This section documents the GP defaults,
that can be set either by the GP function default or in your GPRC.
Be sure to check out parisize and parisizemax !
The bits of this default allow
gp to use less rigid TeX formatting commands in the logfile. This
default is only taken into account when log = 3. The bits of
TeXstyle have the following meaning
2: insert {}right / {}left pairs where appropriate.
4: insert discretionary breaks in polynomials, to enhance the probability of
a good line break. You must then define {}PARIbreak as
follows:
\def\PARIbreak{\hskip 0pt plus \hsize\relax\discretionary{}{}{}}
The default value is 0.
If true, enables the "break loop" debugging mode, see Section se:break_loop.
The default value is 1 if we are running an interactive gp
session, and 0 otherwise.
This default is only usable if gp
is running within certain color-capable terminals. For instance rxvt,
color_xterm and modern versions of xterm under X Windows, or
standard Linux/DOS text consoles. It causes gp to use a small palette of
colors for its output. With xterms, the colormap used corresponds to the
resources Xterm*colorn where n ranges from 0 to 15 (see the
file misc/color.dft for an example). Accepted values for this
default are strings "a1,...,ak" where k ≤ 7 and each
ai is either
* the keyword no (use the default color, usually
black on transparent background)
* an integer between 0 and 15 corresponding to the aforementioned colormap
* a triple [c0,c1,c2] where c0 stands for foreground color, c1 for background color, and c2 for attributes (0 is default, 1 is bold, 4 is underline).
The output objects thus affected are respectively error messages, history numbers, prompt, input line, output, help messages, timer (that's seven of them). If k < 7, the remaining ai are assumed to be no. For instance
default(colors, "9, 5, no, no, 4")
typesets error messages in color 9, history numbers in color 5, output in color 4, and does not affect the rest.
A set of default colors for dark (reverse video or PC console) and light
backgrounds respectively is activated when colors is set to
darkbg, resp. lightbg (or any proper prefix: d is
recognized as an abbreviation for darkbg). A bold variant of
darkbg, called boldfg, is provided if you find the former too
pale.
In the present version, this default is incompatible with PariEmacs. Changing it will just fail silently (the alternative would be to display escape sequences as is, since Emacs will refuse to interpret them). You must customize color highlighting from the PariEmacs side, see its documentation.
The default value is "" (no colors).
Obsolete. This default is now a no-op.
The name of directory containing the optional data files. For now,
this includes the elldata, galdata, galpol, seadata
packages.
The default value is /usr/local/share/pari, or the override specified
via Configure --datadir = .
Windows-specific note. On Windows operating systems, the
special value @ stands for "the directory where the gp
binary is installed". This is the default value.
Debugging level. If it is nonzero, some extra messages may be printed,
according to what is going on (see \g). To turn on and off diagnostics
attached to a specific feature (such as the LLL algorithm), use
setdebug.
The default value is 0 (no debugging messages).
This is a deprecated alias for setdebug("io",). If nonzero,
gp will print information on file descriptors in use and I/O
operations (see \gf).
The default value is 0 (no debugging messages).
Memory debugging level (see \gm). If this is nonzero, gp will
print increasingly precise notifications about memory use:
* debugmem > 0, notify when parisize changes (within the
boundaries set by parisizemax);
* debugmem > 1, indicate any important garbage collection and the
function it is taking place in;
* debugmem > 2, indicate the creation/destruction of
"blocks" (or clones); expect lots of messages.
Important Note:
if you are running a version compiled for debugging (see Appendix A) and
debugmem > 1, gp will further regularly print information on
memory usage, notifying whenever stack usage goes up or down by 1 MByte.
This functionality is disabled on non-debugging builds as it noticeably
slows down the performance.
The default value is 1.
This default can be 0 (off), 1 (on) or 2 (on, raw). When echo
mode is on, each command is reprinted before being executed. This can be
useful when reading a file with the \r or read commands. For
example, it is turned on at the beginning of the test files used to check
whether gp has been built correctly (see \e). When echo is set
to 1 the input is cleaned up, removing white space and comments and uniting
multi-line input. When set to 2 (raw), the input is written as-is, without any
pre-processing.
The default value is 0 (no echo).
This toggle is either 1 (on) or 0 (off). If on,
the integer factorization machinery calls addprimes on prime
factors that were difficult to find (larger than 224), so they are
automatically tried first in other factorizations. If a routine is performing
(or has performed) a factorization and is interrupted by an error or via
Control-C, this lets you recover the prime factors already found. The
downside is that a huge addprimes table unrelated to the current
computations will slow down arithmetic functions relying on integer
factorization; one should then empty the table using removeprimes.
