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    "info": {
        "author": "Stefan Wewers, Julian R\u00fcth",
        "author_email": "stefan.wewers@uni-ulm.de",
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        "classifiers": [
            "Development Status :: 4 - Beta",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: GNU General Public License v2 or later (GPLv2+)",
            "Operating System :: OS Independent",
            "Programming Language :: Python :: 2",
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            "Topic :: Scientific/Engineering :: Mathematics"
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        "description": "# MCLF\n\n[![Documentation Status](https://readthedocs.org/projects/mclf/badge/)](https://mclf.readthedocs.io/?badge=latest)\n[![CircleCI](https://circleci.com/gh/MCLF/mclf/tree/master.svg?style=svg)](https://circleci.com/gh/MCLF/mclf/tree/master)\n[![Coverage Status](https://coveralls.io/repos/github/MCLF/mclf/badge.svg?branch=master)](https://coveralls.io/github/MCLF/mclf?branch=master)\n[![asv](https://img.shields.io/badge/benchmarked%20by-asv-green.svg?style=flat)](https://mclf.github.io/mclf-asv)\n[![PyPI](https://img.shields.io/pypi/v/mclf.svg)](https://pypi.org/project/mclf/)\n\n### A Sage toolbox for computing with **M**odels of **C**urves over **L**ocal **F**ields\n\nThis is still a rather immature version of our toolbox. Nevertheless, you can\nuse it to compute, for a large class of curves over the rationals, the stable\nreduction at primes of bad reduction.\n\nLet Y be a smooth projective curve over a field K and let vK be a discrete valuation on K.\nThe principal goal is to compute  the *semistable reduction* of Y with respect to vK.\nThis means that we want to know\n\n* a finite Galois extension L/K,\n* an extension vL of vK to L,\n* the special fiber of an integral semistable model of Y over the valuation\n  ring of vL, and\n* the action of the decomposition group of vL on that special fiber.\n\nAt the moment we can do this only in certain special cases, which should\nnevertheless be useful.\n\nIf you have at least [Sage 8.2](https://www.sagemath.org/) you can install the\nlatest version of this package with `sage -pip install --user --upgrade mclf`.\n\nIf you can not install Sage on your local machine, you can also click\n[![Launch on mybinder.org](https://camo.githubusercontent.com/d57df63fab21897847014ebaec3e7f5f48951ad2/68747470733a2f2f626574612e6d7962696e6465722e6f72672f62616467652e737667)](https://mybinder.org/v2/gh/mclf/MCLF/master?filepath=example.ipynb)\nto run an interactive Jupyter notebook with mclf preinstalled.\n\nThe package can be loaded with\n```\nsage: from mclf import *\n```\nWe create a Picard curve over the rational number field.      \n```\nsage: R.<x> = QQ[]\nsage: Y = SuperellipticCurve(x^4-1, 3)\nsage: Y\nsuperelliptic curve y^3 = x^4 - 1 over Rational Field\n```\nIn general, the class `SuperellipticCurve` allows you to create a superelliptic curve of the form y<sup>n</sup> = f(x),\nfor a polynomial f over an arbitrary field K. But you can also define any smooth projective curve Y with given\nfunction field.\n\nWe define the 2-adic valuation on the rational field. Then we are able to create an\nobject of the class `SemistableModel` which represents a semistable model of the curve Y with respect to the 2-adic\nvaluation.\n```\nsage: v_2 = QQ.valuation(2)\nsage: Y2 = SemistableModel(Y, v_2)\nsage: Y2.is_semistable() # this may take a while\nTrue\n```\nThe stable reduction of Y at p=2 has four components, one of genus 0 and\nthree of genus 1.\n```\nsage: [Z.genus() for Z in Y2.components()]\n[0, 1, 1, 1]\nsage: Y2.components_of_positive_genus()\n[the smooth projective curve with Function field in y defined by y^3 + x^4 + x^2,\n the smooth projective curve with Function field in y defined by y^3 + x^2 + x,\n the smooth projective curve with Function field in y defined by y^3 + x^2 + x + 1]\n```\nWe can also extract some arithmetic information on the curve Y from the stable reduction.\nFor instance, we can compute the *conductor exponent* of Y at p=2:\n```\nsage: Y2.conductor_exponent()\n6\n```\nNow let us compute the semistable reduction of Y at p=3:\n```\nsage: v_3 = QQ.valuation(3)\nsage: Y3 = SemistableModel(Y, v_3)\nsage: Y3.is_semistable()\nTrue\nsage: Y3.components_of_positive_genus()\n[the smooth projective curve with Function field in y defined by y^3 + y + 2*x^4]\n```\nWe see that Y has potentially good reduction at p=3. The conductor exponent is:\n```\nsage: Y3.conductor_exponent()\n6\n```\n\nFor more details on the functionality and the restrictions of the toolbox, see the\n[Documentation](https://mclf.readthedocs.io/en/latest/).\nFor the mathematical background see\n\n* J. R\u00fcth, [Models of Curves and Valuations](https://oparu.uni-ulm.de/xmlui/handle/123456789/3302), PhD thesis, Ulm University, 2014\n* I.I. Bouw, S. Wewers, [Computing L-Functions and semistable reduction of superellipic curves](https://arxiv.org/abs/1211.4459?context=math.AG),\n  Glasgow Math. J., 59(1), 2017, 77-108\n* I.I. Bouw, S. Wewers,[Semistable reduction of curves and computation of bad Euler factors of L-functions](https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/wewers/course_notes.pdf),\n   lecture notes for a minicourse at ICERM\n* S. Wewers, Semistable reduction of superelliptic curves of degree p, preprint, 2017\n\n#### Known bugs and issues\n\nSee our [issues list](https://github.com/MCLF/mclf/issues), and tell us of any bugs or ommissions that are not covered there.\n\n#### Experimental Changes\n\nWe also have an unstable [experimental](https://github.com/MCLF/mclf/tree/experimental) version with the latest experimental features and bugs that you can try out by clicking on [![Launch on mybinder.org](https://camo.githubusercontent.com/d57df63fab21897847014ebaec3e7f5f48951ad2/68747470733a2f2f626574612e6d7962696e6465722e6f72672f62616467652e737667)](https://mybinder.org/v2/gh/mclf/MCLF/experimental?filepath=example.ipynb), note that this version currently [![CircleCI](https://circleci.com/gh/MCLF/mclf/tree/experimental.svg?style=svg)](https://circleci.com/gh/MCLF/mclf/tree/experimental) our own test suite.\n\n#### Development workflow\n\nMost development happens on feature branches against the `master` branch. The\n`master` branch is considered stable and usually we create a new release and\nupload it to PyPI whenever there is something merged into `master`. We\nsometimes collect a number of experimental changes on the `experimental`\nbranch.\n\n\n",
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