This directory contains:

* the C program mattrans.c using the Pari library described in Chapter 4 of
the users' manual. A generic Makefile (adapted to your system by Configure)
for PARI programs is included.

* Inputrc: an example of .inputrc file for the readline library.

* Several examples of complete and non-trivial GP programs. The rest of this
file gives a brief description of these programs. They should be read into GP
by the command \r file.

1) 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 10 terms (this ratio 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!).

2) cl.gp

  Written entirely in the GP language without using the function
bnfclassunit, the programs included in this file allow you in many cases to
compute the class number, the structure of the class group and a system of
fundamental units of a general number field (this programs sometimes fails to
give an answer). It can work only if nfinit finds a power basis. Evidently it
is much less powerful and much slower than the function bnfclassunit, but it
is given as an example of a sophisticated use of GP.  The first thing to do
is to call the function clareg(pol,limp,lima,extra) 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 clearly it slows down too much before succeeding, abort
and try other values. If it succeeds, it will print the class number, class
group, regulator. These are tentative values. Then use the function
check(lim) (lim=200 is the default value) to check if the value is consistent
with the value of the L-series (the value returned by check should be close
to 1). Finally, the function fu() (no parameters) returns a family of units
which generates the unit group (you must extract a system of fundamental
units yourself).

3) lucas.gp

The half line 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.

4) 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.

5) 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 very nice factoring
method invented in the 70's by D. Shanks for factoring integers, and is 
reasonably fast for numbers having up to 15 or 16 digits. The squfof program
which is given is a very crude implementation. It also prints out some
intermediate information as it goes along. The final result is some factor of
the number to be factored.
