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This file highlights some of the novelties in PARI/GP 2.x compared to 1.39.15
(last release in the 1.x series). The detailed Changelog is in CHANGES.
Incompatible changes are described in COMPAT. See TODO for possible future
improvements.
%%%%%%%%%%%%%%%%%%%%%%%%%%%% VERSION 2.3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
* The GP2C compiler is available at
http://pari.math.u-bordeaux.fr/download.html#gp2c
GP2C compiles GP scripts to the C language, easing the task of writing
PARI programs. It can transparently compile them to object code and
load the resulting functions in gp. Low-level gp2c-compiled scripts
typically run 3 or 4 times faster. Minor hand editing (specifying types)
typically gains a further factor 2.
* Cremona's database of elliptic curves is available through the 'elldata'
package [ to be downloaded separately ]
? E = ellinit([1,1,0,10,10]);
? id = ellidentify(E)[1] \\ [1] = discard change of variables
%2 = ["69950b1", [1, 1, 0, 10, 10], [[-1, 1], [-1/4, 23/8]]]
\\ gives name and generators
? E = ellinit("11a1"); E.disc
%3 = -161051
? ellsearch(11); \\ all curves of conductor 11
? forell(E, 10,20, print(E)) \\ iterate over curves of conductor 10-20
["11a1", [0, -1, 1, -10, -20], []]
...
Kernel:
* Use 'Configure --with-gmp' to replace the native multiprecision kernel by
the GNU MP library (featuring asymptotically fast arithmetic).
* Cleanup of all architecture specific kernels (all macroized); added
support for x86_64, ppc64, hppa and hppa64, ia64, sparc64, m68k.
* Faster algorithms for "transcendental" functions (divide/conquer square
root, AGM for log and Pi, Newton for exp and most trigonometric functions,
AGM for inverse trigonometric functions, rewrite for gamma and zeta =>
faster Bernoulli, Mestre's AGM for ellheight)
* Faster and cleaner kernel for modular arithmetic. Try e.g.
factormod/factorff or polcompositum.
* Major internal cleanups: separate lgef for t_POLs is gone, zero t_SER
and t_POL now handled in a uniform way, heuristic soft copies in
t_INTMOD, t_POLMOD, t_PADIC are gone [ led to fatal errors in complex
scripts, no performance penalty ]
* The "syntax" of GP routines and operators are no longer hard-coded in
the sources, but maintained in a separate database (pari.desc). This
way, external tools like GP2C need not be modified when the GP language
is changed.
Algebraic number Theory:
* Faster integral LLL (still not super fast, but getting better), and
polynomial factorization routines (over finite fields [ new modular
kernel ], Q or general number fields [ van Hoeij's algorithm ])
* Faster maximal order (round4 rewrite) and polredabs (esp. with flag
16: don't factor the discriminant; yields a canonical equation for a
field), faster ideal arithmetic (prime decomposition, approximation,
multiplication).
* Faster and more reliable class-field theoretic functions quadclassunit,
bnfinit, bnfisprincipal, bnrinit (and related functions, e.g. bnrconductor
or bnrdisc), rnfkummer, thue (fast enumeration of small solutions, don't
assume the full unit group is known).
* A set of fast routines for Galois theory (galoisininit, nfgaloisconj,
galoisisabelian, galoisfixedfield, galoissubfields, galoissubcyclo for
abelian fields, galoisidentify to identify large Galois fields up to
degree 127).
'galdata' package [ to be downloaded separately ]: polgalois is safer
and orders of magnitudes faster in tough cases, output is now
human readable
? polgalois(x^11-2)
time = 1,759 ms. \\ used to be ~ 1 hour
%1 = [110, -1, 4, "F_110(11)=11:10"]
Miscellaneous:
* For convenience, the manual was split in two parts: the GP user's manual
and the libpari user's manual, the latter being substantially expanded.
Many formerly private functions have been renamed, specified,
cleaned up and documented.
* Initial implementation of the APR-CL primality prover, faster
compositeness tests (BPSW)
* A new set of fast numerical summation and integration routine,
variations on the Ooura-Mori "double exponential" method. See ??intnum
Library interface to all these functions and standard iterators (e.g.
forvec)
* Error messages now mention the GP function where the error occured.
* Input/output and convenience functions: Str(a,1,c) --> "a1c",
Strexpand("~") --> "/home/a2x/belabas", substvec (parallel substitutions),
substpol(expr, x^2, y), writebin (write objets in binary format for
fast retrieval), readvec (load a file's content into a vector)
* Support for new graphic libraries (Qt, FLTK) [ ==> hi-res plots now
also available under Mac OS X and Windows ]
%%%%%%%%%%%%%%%%%%%%%%%%%%%% VERSION 2.1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
* PARI/GP is now released under the GNU General Public License.
* PARI now has a CVS server which is intended for PARI lovers who want
the very latest bleeding edge release (see the CVS.txt file).
* Argument checks have been added to prevent unpredictable results when
the input is incorrect.
* Errors can be trapped to avoid abort and recover computations.
* extended on-line help:
?? (no arguments) opens the users'manual in xdvi,
?? tutorial / refcard opens tutorial / refcard in xdvi,
??? keyword searches for topic in the manual.
* Arithmetic: much faster integer factorization with several factoring
engines including Pollard Rho, SQUFOF, improved ECM, and an MPQS/PMPQS
implementation derived from LiDIA's, with kind permission from the LiDIA
team
* Polynomials:
- much faster factorization over Z[X] (van Hoeij's algorithm) or Fq[X]
(more efficient modular kernel), esp. when the polynomial is defined
over Fp.
