-- bench.gp: This program computes the first 1000 terms of the Fibonacci sequence, the product p of successive terms, and the lowest common multiple q. It outputs the ratio log(p)/log(q) every 50 terms, which tends to Pi^2/6 as k tends to infinity. The name bench.gp comes from the fact that this program is one (among many) examples where GP/PARI performs orders of magnitude faster than systems such as Maple or Mathematica. (Try it!) -- cl.gp: Written entirely in the GP language without using bnfinit, the programs included in this file computes the class number, the structure of the class group and a system of fundamental units of a general number field. It sometimes fail to give an answer and works only if nfinit finds a power basis. Evidently it is less powerful, less reliable and much slower than bnfinit, but it is given as an example of a sophisticated use of GP. The first thing to do is to call clareg(pol, {limp=19},{lima=50},{extra=5}) where pol is the monic irreducible polynomial defining the number field, limp is the prime factor base limit (try values between 19 and 113), lima is another search limit (try 50 or 100) and extra is the number of desired extra relations (try 2 to 10). Default values are provided, so that you need only supply pol. The program prints the number of relations that it needs, and tries to find them. If you see that it slows down too much before succeeding, abort and try other values. If it succeeds, it will print the class number, class group and regulator. These are tentative values. Then use check({lim = 100}) to check if the value is consistent with the value of the L-series (the value returned should be close to 1). Finally, fu() (no parameters) returns a family of units which generates the unit group (you must extract a system of fundamental units yourself). -- classno.gp: a simple function to compute analytically the class number of imaginary quadratic fields (written by Fernando Rodriguez Villegas) -- contfrac.gp: period(D) computes period of continued fraction for sqrt(D) [slower than quadregulator, which does a bit more work, but is written in C!] (written by Igor Schein) -- lucas.gp: The function lucas(p) defined in this file performs the Lucas-Lehmer primality test on the Mersenne number 2^p-1. If the result is 1, the Mersenne number is prime, otherwise not. -- rho.gp: a simple implementation of Pollard's rho method. The function rho(n) outputs the complete factorization of n in the same format as factor. -- squfof.gp: This defines a function squfof of a positive integer variable n, which may allow you to factor the number n. SQUFOF is a nice factoring method invented in the 70's by Dan Shanks for factoring integers, and is reasonably fast for numbers having up to 15 or 16 digits. The squfof program given here is a crude implementation, which prints out some intermediate information as it goes along. The final result is some factor of the number to be factored. -- taylor.gp: the function plot_taylor(f,xmin,xmax, ordlim, first,step) plots the Taylor polynomials T_i (truncated series expansion of order i) of the function f in the interval [xmin,xmax]; i goes from first to ordlim in increments of steps. Sensible default values are provided for all arguments (adapted from an original idea by Ilya Zakharevich). A few examples are provided, together with a simple colormap generator