PARILink

PARILink connects Wolfram Language to PARI/GP for number theory.

Documentation · Cloud resource · Releases

Requirements

• Wolfram Language 15.0 or later
• PARI/GP 2.17 or later

Uses an existing GP installation. Tested on Linux x86-64 and macOS Apple silicon with GP 2.17.4 and 2.19.0. See the compatibility report.

Install

Install the latest release from Wolfram Cloud:

PacletInstall[
	ResourceObject[
		"https://www.wolframcloud.com/obj/wolframinstitute/" <>
			"DeployedResources/Paclet/WolframInstitute/PARILink"
	]["PacletFile"],
	ForceVersionInstall -> True,
	"ShowProgress" -> True
];

Versioned paclets and SHA-256 checksums are also on GitHub Releases.

Load the package:

Needs["WolframInstitute`PARILink`"];

Examples

Start GP:

session = StartPARISession[];

Find the Galois group of a quintic:

polynomial = PARIEvaluate[session, "x^5 - x - 1"];

Last[PARICall[session, "polgalois", polynomial]]

Returns "S5", the symmetric group on five letters.

Count points on an elliptic curve over the field with 101 elements:

curve = PARICall[session, "ellinit", {0, 0, 0, -1, 0}, 101,
	"ReturnType" -> "Object"];

PARICall[session, "ellcard", curve]

Returns 104, including the point at infinity.

Compute Fourier coefficients of a weight 2, level 11 newform:

form = PARIEvaluate[session, "mfeigenbasis(mfinit([11,2],0))[1]",
	"ReturnType" -> "Object"];

PARICall[session, "mfcoefs", form, 10]

Returns {0, 1, -2, -1, 2, 1, 2, -2, 0, -2, -2} (degrees 0 through 10).

Close GP and release its objects:

DeleteObject[session];

Values

GP result	Wolfram Language result
Integers, rationals, exact complex numbers, strings	Copied values
Vectors and matrices	Lists
Other values	PARIObject

Use "ReturnType" -> "Object" to reuse a GP structure in later calls. Normal[object] copies a supported retained value. Mutable lists and maps remain objects; copy their contents with Vec or Mat.

Errors

• GP evaluation errors return Failure and leave the session usable.
• Timeouts, interruptions, and lost connections stop the session.

See PARICall for time limits and output options.

Development

To use a source checkout, load its paclet directory before Needs:

PacletDirectoryLoad["/path/to/PARILink/PARILink"];

make all

make test-pari

Build and publishing instructions: CONTRIBUTING.md. Security reports: SECURITY.md.

License

PARILink code uses the MIT License. PARI/GP is separately licensed; see third-party notices.