principal_part_bound can be wrong when key has multiple slopes

[saraedum]

Currently, the following fails:

sage: R.<x> = QQ[]
sage: v_2 = QQ.valuation(2)
sage: f = x^36 + 1160/81*x^31 + 9920/27*x^30 + 1040/81*x^26 + 52480/81*x^25 + 220160/81*x^24 - 5120/81*x^21 - 143360/81*x^20 - 573440/81*x^19 + 12451840/81*x^18 - 266240/567*x^16 - 20316160/567*x^15 - 198737920/189*x^14 - 1129840640/81*x^13 - 1907359744/27*x^12 + 8192/81*x^11 + 655360/81*x^10 + 5242880/21*x^9 + 2118123520/567*x^8 + 15460204544/567*x^7 + 6509559808/81*x^6 - 16777216/567*x^2 - 268435456/567*x - 1073741824/567
sage: v_2.mac_lane_approximants(f)
AssertionError

with the changes proposed by this ticket, this is

[[ Gauss valuation induced by 2-adic valuation, v(x + 2056) = 23/2 ],
 [ Gauss valuation induced by 2-adic valuation, v(x) = 11/9 ],
 [ Gauss valuation induced by 2-adic valuation, v(x) = 2/5, v(x^5 + 4) = 7/2 ],
 [ Gauss valuation induced by 2-adic valuation, v(x) = 3/5, v(x^10 + 8*x^5 + 64) = 7 ],
 [ Gauss valuation induced by 2-adic valuation, v(x) = 3/5, v(x^5 + 8) = 5 ]]

CC: @sagetrac-swewers

Component: padics

Author: Julian Rüth

Branch/Commit: e47eded

Reviewer: Stefan Wewers

Issue created by migration from https://trac.sagemath.org/ticket/26144

[saraedum]

Branch: u/saraedum/26144

[saraedum]

New commits:

e8b1d62

Properly handle repeated key polynomials

[saraedum]

Commit: e8b1d62

[saraedum]

Work Issues: is the patchbot happy?

[sagetrac-git]

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

7186bc6

Improve documentation of mac_lane_step()

[sagetrac-git]

Changed commit from e8b1d62 to 7186bc6

[sagetrac-git]

Changed commit from 7186bc6 to 8bf1144

[sagetrac-git]

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

8bf1144

Comment on principal_part_bound correctness

[sagetrac-git]

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

bde9084

Clarify the meaning of principal_part_bound

[sagetrac-git]

Changed commit from 8bf1144 to bde9084

[saraedum]

Changed work issues from is the patchbot happy? to none

[saraedum]

comment:7

The patchbot errors are Magma errors and unrelated.

---

New commits:

bde9084

Clarify the meaning of principal_part_bound

[sagetrac-swewers]

Reviewer: Stefan Wewers

[vbraun]

comment:9

merge conflict

[sagetrac-git]

Changed commit from bde9084 to e47eded

[sagetrac-git]

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

e47eded

Merge remote-tracking branch 'trac/develop' into 26144

[saraedum]

Work Issues: is the patchbot happy ⇒ positive review

[saraedum]

Changed work issues from is the patchbot happy ⇒ positive review to none

[vbraun]

Changed branch from u/saraedum/26144 to e47eded

[embray]

comment:15

This tickets were closed as fixed after the Sage 8.5 release.