f.residue() now returns a polynomial over the residue field

[ThibautVerron]

Changed branch from u/caruso/tate_algebras to u/gh-ThibautVerron/tate_algebras

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

a5b9d36

Partial documentation of Tate algebra term elements

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[xcaruso]

Changed branch from u/gh-ThibautVerron/tate_algebras to u/caruso/tate_algebras

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

fc5d3c4	Implement rich comparison for terms
cfc09d7	Implement monomials() and leading_monomial()

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7c2ac0b

Implement a factory

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Changed commit from cfc09d7 to 7c2ac0b

[ThibautVerron]

Changed branch from u/caruso/tate_algebras to u/gh-ThibautVerron/tate_algebras

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

2a4044c

Documentation for Tate terms