This file lists the things that ought to be implemented / fixed. It is
hopelessly incomplete right now, but it's a start. Most items require major
work, and may not be that desireable after all. If you intend to work on
any of these things, have a look at CVS.txt and drop an email to pari-dev.

Priority classification (first column): [subjective and debatable!]
5    as soon as possible
4    should be done
3    nice to have
2    maybe not
1    probably not
0    no
-    unclassified

***************************   BUGS (general)     ****************************
Unless specified otherwise, examples assume 32bit machine and default precision 

5  bnfinit sometimes gives wrong answers because we cheat on the value of
Bach's bound, using 0.3 log^2 D by default, where 0.3 should really be 12
(under GRH). If it's not enough, we compute a subquotient of the classgroup,
i.e junk. Ex:
 * setrand(3); bnfinit(y^4 + 1190*y^2 + 1416100).cyc --> [8,2,2,2].
   Wrong. The correct structure is [8,4,2].

 * setrand(1414185642); bnf = bnfinit(y^4 + 635*y^2 + 403225).reg is twice
the correct value.

5  polgalois(x^8-1864259299553450972214799899167226732549697977945716*x^6+331143259018657601105207922631212331088735421305543663274125986698777318014979969*x^4-2225286541902342283500014249183311190477390*x^2+5);
  ***   degree too large in tschirn.

4  precision problems in polgalois:
   setrand(7);
   polgalois(x^8+162644002617632464507038884216211529274267271168000002)
   gives wrong result at \p28 [32,-1,17], correct at \p38 [32,-1,15]

4  gcmp/gegal not transitive: [] == 0, [0] == 0, but [0] != []

4  rnfpolred is numerically unstable:
   ? rnfpolred(nfinit(quadpoly(904,y)),quadray(904,1))
     ***   division by zero in gdiv, gdivgs or ginv

4  qfbclassno(x < 0) may give a wrong result [e.g x = -2878367]

3  many functions assume MAXVARN is a free variable, yielding bogus
   results if the input involves it (only affects library programming).

3  quadclassunit not reliable when fed non fundamental discriminants
   (infinite loop [e.g quadclassunit(-352)], wrong result)

3  ellinit over Q_2 doesn't work (AGM loses too much precision)

3  ellpointtoz over Q_p makes no difference between P and -P (corrected over
   C by a cheap trick)

3  recursive plot easily fooled. One could split intervals in 3 + make sure
   size of neighbouring intervals don't differ too much.

***************************   BUGS (GP specific) ****************************

5  readline: assume a file 'foo' exists, \rf<TAB> --> \foo [\r f<TAB> is OK]

4  changing primelimit from within forprime loop yields unpredictable results

3  after allocatemem() / default(parisize, ...), the rest of the command is
   discarded (ends by a longjmp).

2  under GP after an error, memory is only recovered from "entire variables".
   Individual components of lists/vectors/matrices are left alone if the
   GLOBAL object wasn't modified during the last cycle (i.e only v[x] = ... 
   occured)

1  sum(i=1,3000, exp(-i^2)) --> overflow in R*R
   The "negligible" terms should be neglegted, not overflow because of the
   way the computation is done. [ Tough to correct! ]

***************************  DOCUMENTATION    ****************************

5  complete/update the tutorial (esp. section 11 and 12)

4  add examples for all functions in Chapter 3

4  separate chapter 4 and 5 and document the innards of PARI (entree,
   pariFILE, bloc ...)

2  HTML version (pod ? SGML ? yodl ???)

***************************  MISCELLANEOUS    ****************************

5  write decent (specialized) benches

3  switch to autoconf

3  use stat() instead of opendir() to check if a file is a directory.

***************************   ALGORITHMS      ****************************

Kernel:
=======
5  check NaN in dbltor and related routines

4  benchmark / profile basic functions and see what needs to be done

4  finish t_REAL Karatsuba and diviiexact

4  inline level0 routines should operate on _limbs_, not on words.

3  FFT for basic types and polynomials (say in A[X], for A = Z, F_q, ...)

2  add support for different multiprecision kernels (a la LiDIA)

Misc:
=====
4  decent finite field package (remove all the nfxxxmodpr functions)

4  rnfkummer (very slow)

4  nfsubfields [use known subfields to discard blocs right away] (current uses
   far too much memory)

3  zetak is very inefficient and unable to handle most fields of degree > 8

3  have quadclassunit return bnf structure

3  2-adic initell

3  p-adic ellztopoint

0  graphics: allow FIG output (besides PostScript) [easier to edit!]
   [ No: use pstoedit ]

***************************   LIBRARY DESIGN   ****************************

4  a system of DEBUGLEVEL classes [e.g \g 5 "LLL" ] (such that the user can
   easily define new ones)

4  allow generic functions to process and produce t_SMALL's

4  remove all dependences on types ordering [if (typ(x) < t_POL) ...]

3  remove global variables gpi, geuler: their precision is unpredictable
   (at least as much as requested in last const[pi|euler](), possibly much
   more). Explicit call to mp[pi|euler] should be required. Will break
   existing code...

3  rename library functions following GP names

3  rewrite the generic functions (gadd/gmul/gdiv plus a couple of others) to
   use (two-dimensional) table lookups instead of switches

3  introduce "special" types for objects which are really containers and
   should be defined by a secondary type (e.g number fields, finite fields,
   p-adic fields, elliptic curves, ...). Would keep list of types small
   (and fast)

3  better representations for multivariate polynomials

3  type "element in" ([number|finite] field...), "point" on elliptic curve

3  find a way to deal (generically) with "integral object + its content"
   Application (e.g): fractional ideals much more efficient.

2  "mute" variables for t_POLMOD. Should have Mod(x,x^2+1) == Mod(y,y^2+1).

2  have some header magic (transparently) prepend some prefix (e.g "pari_")
   before all exported functions to prevent name conflicts. Build alias
   files for debuggers

***************************   GP DESIGN       ****************************

5  remove limitation to 8 arguments for static functions (argvec[9])

4  use divide & conquer approach in string / integer conversions

4  extend forprime(n=a,b,...) so that b can go over primelimit [cut [a,b]
   in large intervals, sieve out multiple of small primes there, then use
   isprime() on the rest]

3  changevar with explicit (incomplete) permutation. E.g
   changevar(p, [x,y], [a,b]) for x -> a, y -> b
   add a flag to substitute in succession or in parallel (e.g if a involves y)

3  possibility to save and load a session (variables, functions, defaults)

3  a type t_FILE [current: stream re-opened/flushed/closed after every single
   write(): disaster when one wants to write often to the same file]

3  add a possibility to increase the maximal recursion depth (need to 
   increase the GP process stack: use setrlimit(RLIMIT_STACK,) + fork)

***************************   TOOLS           ****************************

4  a script converting prototype to parser code (e.g GEN f(GEN,GEN) --> "GG")

3  a script to translate "legacy" GP code into something using GP2 function
   names

3  write an analog of the 'echo' default which would print code as it is
   executed, not as it is read

2  write a GP scripts debugger

2  write a GP scripts profiler