Adding basic modules including python and cython code + setup file + etc.

MANIFEST.in

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+include README.rst

README.rst

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+Basic Sage Optional Package
+===========================
+
+This is a basic `Sage <http://www.sagemath.org/>`_ optional package containing
+nice modules to share to others.
+
+Installation::
+
+    sage -pip install sage_sample
+
+Usage::
+
+    sage: from sage_sample import *
+
+Links: Github__, `Python Package Index`__
+
+__ https://github.com/nthiery/sage_sample
+__ http://pypi.python.org/pypi/sage_sample
+
+Version 0.1a0
+-------------
+
+First version.
+

VERSION

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+0.1a0

makefile

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+all: install test
+
+install:
+	sage -pip install --upgrade --no-index -v .
+
+develop:
+	sage -pip install --upgrade --no-index -e .
+
+test: 
+	sage -tp --force-lib sage_sample/*.py sage_sample/*.pyx
+
+coverage:
+	sage -coverage sage_sample/*
+
+doc:
+	cd docs && sage -sh -c "make html"
+
+doc-pdf:
+	cd docs && sage -sh -c "make latexpdf"
+
+dist:
+	sage -python setup.py sdist
+
+register: dist
+	VERSION=`cat VERSION`; sage -sh -c "twine register dist/sage_sample-$$VERSION.tar.gz"
+
+upload: dist
+	VERSION=`cat VERSION`; sage -sh -c "twine upload dist/sage_sample-$$VERSION.tar.gz"
+
+clean: clean-doc
+
+clean-doc:
+	cd docs && sage -sh -c "make clean"
+
+.PHONY: all install develop test coverage clean clean-doc doc doc-pdf dist register upload

sage_sample/__init__.py

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+# For sphinx to work, we first need to import the sage library
+from sage.all_cmdline import *
+
+# import stuff of the package
+from diophantine_approximation import diophantine_approx
+from dirichlet import dirichlet

sage_sample/diophantine_approximation.py

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+# -*- coding: utf-8 -*-
+r"""
+Diophantine approximation
+
+EXAMPLES::
+
+    sage: from sage_sample import diophantine_approx
+    sage: diophantine_approx(pi, 10)
+    (22, 7)
+
+AUTHORS:
+
+- Sébastien Labbé, November 23, 2016, Sage Days 79, Jerusalem
+"""
+#*****************************************************************************
+#       Copyright (C) 2016 Sebastien Labbe <slabqc@gmail.com>
+#
+#  Distributed under the terms of the GNU General Public License (GPL)
+#  as published by the Free Software Foundation; either version 2 of
+#  the License, or (at your option) any later version.
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+
+# Use `import_statements` command to know how to import each sage commands::
+#
+#     sage: import_statements('round')
+#     from sage.misc.functional import round
+
+from sage.functions.other import frac
+from sage.misc.functional import round
+
+def diophantine_approx(alpha, Q):
+    r"""
+    Return a diophantine approximation p/q to real number alpha following
+    Dirichlet Theorem (1842).
+
+    .. NOTES::
+
+        This function is very slow compared to using continued fractions.
+        It tests all of the possible values of q.
+
+    INPUT:
+
+    - `alpha` -- real number
+    - `Q` -- real number > 1
+
+    OUTPUT:
+
+    - a tuple of integers (p,q) such that `|\alpha q-p|<1/Q`.
+
+    EXAMPLES::
+
+        sage: from sage_sample import diophantine_approx
+        sage: diophantine_approx(pi, 10)
+        (22, 7)
+        sage: diophantine_approx(pi, 100)
+        (22, 7)
+        sage: diophantine_approx(pi, 200)
+        (355, 113)
+        sage: diophantine_approx(pi, 1000)
+        (355, 113)
+        sage: diophantine_approx(pi, 35000) # not tested, code is very slow
+    """
+    for q in range(1, Q):
+        if frac(alpha*q) <= 1./Q or 1-1./Q <= frac(alpha*q):
+            p = round(alpha*q)
+            return (p,q)
+
+

