File: [local] / OpenXM_contrib / pari / Attic / TODO (download)
Revision 1.1.1.1 (vendor branch), Sun Jan 9 17:35:29 2000 UTC (24 years, 8 months ago) by maekawa
Branch: PARI_GP
CVS Tags: maekawa-ipv6, VERSION_2_0_17_BETA, RELEASE_20000124, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, RELEASE_1_1_3, RELEASE_1_1_2 Changes since 1.1: +0 -0
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Import PARI/GP 2.0.17 beta.
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For PARI/GP version 2.0.17
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.DOC 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
- unclassified
*************************** 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 ...)
3 clean up gphelp / TeX macros
2 HTML version (pod ? SGML ? yodl ???)
*************************** BUGS ****************************
- 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, even with a way to trap
exceptions
5 nfgaloisconj still misses some conjugates. Symptom: try it on
polcompositum(quadpoly(11321), x^15-3*x^14-46*x^13+69*x^12+794*x^11-50*x^10-5226*x^9-4559*x^8+9682*x^7+15656*x^6+3342*x^5-5950*x^4-4386*x^3-1136*x^2-100*x+1)
[Hilbert class field extension]
5 silent overflows in codeword-handling macros: O(2^50000) --> O(2^-15535)
5 some doubles can overflow in rootpol.c, should use t_REAL everywhere
? polroots(x^3 + 2^1024*x + 1)
*** underflow or overflow in a R->dbl conversion
4 gcmp is not transitive: [] == 0, [0] == 0, but [0] != []
4 mateigen([1,1;1,2]) won't succeed at default precision (28 digits).
Should use iterative methods.
3 polgalois should handle precision problems. Symptom: applied to
polzagier(11,0)/polzagier(1,0), gives wrong result with 38 digits
3 after allocatemem() / default(parisize, ...), the rest of the command is
discarded (ends by a longjmp).
3 recursive plot easily fooled. One could split intervals in 3 + make sure
size of neighbouring intervals don't differ too much.
*************************** DEVELOPMENT ****************************
5 write decent (specialized) benches
3 switch to autoconf
*************************** 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:
=====
5 (easy) modify invmod to get Jebelean extended gcd
4 decent finite field package (remove all the nfxxxmodpr functions)
4 round 4 (too slow, use modular techniques)
4 rnfkummer (doesn't work)
4 nfsubfields [use known subfields to discard blocs right away] (current uses
far too much memory)
4 LLL over R (not stable). Clean up bibli1.c (remove duplicate code)
4 rethink the element_mul type of functions: multiplication table is O(n^3),
polynomial multiplication + remainder is O(n^2) [+ can use Karatsuba/FFT]
3 have quadclassunit return bnf structure
3 have quadclassunit treat reliably non fundamental discriminants (at
least, make relevant checks before entering infinite loops)
3 2-adic initell
*************************** LIBRARY DESIGN ****************************
4 a way to trap PARI errors, esp. all kinds of overflows (exponent, degree,
stack, ...). Something like:
trap(errpile, &stack_overflow_handler)
4 allow generic functions to process and produce t_SMALL's
4 remove all dependences on types ordering [if (typ(x) < t_POL) ...]
3 integrate Ilya's code for yet bigger prime tables. Unify functions using
diffptr
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
2 should use vsnprintf instead of vsprintf in pariputsf. Requires GNU libio.
[paripusf uses static buffer which should be ok for "most" purposes]
*************************** GP DESIGN ****************************
5 remove limitation to 8 arguments for static functions (argvec[9])
4 use divide & conquer approach in string / integer conversions
4 a way to trap PARI errors (esp. stack overflow). Something like:
trap(errpile, "GP_command_to_be_executed_when_stack_overflows")
3 split matrix_block in 2 parts: exploration + assignment. Would allow
Math::Pari to use complicated x[][][][] constructs
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]
*************************** 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 a gp-to-C compiler (adding #defines in anal.c + modifying the
table of functions in init.c, etc, to include the explicit function name).
Should be easy: the code is mostly there.
2 write a GP scripts debugger (cf above)
2 write a GP scripts profiler (cf above)