Differences between revisions 1 and 4 (spanning 3 versions)
⇤ ← Revision 1 as of 2010-12-02 19:34:41 →
Size: 235
Editor: DavidRoe
Comment:
← Revision 4 as of 2010-12-03 00:25:28 → ⇥
Size: 1229
Editor: DavidRoe
Comment:
Deletions are marked like this. Additions are marked like this.
Line 1: Line 1:
 * ''Goal'' --
 * ''Type'' --
 * ''Priority'' --
 * ''Difficulty'' --
 * ''Prerequisites'' -- 		 * ''Goal'' -- Define Hensel lifting for roots and factorizations of polynomials over Henselian rings.
 * ''Type'' -- basic features
 * ''Priority'' -- High
 * ''Difficulty'' -- Medium-Easy
 * ''Prerequisites'' -- [[../PolynomialPrecision | p-adic polynomial precision]]
Line 7: Line 7:
 * ''Contributors'' --
 * ''Progress'' - 		 * ''Contributors'' -- David Roe
 * ''Progress'' - not started
Line 13: Line 13:
This is easy once the implementation of polynomials stabilizes...
Line 14: Line 16:

 1. Write a category `HenslianRings` (or maybe `HenselianRingsWithUniformizer`) as a place to write 2-5. Also a category for polynomials over such rings...

 1. Write a function that lifts a root of a polynomial (defined to sufficient precision) up one precision.

 1. Write a function that lifts a root of a polynomial (defined to sufficient precision) to double precision.

 1. Write a function that lifts a coprime factorization up one precision.

 1. Write a function that lifts a coprime factorization to double precision.

 1. Write functions that determine precisions of the resulting objects given the precision of the original polynomial.

 1. Write optimized versions of 2-5 for polynomials over Zp and Qp.

  • Goal -- Define Hensel lifting for roots and factorizations of polynomials over Henselian rings.

  • Type -- basic features

  • Priority -- High

  • Difficulty -- Medium-Easy

  • Prerequisites -- p-adic polynomial precision

  • Background --

  • Contributors -- David Roe

  • Progress - not started

  • Related Tickets --

Discussion

This is easy once the implementation of polynomials stabilizes...

Tasks

  1. Write a category HenslianRings (or maybe HenselianRingsWithUniformizer) as a place to write 2-5. Also a category for polynomials over such rings...

  2. Write a function that lifts a root of a polynomial (defined to sufficient precision) up one precision.
  3. Write a function that lifts a root of a polynomial (defined to sufficient precision) to double precision.
  4. Write a function that lifts a coprime factorization up one precision.
  5. Write a function that lifts a coprime factorization to double precision.
  6. Write functions that determine precisions of the resulting objects given the precision of the original polynomial.
  7. Write optimized versions of 2-5 for polynomials over Zp and Qp.

padics/HenselLifting (last edited 2010-12-03 00:25:28 by DavidRoe)