Miscellaneous PARI/GP Tutorials

Tutorials written by the PARI group

• The GP CALCULATOR TUTORIAL in latest stable release.

• English atelier tutorials (slides and GP code):
  • Installation manual (16 pages) | shell Code
  • PARI environment for Windows (5 pages)
  • Introduction to PARI/GP (14 pages) | GP Code [basic]
  • Another introduction to PARI/GP (18 pages) | GP Code [includes more advanced number theory]
  • Programming in GP (12 pages) | GP Code
  • Parallel programming in GP (18 pages) | GP Code
  How to contribute to PARI/GP (12 pages) | Doctesting commands | Example script | Example tests

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  • Algebraic number theory (31 pages) | GP Code
  • Algebraic number theory (advanced) (30 pages) | GP Code
  • Subfields and Abelian overfields (29 pages) | GP Code | Video
  • The nflist function (14 pages) | GP Code
  • Euclidean lattices (19 pages) | GP Code | Video
  • S-units and compact representations in number fields (13 pages) | GP Code | Video
  • Finite Fields (15 pages) | GP Code

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  • Elliptic curves (24 pages) | GP Code
  • Elliptic curves over finite fields (5 pages) | GP Code | Exercises | Solutions
  • Computing the rank of an elliptic curve (9 pages) | GP Code
  • L-functions (21 pages) | GP Code
  • basic L-functions and Dirichlet characters (19 pages) | GP Code
  • L-functions (17 pages) | Code | Exercices
  • Dirichlet characters (10 pages) | GP Code
  • Hecke Grossencharacters (27 pages) | GP code
  • Modular forms (62 pages) | GP Code
  • Quaternion algebras (33 pages) | GP code
• Exercices in English:
  • Algebraic number theory (from scratch, with exercices) [WORK IN PROGRESS] (19 pages)
  • Polynomials, Galois extensions, finite fields (2 pages)
  • Number fields, class field theory (3 pages)
  • Elliptic curves (2 pages)
  • L-functions (1 pages)
• Tutoriels des ateliers en français (diapositives et code GP) :
  • Initiation à PARI/GP (13 pages) | Code GP
  • Programmation en GP (11 pages) | Code GP
  • Théorie algébrique des nombres (47 pages) | Code GP
  • Théorie algébrique des nombres avancée (35 pages) | Code GP
  • Courbes elliptiques sur les corps finis (4 pages) | Code GP
  • Introduction à la théorie algébrique des nombres (16 pages) | Jupyter notebook

English

• The PARI/GP entry in the Rosetta code wiki.

• Dictionaries between PARI/GP and the algorithms in Henri Cohen's first two books GTM138 and GTM193 (for efficiency's sake the implementations may not follow the text's description or implement superior variants).

• Sample GP scripts from the documentation, as seen from within the Vim editor: [README]

  These scripts are HTML-ified and provided for online browsing only. You may copy-paste them into GP, but downloading them is unlikely to be useful.

  [ bench.gp | cl.gp | classno.gp | contfrac.gp | lucas.gp | rho.gp | squfof.gp | taylor.gp ]

• Online reference manual for GNU readline (line editing under gp).

• How to integrate PARI within Mathematica using MathLink.
• How to call external programs using extern (worked out example: John Cremona's mwrank).

En Français

• Une présentation pour les enseignants du secondaire.
• Une présentation/tutoriel du système [PDF]

Links

• The book Numerical Algorithms for Number Theory (2021) by Karim Belabas and Henri Cohen contains a wealth of advanced modern GP scripts.
• A series of introductory lectures about number theory (2001), written by William Stein. Contains an introduction to GP and many fun scripts.
• The SIAM 100-digit challenge book (2004), written by Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel. Contains many advanced GP scripts written to solve Trefethen's challenge problems.