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version 1.1, 2001/10/02 11:16:59 version 1.2, 2002/09/11 07:26:45
Line 13  by the command \r file.
Line 13  by the command \r file.
 -- bench.gp: This program computes the first 1000 terms of the Fibonacci  -- bench.gp: This program computes the first 1000 terms of the Fibonacci
 sequence, the product p of successive terms, and the lowest common multiple  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  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  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  this program is one (among many) examples where GP/PARI performs orders of
 magnitude faster than systems such as Maple or Mathematica (try it!).  magnitude faster than systems such as Maple or Mathematica (try it!).
   
Line 21  magnitude faster than systems such as Maple or Mathema
Line 21  magnitude faster than systems such as Maple or Mathema
 programs included in this file allows you in many cases to compute the class  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  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  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  only if nfinit finds a power basis. Evidently it is much less powerful, less
 much slower than bnfinit, but it is given as an example of a sophisticated  reliable and much slower than bnfinit, but it is given as an example of a
 use of GP.  The first thing to do is to call the function clareg(pol,  sophisticated use of GP.  The first thing to do is to call
 {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.  
   
      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    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  them. If you see that it slows down too much before succeeding, abort and try
 and try other values. If it succeeds, it will print the class number, class  other values. If it succeeds, it will print the class number, class group,
 group, regulator. These are tentative values. Then use the function  regulator. These are tentative values. Then use
 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).  
   
      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  -- classno.gp: A very simple function to compute analytically the class
 number of imaginary quadratic fields (written by Fernando Rodriguez Villegas)  number of imaginary quadratic fields (written by Fernando Rodriguez Villegas)
   
Line 63  some intermediate information as it goes along. The fi
Line 71  some intermediate information as it goes along. The fi
 factor of the number to be factored.  factor of the number to be factored.
   
 -- taylor.gp: Given a user function f (e.g defined by f(x) = sin(x)), defines  -- 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  a function
 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.     plot_taylor(xmin,xmax, ordlim, first,step)
 Sensible default values are provided for all arguments (written by Ilya  
 Zakharevich)  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)
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