The default value is 0.
This toggle is either 1 (on) or 0 (off). By
default, the factors output by the integer factorization machinery are
only pseudo-primes, not proven primes. If this toggle is
set, a primality proof is done for each factor and all results depending on
integer factorization are fully proven. This flag does not affect partial
factorization when it is explicitly requested. It also does not affect the
private table managed by addprimes: its entries are included as is in
factorizations, without being tested for primality.
The default value is 0.
Of the form x.n, where x (conversion style)
is a letter in {e,f,g}, and n (precision) is an
integer; this affects the way real numbers are printed:
* If the conversion style is e, real numbers are printed in
scientific format, always with an explicit exponent,
e.g. 3.3 E-5.
* In style f, real numbers are generally printed in
fixed floating point format without exponent, e.g. 0.000033. A
large real number, whose integer part is not well defined (not enough
significant digits), is printed in style e. For instance
10.^100 known to ten significant digits is always printed in style
e.
* In style g, nonzero real numbers are printed in f format,
except when their decimal exponent is < -4, in which case they are printed
in e format. Real zeroes (of arbitrary exponent) are printed in e
format.
The precision n is the number of significant digits printed for real
numbers, except if n < 0 where all the significant digits will be printed
(initial default 28, or 38 for 64-bit machines). For more powerful formatting
possibilities, see printf and strprintf.
The default value is "g.28" and "g.38" on 32-bit and
64-bit machines, respectively.
A vector of colors, to be used by hi-res graphing routines. Its length is
arbitrary, but it must contain at least 3 entries: the first 3 colors are
used for background, frame/ticks and axes respectively. All colors in the
colormap may be freely used in plotcolor calls.
A color is either given as in the default by character strings or by an RGB
code. For valid color names, see the standard rgb.txt file in X11
distributions, where we restrict to lowercase letters and remove all
whitespace from color names. An RGB code is a vector with 3 integer entries
between 0 and 255 or a # followed by 6 hexadecimal digits.
For instance [250, 235, 215], "#faebd7" and
"antiquewhite" all represent the same color.
The default value is ["white", "black", "blue",
"violetred", "red", "green", "grey",
"gainsboro"].
Entries in the
graphcolormap that will be used to plot multi-curves. The successive
curves are drawn in colors
graphcolormap[graphcolors[1]], graphcolormap[graphcolors[2]],
...
cycling when the graphcolors list is exhausted.
The default value is [4,5].
Name of the external help program to use from within gp when
extended help is invoked, usually through a ?? or ??? request
(see Section se:exthelp), or M-H under readline (see
Section se:readline).
Windows-specific note. On Windows operating systems, if the
first character of help is @, it is replaced by "the directory
where the gp binary is installed".
The default value is the path to the gphelp script we install.
Name of a file where
gp will keep a history of all input commands (results are
omitted). If this file exists when the value of histfile changes,
it is read in and becomes part of the session history. Thus, setting this
default in your gprc saves your readline history between sessions. Setting
this default to the empty string "" changes it to
< undefined > . Note that, by default, the number of history entries
saved is not limited: set history-size in readline's .inputrc
to limit the file size.
The default value is < undefined > (no history file).
gp keeps a history of the last
histsize results computed so far, which you can recover using the
% notation (see Section se:history). When this number is exceeded,
the oldest values are erased. Tampering with this default is the only way to
get rid of the ones you do not need anymore.
The default value is 5000.
If set to a positive value, gp prints at
most that many lines from each result, terminating the last line shown with
[+++] if further material has been suppressed. The various print
commands (see Section se:gp_program) are unaffected, so you can always type
print(%) or \a to view the full result. If the actual screen width
cannot be determined, a "line" is assumed to be 80 characters long.
The default value is 0.
If set to a positive value, gp wraps every single line after
printing that many characters.
The default value is 0 (unset).
This can be either 0 (off) or 1, 2, 3
(on, see below for the various modes). When logging mode is turned on, gp
opens a log file, whose exact name is determined by the logfile
default. Subsequently, all the commands and results will be written to that
file (see \l). In case a file with this precise name already existed, it
will not be erased: your data will be appended at the end.
The specific positive values of log have the following meaning
1: plain logfile
2: emit color codes to the logfile (if colors is set).
3: write LaTeX output to the logfile (can be further customized using
TeXstyle).
The default value is 0.
