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https://github.com/edgarcosta/controlledreduction
An implementation of the controlled reduction method for computing the Hasse-Weil zeta functions of smooth projective hypersurfaces over finite fields
https://github.com/edgarcosta/controlledreduction
arithmetic calabi-yau-manifolds geometry hasse-weil-zeta-function k3-surfaces p-adic-cohomology smooth-hypersurfaces
Last synced: about 2 months ago
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An implementation of the controlled reduction method for computing the Hasse-Weil zeta functions of smooth projective hypersurfaces over finite fields
- Host: GitHub
- URL: https://github.com/edgarcosta/controlledreduction
- Owner: edgarcosta
- License: other
- Created: 2017-08-22T22:41:50.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2024-11-04T17:48:46.000Z (2 months ago)
- Last Synced: 2024-11-04T18:29:33.656Z (2 months ago)
- Topics: arithmetic, calabi-yau-manifolds, geometry, hasse-weil-zeta-function, k3-surfaces, p-adic-cohomology, smooth-hypersurfaces
- Language: C++
- Homepage: https://edgarcosta.org
- Size: 234 KB
- Stars: 6
- Watchers: 5
- Forks: 3
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# controlled-reduction
## PyPI package
For a PyPI package that integrates most of controlled-reduction into SageMath, see [pycontrolledreduction](https://github.com/edgarcosta/pycontrolledreduction/).
## Abstract
An implementation of the controlled reduction method for computing the
Hasse-Weil zeta functions of smooth projective hypersurfaces over finite
fields. Explicitly, by computing a p-adic approximation of Frobenius
action on p-adic cohomology (Monsky-Washnizter) with sufficient precision
and then lifting its characteristic polynomial to the integers.
An overview of the method can be found in:
- "Computing zeta functions of nondegenerate projective hypersurfaces over
finite fields", (under preparation) by Edgar Costa and David Harvey.
- "Effective computations of Hasse-Weil zeta functions", by Edgar Costa
## Dependencies
It majorly depends on:
- [NTL: A Library for doing Number Theory](http://www.shoup.net/ntl/)
- [FLINT: Fast Library for Number Theory](http://flintlib.org/)
Which depend on:
- [GMP: GNU Multiple Precision Arithmetic Library](https://gmplib.org/) (for NTL and FLINT)
- [MPIR: Multiple Precision Integers and Rationals](mpir.org) (for FLINT)
- [MPFR: GNU Multiple Precision Floating-Point Reliably](http://www.mpfr.org/) (for FLINT)
However, [SageMath](http://www.sagemath.org/) comes with all this libraries.
## Installation
There are 3 options:
### Using SageMath to provide the dependencies
1. Figuring out where `SageMath` is installed.
We recommend doing this and storing in an environmental variable by doing:
```
SAGE_ROOT=$(sage -c "print SAGE_ROOT")
```
Alternatively, in Sage do `print SAGE_ROOT` and on the unix terminal:
`
SAGE_ROOT=
`
2. Download controlled reduction
```
git clone https://github.com/edgarcosta/controlledreduction.git
```
3. Change your working directory and run the configure file
```
cd controlledreduction && ./configure --with-ntl=$SAGE_ROOT/local
```
4. Compile everything by doing
```
make
```
5. Set up the variable `$LD_LIBRARY_PATH`, so the executables can find the libraries at run time.
One can do this for the current terminal by doing:
```
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$SAGE_ROOT/local/lib
```
and for this line to be ran at the start of every session one can do
```
echo export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$SAGE_ROOT/local/lib >> ~/.bashrc
```
6. You can optionaly run some tests by doing
```
make check
```
or check out some of the examples
```
build/examples/K3_dwork
```
### Manually specifying the path for the dependencies
1. make sure you have the dependencies (see the source of the script `build_dependencies` if you would prefer to build them manually), if they are installed in a non-standard path, be sure to set `$LD_LIBRARY_PATH` accordingly.
2. `./configure` to generate the makefile.
To link against the libaries by SageMath it should be sufficient to run `./configure --with-ntl=/local/`.
Run `./configure --help` for more options.
3. `make` to build everything
4. `make check` to run some tests.