README.rst
1CyPari 2
2========
3
4.. image:: https://travis-ci.org/sagemath/cypari2.svg?branch=master
5 :target: https://travis-ci.org/sagemath/cypari2
6.. image:: https://readthedocs.org/projects/cypari2/badge/?version=latest
7 :target: https://cypari2.readthedocs.io/en/latest/?badge=latest
8 :alt: Documentation Status
9
10A Python interface to the number theory library `PARI/GP <http://pari.math.u-bordeaux.fr/>`_.
11
12This library supports both Python 2 and Python 3.
13
14Installation
15------------
16
17GNU/Linux
18^^^^^^^^^
19
20A package `python-cypari2` or `python2-cypari2` or `python3-cypari2` might be
21available in your package manager.
22
23Using pip
24^^^^^^^^^
25
26Requirements:
27
28- PARI/GP >= 2.9.4 (header files and library)
29- Python 2.7 or Python >= 3.4
30- pip
31- `cysignals <https://pypi.python.org/pypi/cysignals/>`_ >= 1.7
32- Cython >= 0.28
33
34Install cypari2 via the Python Package Index (PyPI) via
35
36::
37
38 $ pip install cypari2 [--user]
39
40(the optional option *--user* allows to install cypari2 for a single user
41and avoids using pip with administrator rights). Depending on your operating
42system the pip command might also be called pip2 or pip3.
43
44If you want to try the development version use
45
46::
47
48 $ pip install git+https://github.com/sagemath/cypari2.git [--user]
49
50If you have an error saying libpari-gmp*.so* is missing and have all requirements
51already installed, try to reinstall cysignals and cypari2
52
53::
54
55 $ pip install cysignals --upgrade [--user]
56 $ pip install cypari2 --upgrade [--user]
57
58Other
59^^^^^
60
61Any other way to install cypari2 is not supported. In particular, ``python
62setup.py install`` will produce an error.
63
64Usage
65-----
66
67The interface as been kept as close as possible from PARI/GP. The following
68computation in GP
69
70::
71
72 ? zeta(2)
73 %1 = 1.6449340668482264364724151666460251892
74
75 ? p = x^3 + x^2 + x - 1;
76 ? modulus = t^3 + t^2 + t - 1;
77 ? fq = factorff(p, 3, modulus);
78 ? centerlift(lift(fq))
79 %5 =
80 [ x - t 1]
81
82 [x + (t^2 + t - 1) 1]
83
84 [ x + (-t^2 - 1) 1]
85
86translates into
87
88::
89
90 >>> import cypari2
91 >>> pari = cypari2.Pari()
92
93 >>> pari(2).zeta()
94 1.64493406684823
95
96 >>> p = pari("x^3 + x^2 + x - 1")
97 >>> modulus = pari("t^3 + t^2 + t - 1")
98 >>> fq = p.factorff(3, modulus)
99 >>> fq.lift().centerlift()
100 [x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]
101
102The object **pari** above is the object for the interface and acts as a
103constructor. It can be called with basic Python objects like integer
104or floating point. When called with a string as in the last example
105the corresponding string is interpreted as if it was executed in a GP shell.
106
107Beyond the interface object **pari** of type **Pari**, any object you get a
108handle on is of type **Gen** (that is a wrapper around the **GEN** type from
109libpari). All PARI/GP functions are then available in their original names as
110*methods* like **zeta**, **factorff**, **lift** or **centerlift** above.
111
112Alternatively, the pari functions are accessible as methods of **pari**. The
113same computations be done via
114
115::
116
117 >>> import cypari2
118 >>> pari = cypari2.Pari()
119
120 >>> pari.zeta(2)
121 1.64493406684823
122
123 >>> p = pari("x^3 + x^2 + x - 1")
124 >>> modulus = pari("t^3 + t^2 + t - 1")
125 >>> fq = pari.factorff(p, 3, modulus)
126 >>> pari.centerlift(pari.lift(fq))
127 [x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]
128
129The complete documentation of cypari2 is available at http://cypari2.readthedocs.io and
130the PARI/GP documentation at http://pari.math.u-bordeaux.fr/doc.html
131
132Contributing
133------------
134
135Submit pull request or get in touch with the SageMath developers.
136
