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 - unclassified *************************** BUGS (general) **************************** Unless specified otherwise, examples assume 32bit machine and default precision 5 setrand(5);thueinit(x^3 + x^2 - 43690*x - 3529208) *** non positive argument in mplog. \\ precision problem 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] 4 t_SER computations much too slow when number of terms increase, even when applying a trivial formula, e.g cos(x) at \ps 10000 3 many functions assume MAXVARN is a free variable, yielding bogus results if the input involve it (only affect 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 life of GP variables too short in pathological cases: v = concat(v, [v=1,v=2]); concat(v, [v=1,v=2]) --> SEGV 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 ???) *************************** 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 inline more assembler kernels, alpha in particular (ix86 and sparc are already inline). 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 don't assume that nf.zk is HNF. Allow using LLL-T2-reduced bases (with first element 1) --> huge improvement to all idealred computations (esp. bnfisprincipal, bnfinit) 4 graphics: allow FIG output (besides PostScript) [easier to edit!] 4 decent finite field package (remove all the nfxxxmodpr functions) 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 \ and % (euclidean division) could accept more arguments (e.g t_REAL) x \ y := floor(x/y) if y > 0 and floor(x/y) + 1 if y < 0 x % y := x - y(x\y) [ hence 0 <= x%y < |y| ] 3 zetak is very inefficient and unable to handle most fields of degree > 6 3 have quadclassunit return bnf structure 3 2-adic initell 3 p-adic ellztopoint *************************** 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 integrate Ilya's code for yet bigger prime tables (pari-dev-435). Unify functions using diffptr (if possible correcting the forprime bug above) 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 let forprime(n=a, b, ...) work even if a,b above primelimit (maybe with a Warning), via simple sieve + pseudo primality test 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] 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 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. 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 (cf above) 2 write a GP scripts profiler (cf above)