sage_sample/dirichlet.pyx

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+# -*- coding: utf-8 -*-
+r"""
+Dirichlet Diophantine approximation
+
+EXAMPLES::
+
+    sage: from sage_sample import dirichlet
+    sage: dirichlet(pi, 10)
+    7
+
+AUTHORS:
+
+- Sébastien Labbé, November 23, 2016, Sage Days 79, Jerusalem
+"""
+#*****************************************************************************
+#       Copyright (C) 2016 Sebastien Labbe <slabqc@gmail.com>
+#
+#  Distributed under the terms of the GNU General Public License (GPL)
+#  as published by the Free Software Foundation; either version 2 of
+#  the License, or (at your option) any later version.
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+from libc.math cimport floor
+
+include "cysignals/signals.pxi"   # ctrl-c interrupt block support
+include "cysignals/memory.pxi"
+
+def dirichlet(alpha, Q):
+    r"""
+    Return a diophantine approximation p/q to real number alpha following
+    Dirichlet Theorem (1842).
+
+    .. NOTES::
+
+        This function is slow compared to using continued fractions.
+        It tests all of the possible values of q.
+
+    INPUT:
+
+    - `alpha` -- real number
+    - `Q` -- real number > 1
+
+    OUTPUT:
+
+    - a tuple of integers (p,q) such that `|\alpha q-p|<1/Q`.
+
+    EXAMPLES::
+
+        sage: from sage_sample import dirichlet
+        sage: dirichlet(pi, 10)
+        7
+        sage: dirichlet(pi, 100)
+        7
+        sage: dirichlet(pi, 200)
+        113
+        sage: dirichlet(pi, 1000)
+        113
+        sage: dirichlet(pi, 35000) # long (1.38s)
+        33102
+    """
+    if not Q > 1:
+        raise ValueError("argument Q(={}) must be > 1".format(Q))
+    cdef double Qinv = 1. / Q
+    cdef double one_minus_Qinv = 1 - Qinv
+    cdef double a
+    cdef long q
+    for q in range(1, Q):
+        sig_check() # Check for Keyboard interupt
+        a = q*alpha
+        a = a - floor(a) 
+        if a <= Qinv or one_minus_Qinv <= a:
+            return q
+
+

setup.py

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+from setuptools import setup
+from codecs import open # To use a consistent encoding
+from os import path
+
+# The next block is if there are some cython files
+from setuptools import Extension
+from Cython.Build import cythonize
+import Cython.Compiler.Options
+from sage.env import sage_include_directories
+
+# Get the long description from the README file
+here = path.abspath(path.dirname(__file__))
+with open(path.join(here, 'README.rst'), encoding='utf-8') as f:
+    long_description = f.read()
+with open(path.join(here, 'VERSION'), encoding='utf-8') as f:
+    version = f.read().strip()
+
+# Cython modules
+ext_modules = [
+        Extension('sage_sample.dirichlet',
+            sources = [path.join('sage_sample','dirichlet.pyx')],
+            include_dirs=sage_include_directories())
+        ]
+
+setup(name='sage_sample',
+    version=version,
+    description="Basic Sage Optional Package",
+    long_description=long_description,
+    classifiers=[
+      # How mature is this project? Common values are
+      #   3 - Alpha
+      #   4 - Beta
+      #   5 - Production/Stable
+      'Development Status :: 3 - Alpha',
+      'Intended Audience :: Science/Research',
+      'License :: OSI Approved :: GNU General Public License v2 or later (GPLv2+)',
+      'Programming Language :: Python :: 2.7',
+      'Topic :: Scientific/Engineering :: Mathematics',
+    ],
+    keywords='sagemath',
+    #keywords='sagemath combinatorics geometry symbolic dynamics',
+    author='Sebastien Labbe',
+    author_email='slabbe@ulg.ac.be',
+    url='https://github.com/nthiery/sage_sample',
+    license = "GPL",
+    packages=['sage_sample'],
+    ext_modules=cythonize(ext_modules),
+)
+