Note. Logging starts as soon as log is set to a nonzero
value. In particular, when log is set in gprc, warnings and
errors triggered from the rest of the file will be written in the logfile.
For instance, on clean startup, the logfile will start by Done.
(from the Reading GPRC:...Done. diagnostic printed when starting
gp), then the gp header and prompt.
Name of the log file to be used when the log toggle is on.
Environment and time expansion are performed.
The default value is "pari.log".
This default is specific to the parallel version of PARI and gp
(built via Configure --mt = prthread or mpi) and is ignored
otherwise. In parallel mode, it governs the number of threads to use for
parallel computing. The exact meaning and default value depend on the
mt engine used:
* single: not used (always a single thread).
* pthread: number of threads (unlimited, default: number of cores)
* mpi: number of MPI processes to use (limited to the number
allocated by mpirun, default: use all allocated processes).
See also threadsize and threadsizemax.
This toggle is either 1 (on) or 0 (off). If on,
the polgalois command will use a different, more
consistent, naming scheme for Galois groups. This default is provided to
ensure that scripts can control this behavior and do not break unexpectedly.
The default value is 0. This value will change to 1 (set) in the next
major version.
There are three possible values: 0
( = raw), 1 ( = prettymatrix), or 3
( = external prettyprint). This
means that, independently of the default format for reals which we
explained above, you can print results in three ways:
* raw format, i.e. a format which is equivalent to what you input, including explicit multiplication signs, and everything typed on a line instead of two dimensional boxes. This can have several advantages, for instance it allows you to pick the result with a mouse or an editor, and to paste it somewhere else.
* prettymatrix format: this is identical to raw format, except that matrices are printed as boxes instead of horizontally. This is prettier, but takes more space and cannot be used for input. Column vectors are still printed horizontally.
* external prettyprint: pipes all gp
output in TeX format to an external prettyprinter, according to the value of
prettyprinter. The default script (tex2mail) converts its input
to readable two-dimensional text.
Independently of the setting of this default, an object can be printed
in any of the three formats at any time using the commands \a and \m
and \B respectively.
The default value is 1 (prettymatrix).
gp, and in fact any program using the PARI
library, needs a stack in which to do its computations; parisize
is the stack size, in bytes. It is recommended to increase this
default using a gprc, to the value you believe PARI should be happy
with, given your typical computation. We strongly recommend to also
set parisizemax to a much larger value in your gprc, about what
you believe your machine can stand: PARI will then try to fit its
computations within about parisize bytes, but will increase the stack
size if needed (up to parisizemax). Once the memory intensive
computation is over, PARI will restore the stack size to the originally
requested parisize.
If parisizemax is unset, this command has a very unintuitive behaviour
since it must abort pending operations, see ??allocatemem.
The default value is 4M, resp. 8M on a 32-bit, resp. 64-bit machine.
gp, and in fact any program using the PARI library, needs a
stack in which to do its computations. If nonzero, parisizemax
is the maximum size the stack can grow to, in bytes. If zero, the stack will
not automatically grow, and will be limited to the value of parisize.
When parisizemax is set, PARI tries to fit its
computations within about parisize bytes, but will increase the stack
size if needed, roughly doubling it each time (up to parisizemax
of course!) and printing a message such as Warning: increasing stack size to
some value. Once the memory intensive computation is over, PARI
will restore the stack size to the originally requested parisize
without printing further messages.
We strongly recommend to set parisizemax permanently to a large
nonzero value in your gprc, about what you believe your machine can
stand. It is possible to increase or decrease parisizemax inside a
running gp session, just use default as usual.
The default value is 0, for backward compatibility reasons.
This is a list of directories, separated by colons ':'
(semicolons ';' in the DOS world, since colons are preempted for drive names).
When asked to read a file whose name is not given by an absolute path
(does not start with /, ./ or ../), gp will look for
it in these directories, in the order they were written in path. Here,
as usual, . means the current directory, and .. its immediate
parent. Environment expansion is performed.
The default value is ".:~:~/gp" on UNIX systems,
".;C:\;C:\GP" on DOS, OS/2 and Windows, and "." otherwise.
If the graphic driver allows it, the array contains the size of the terminal, the size of the font, the size of the ticks.
The name of an external prettyprinter to use when
output is 3 (alternate prettyprinter). Note that the default
tex2mail looks much nicer than the built-in "beautified
format" (output = 2).
