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Upgraded pari-2.2 to pari-2.2.4.

This directory contains:

* the C program matexp.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.

-- 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!).

-- 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, 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,
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 very 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)
[much 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 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.

-- 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)

which 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)