sagemath_pari: Computational Number Theory with PARI/GP

This pip-installable distribution passagemath-pari is a small distribution that provides modules that depend on PARI/GP, the computer algebra system designed for fast computations in number theory: factorizations, algebraic number theory, elliptic curves, modular forms, L-functions…

What is included

Examples

Starting the GP calculator from the command line:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-pari" sage -gp
GP/PARI CALCULATOR Version 2.17.2 (released)
...

Using the pexpect interface to the GP calculator:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-pari[test]" ipython

In [1]: from sage.interfaces.gp import gp

In [2]: E = gp.ellinit([1,2,3,4,5])

In [3]: E.ellglobalred()
Out[3]: [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]

Using the cypari2 library interface:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-pari" python

>>> import cypari2
>>> pari = cypari2.Pari()

>>> pari(2).zeta()
1.64493406684823

>>> p = pari("x^3 + x^2 + x - 1")
>>> modulus = pari("t^3 + t^2 + t - 1")
>>> fq = p.factorff(3, modulus)
>>> fq.lift().centerlift()
[x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]

Available as extras, from other distributions

PARI/GP data packages

See https://pari.math.u-bordeaux.fr/packages.html for detailed descriptions.

pip install "passagemath-pari[elldata]"

pip install "passagemath-pari[galdata]"

pip install "passagemath-pari[galpol]"

pip install "passagemath-pari[nflistdata]"

pip install "passagemath-pari[nftables]"

pip install "passagemath-pari[seadata]"

pip install "passagemath-pari[seadata-big]"

pip install "passagemath-pari[seadata-small]"

Type

standard

Dependencies

Version Information

package-version.txt:

10.6.3

version_requirements.txt:

passagemath-pari ~= 10.6.3.0

Equivalent System Packages

(none known)