The default value is "tex2mail -TeX -noindent -ragged -by_par".
gp precomputes a list of
all primes less than primelimit at initialization time, and can build
fast sieves on demand to quickly iterate over primes up to the square
of primelimit. These are used by many arithmetic functions, usually for
trial division purposes. The maximal value is 232 - 2049 (resp 264 -
2049) on a 32-bit (resp. 64-bit) machine, but values beyond 10^8,
allowing to iterate over primes up to 1016, do not seem useful.
Since almost all arithmetic functions eventually require some table of prime
numbers, PARI guarantees that the first 6547 primes, up to and
including 65557, are precomputed, even if primelimit is 1.
This default is only used on startup: changing it will not recompute a new table.
Deprecated feature. primelimit was used in some
situations by algebraic number theory functions using the
nf_PARTIALFACT flag (nfbasis, nfdisc, nfinit,...):
this assumes that all primes p > primelimit have a certain
property (the equation order is p-maximal). This is never done by default,
and must be explicitly set by the user of such functions. Nevertheless,
these functions now provide a more flexible interface, and their use
of the global default primelimit is deprecated.
Deprecated feature. factor(N, 0) was used to partially
factor integers by removing all prime factors ≤ primelimit.
Don't use this, supply an explicit bound: factor(N, bound),
which avoids relying on an unpredictable global variable.
The default value is 500k.
A string that will be printed as
prompt. Note that most usual escape sequences are available there: \e for
Esc, \n for Newline,..., \\ for \. Time expansion is
performed.
This string is sent through the library function strftime (on a
Unix system, you can try man strftime at your shell prompt). This means
that % constructs have a special meaning, usually related to the time
and date. For instance, %H = hour (24-hour clock) and %M =
minute [00,59] (use %% to get a real %).
If you use readline, escape sequences in your prompt will result in
display bugs. If you have a relatively recent readline (see the comment
at the end of Section se:def,colors), you can brace them with special sequences
(\[ and \]), and you will be safe. If these just result in
extra spaces in your prompt, then you'll have to get a more recent
readline. See the file misc/gprc.dft for an example.
S< >Caution: PariEmacs needs to know about the prompt pattern to
separate your input from previous gp results, without ambiguity. It is
not a trivial problem to adapt automatically this regular expression to an
arbitrary prompt (which can be self-modifying!). See PariEmacs's
documentation.
The default value is "? ".
A string that will be printed
to prompt for continuation lines (e.g. in between braces, or after a
line-terminating backslash). Everything that applies to prompt
applies to prompt_cont as well.
The default value is "".
This default is obsolete, use one of plotexport, plothexport or plothrawexport functions and write the result to file.
Switches readline line-editing
facilities on and off. This may be useful if you are running gp in a Sun
cmdtool, which interacts badly with readline. Of course, until readline
is switched on again, advanced editing features like automatic completion
and editing history are not available.
The default value is 1.
The number of significant bits used to convert exact inputs given to
transcendental functions (see Section se:trans), or to create
absolute floating point constants (input as 1.0 or Pi for
instance). Unless you tamper with the format default, this is also
the number of significant bits used to print a t_REAL number;
format will override this latter behavior, and allow you to have a
large internal precision while outputting few digits for instance.
Note that most PARI's functions currently handle precision on a word basis (by increments of 32 or 64 bits), hence bit precision may be a little larger than the number of bits you expected. For instance to get 10 bits of precision, you need one word of precision which, on a 64-bit machine, correspond to 64 bits. To make things even more confusing, this internal bit accuracy is converted to decimal digits when printing floating point numbers: now 64 bits correspond to 19 printed decimal digits (19 < log10(264) < 20).
The value returned when typing default(realbitprecision) is the internal
number of significant bits, not the number of printed decimal digits:
? default(realbitprecision, 10)
? \pb
realbitprecision = 64 significant bits
? default(realbitprecision)
%1 = 64
? \p
realprecision = 3 significant digits
? default(realprecision)
%2 = 19
Note that realprecision and \p allow
to view and manipulate the internal precision in decimal digits.
The default value is 128, resp. 96, on a 64-bit, resp .32-bit,
machine.
The number of significant digits used to convert exact inputs given to
transcendental functions (see Section se:trans), or to create
absolute floating point constants (input as 1.0 or Pi for
instance). Unless you tamper with the format default, this is also
the number of significant digits used to print a t_REAL number;
format will override this latter behavior, and allow you to have a
large internal precision while outputting few digits for instance.
