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Import PARI/GP 2.0.17 beta.

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 50 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 bnfclassunit, the
programs included in this file allows 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 (they sometimes fail to give an answer). It can work
only if nfinit finds a power basis. Evidently it is much less powerful 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 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) classno.gp: A very simple function to compute analytically the class
number of imaginary quadratic fields (written by Fernando Rodriguez Villegas)

4) 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.

5) 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.

6) 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.

7) taylor.gp: Given a user function f (e.g defined by f(x) = sin(x)), defines
a function plot_taylor(xmin,xmax, ordlim, first,step) plots f together with
its Taylor polynomials T_i (truncated series expansion of order i) in the
interval [xmin,xmax]; i goes from first to ordlim in increments of steps.
Sensible default values are provided for all arguments (written by Ilya
Zakharevich)