A package for exact p-adic computation for the Magma computer algebra system.
The aim of this package is to provide the user with a higher-level interface to computing with p-adics, making it easier to perform everyday computations and coding more complex algorithms.
See the user manual. The rationale for the design of the package and an overview of the internal structure can be found in this article.
The package is hosted here on GitHub and can be downloaded from here. The user manual is here.
Please direct any comments, queries or complaints to the GitHub issue tracker.
! Bug fix (no change to user interface, increment patch version)
~ Improvement (no change to user interface, increment patch version)
+ New feature (backwards-compatible change to user interface, increment minor version)
- Remove (backwards-incompatible change to user interface, increment major version)
! Fixes some bugs in `Factorization` code.
+ Adds `RelativeApproximation` and `BaselineApproximation` intrinsics, `_Lazy` versions and `Weak` versions (which are capped by the absolute precision)
+ Adds an implementation of the "OM" factoring algorithm, which is now the default algorithm used by `Factorization` and `Roots`. These are directly accessible as `ExactpAdics_Factorization` and `ExactpAdics_Roots`, with versions for `RngUPolElt[FldPad]` available too. The original behaviour, wrapping Magma's implementation, is available by passing `Alg:="Builtin"`, or calling `Builtin_Factorization` or `Builtin_Roots` directly.
! `ExactpAdicField(L :: FldPad)` not working when `L` has a finite precision
! Bug in `ShiftValuation`, caused by `R.1` not being to full precision where `R::RngUPol[FldPad]` (a Magma feature/bug)
+ Adds abstract types `StrPadExact`, `PadExactElt` and `Val_PadExactElt`, from which most other types are now derived, and inherit a common interface.
+ Adds types `SetCart_PadExact`, `Tup_PadExact` and `Val_Tup_PadExact` for representing tuples of p-adic objects.
+ Adds intrinsic NewtonPolygonFactorization.
+ Adds intrinsic IsHenselLiftable (for univariate polynomial factorizations).
+ Adds Support parameter to NewtonPolygon.
+ Adds parameter UseNP to Roots and Factorization.
+ Adds intrinsic AreAllWeaklyZero.
~ Improves IsHenselLiftable (for multivariate roots).
! Minor bug fixes.
! Internal function `assignResidueClassFieldNames` now works with fields of degree 1.
~ `Factorization` is easier to debug.
~ Removes a hacky `try`-`catch` block, which are slow to execute in Magma.
~ Warnings are now controlled by intrinsics, their behaviour can be altered via `ExactpAdics_SetWarningAction`.
! `ExactCompletion` precision errors
! Obsolete calls to `ExactpAdics_ExecutePrecisionStrategy`
! Minor bug in `IsHenselLiftable`
! Tweak to the update mechanism to catch under-precise updates in-place: The `Update` intrinsic now checks if the field `update_expecting_apr` is set, and if so asserts that the absolute precision is at least this; the dependency-checking framework sets this field whenever an element is about to be updated.
Initial release
This and the new ExactpAdics2 share some common code from the ExactpAdicsCommon repository. The code there should be periodically copied into the common directory (no fancy git merging currently).
Documentation is generated using magdoc with the following command:
magdoc.py -o docs Generics.mag Getter.mag ExactpAdics.mag Factorization.mag Factorization_new.mag Val_FldPadElt.mag Val_RngUPolElt_FldPad.mag Val_RngMPolElt_FldPad.mag Val_Tup_PadExact.mag PrecisionStrategy.mag Tuples.mag DefaultAssociativeArray.mag State.mag Promotion.mag LowerBound.mag MultivariatePolynomials.mag
Copyright (C) 2018 Christopher Doris
ExactpAdics is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
ExactpAdics is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with ExactpAdics. If not, see http://www.gnu.org/licenses/.