- Ducos' subresultant algorithm for resultants
* Number field:
- improved ROUND 4 for computations of integral basis/discriminant
- faster polredabs / rnfpolredabs polynomial reductions functions
- Galois extensions of Q: Fixed fields, Galois conjugates using
Allombert's algorithm.
* Class group, ray-class group:
- improved bnf/bnr functions (faster, numerically stabler), in
particular bnfisprincipal
- computations of explicit defining equations of abelian extensions of
imaginery quadratic fields (using complex multiplication) of totally
real abelian extensions (using Stark units).
* Elliptic functions: Weierstrass and Weber functions.
* Plotting: support of gnuplot, new functions (possiblity to plot directly
in a file).
%%%%%%%%%%%%%%%%%%%%%%%%%%%% VERSION 2.0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The GP/PARI structure has been cleaned up.
* The whole configuration process has been automated, and a Configure
file is provided. Just typing `./Configure' should see you home in most
cases.
* PARI is now available as a dynamic library, thanks to Louis Granboulan.
(you can link GP with it, if you wish to). This saves a tremendous
amount of disk space, and is generally more convenient as you don't need
to re-link your files when updating the library (or when debugging.
or profiling, or...).
* types now have a symbolic mnemonic name (e.g t_INT for an integer,
t_VEC for a vector, and so on).
* General speed-up (depends on your applications, about 40% for our
generic testing file).
* Experimental module loading structure (the actual function tree
has not yet been cut into modules, but for the GP specific functions).
==========================================================================
Many new or improved functions in the PARI library.
* MANY class-field related functions. In particular:
- is it now possible to try and remove the GRH assumption on class group
computations.
- ray class groups computations (including discrete log).
- explicit defining equations in simple cases (Kummer extensions of prime
degree, quadratic base field).
* computation of Galois groups up to degree 11
* roots is now entirely reliable, thanks to Xavier Gourdon.
* some core routines have been optimized: Karatsuba fast multiplication,
a specific function gsqr() for squarings,...
* input/output is much more flexible now:
- a function GENtostring has been added, generalizing gitoascii to any
PARI object (with a simpler syntax: GENtostring(g) returns a malloc'ed
string containing g as gp would print it).
- readexpr has a relative freadexpr (for filtered readexpr), which enables
you to use input containing whitespaces.
- you can use GENs in formatted output, a la printf.
* improved garbage collecting.
* private variables can be created without an explicit readexpr(), using
fetch_var() and delete_var().
==========================================================================
GP has been completely re-written:
* lowercase/uppercase are now significant. All predefined constants
(Euler, I, Pi) have been renamed (as well, the o() notation for series
and padics has been superseded by O()).
for (i=1,10, print(i)) will not yield an error anymore.
* human-readable error messages, including a caret to indicate where
a GP syntax error occurred.
* function names were renamed according to a more logical scheme. The
file new.dico provides a translation (available under GP using "whatnow")
* You can retrieve basic information from complicated objects using member
functions. For instance x.disc will yield the discriminant of x, whether
it was created by nfinit (aka initalg), bnfinit (aka buchinit), ellinit
(aka initell).
* A `gprc' file is available to set "permanent" defaults (such as
global variables, aliases, custom user functions, etc...). For instance,
you can put all your scripts in some special directories, and
point them out to GP using "path". See misc/gprc.dft for examples.
The function "default" enables to change most defaults under gp.
For instance: default(compatible, 2) will give you back the former gp
function names and helpmessages. [default(compatible, 3) undoes the
lowercaps/uppercaps changes as well]. Try "default".
* basic C idiosyncrasies such as for instance i++ (for i=i+1), i<<1
(for left shift) or i+=j (for i=i+j) are now allowed within GP scripts.
/* */ multi-line comments are understood.
* lists and (primitive) string support have been added. Characters can be
quoted with the usual meaning. As a result, set functions can now be
used with arbitrary elements.
* if your terminal supports color (variants of color_xterm for instance),
you can tell GP to highlight its output in different (user configurable)
colors. This is done by fiddling with the default "colors".
* The familiar functions "break", "next" and "return" are now available.
These should supersede the buggy label/goto provided in older versions.
* Enhanced on-line help. If you have perl on your system, try
?? function-name (e.g ?? bnfinit)
This is provided by external scripts which can be used independently,
outside of the GP session.
* If readline is installed on your system, a context-dependent completion
(not yet user-programmable) is now available (try hitting <TAB> here and
there). Try ?? readline.
* many functions now have default arguments (shown between braces {} in
the on-line description). gp first reads user-supplied arguments, and
then fills in the arg list with these default values. Optional args can
be entirely omitted, comma included (for a function with no mandatory
arguments, even parentheses are optional !). For instance:
Mat = Mat()
bnfclassunit(x^2+1,0) = bnfclassunit(x^2+1)
bnfclassunit(x^2+1,,[0.2,0.2]) = bnfclassunit(x^2+1,0,[0.2,0.2])
The "else" part of the "if" function can be entirely omitted.
if (a,1) is now correct; of course, the former syntax if (a,1,) is
still valid.
* functions "extern" and "system" have been added to interface with
external programs (UNIX only). You can do for instance
extern("myprog"), or system("ls -l *.gp").
* even better, "install" enables you to load any function provided by
a dynamically linked library, and have the GP interpreter use it. This
makes it easy to have your own customized version of GP with your own set
of functions on startup (you can document them using "addhelp").
* On 32-bit machines, maximum number of variables has been increased from
254 to 16382. Arrays can have up to 16777214 elements (instead of 65534).
In addition vector/matrix operations in GP now perform orders of
magnitudes faster than in version 1.39