Note that PARI's internal precision works on a word basis (by increments of
32 or 64 bits), hence may be a little larger than the number of decimal
digits you expected. For instance to get 2 decimal digits you need one word
of precision which, on a 64-bit machine, actually gives you 19 digits (19 <
log10(264) < 20). The value returned when typing
default(realprecision) is the internal number of significant digits,
not the number of printed digits:
? default(realprecision, 2)
realprecision = 19 significant digits (2 digits displayed)
? default(realprecision)
%1 = 19
The default value is 38, resp. 28, on a 64-bit, resp. 32-bit,
machine.
This toggle is either 1 (on) or 0 (off). If you change this to 0, any error becomes fatal and causes the gp interpreter to exit immediately. Can be useful in batch job scripts.
The default value is 1.
This toggle is either 1 (on) or 0 (off). If on, the system and
extern command are disabled. These two commands are potentially
dangerous when you execute foreign scripts since they let gp execute
arbitrary UNIX commands. gp will ask for confirmation before letting
you (or a script) unset this toggle.
The default value is 0.
Number of significant terms
when converting a polynomial or rational function to a power series
(see \ps).
The default value is 16.
This toggle is either 1 (on) or 0 (off). When the PARI library computes
something, the type of the
result is not always the simplest possible. The only type conversions which
the PARI library does automatically are rational numbers to integers (when
they are of type t_FRAC and equal to integers), and similarly rational
functions to polynomials (when they are of type t_RFRAC and equal to
polynomials). This feature is useful in many cases, and saves time, but can
be annoying at times. Hence you can disable this and, whenever you feel like
it, use the function simplify (see Chapter 3) which allows you to
simplify objects to the simplest possible types recursively (see \y).
The default value is 1.
This is a list of directories, separated by colons ':'
(semicolons ';' in the DOS world, since colons are preempted for drive names).
When asked to install an external symbol from a shared library whose
name is not given by an absolute path (does not start with /, ./
or ../), gp will look for it in these directories, in the order
they were written in sopath. Here, as usual, . means the current
directory, and .. its immediate parent. Environment expansion is
performed.
The default value is "", corresponding to an empty list of
directories: install will use the library name as input (and look in
the current directory if the name is not an absolute path).
This toggle is either 1 (on) or 0 (off). If on, all arguments to new user functions are mandatory unless the function supplies an explicit default value. Otherwise arguments have the default value 0.
In this example,
fun(a,b=2)=a+b
a is mandatory, while b is optional. If strictargs is on:
? fun() *** at top-level: fun() *** ^ — -- *** in function fun: a,b=2 *** ^ — -- *** missing mandatory argument 'a' in user function.
This applies to functions defined while strictargs is on. Changing strictargs
does not affect the behavior of previously defined functions.
The default value is 0.
Obsolete. This toggle is now a no-op.
This default is specific to the parallel version of PARI and gp
(built via Configure --mt = prthread or mpi) and is ignored
otherwise. In parallel mode,
each thread allocates its own private stack for its
computations, see parisize. This value determines the size in bytes of
the stacks of each thread, so the total memory allocated will be
parisize+nbthreads x threadsize.
If set to 0, the value used is the same as parisize. It is not
easy to estimate reliably a sufficient value for this parameter because PARI
itself will parallelize computations and we recommend to not set this value
explicitly unless it solves a specific problem for you. For instance if you
see frequent messages of the form
*** Warning: not enough memory, new thread stack 10000002048
(Meaning that threadsize had to be temporarily increased.)
On the other hand we strongly recommend to set parisizemax and
threadsizemax to a nonzero value.
The default value is 0.
This default is specific to the parallel version of PARI and gp
(built via Configure --mt = pthread or mpi) and is ignored
otherwise. In parallel mode,
each threads allocates its own private stack for
its computations, see parisize and parisizemax. The
values of threadsize and threadsizemax determine the usual
and maximal size in bytes of the stacks of each thread, so the total memory
allocated will
be between parisize+nbthreads x threadsize. and
parisizemax+nbthreads x threadsizemax.
If set to 0, the value used is the same as threadsize. We strongy
recommend to set both parisizemax and threadsizemax to a
nonzero value.
The default value is 0.
This toggle is either 1 (on) or 0 (off). Every instruction sequence
in the gp calculator (anything ended by a newline in your input) is timed,
to some accuracy depending on the hardware and operating system. When
timer is on, each such timing is printed immediately before the
output as follows:
? factor(2^2^7+1) time = 108 ms. \\ this line omitted if 'timer' is 0 %1 = [ 59649589127497217 1] [5704689200685129054721 1]
(See also # and ##.)
The time measured is the user CPU time, not including the time for printing the results. If the time is negligible ( < 1 ms.), nothing is printed: in particular, no timing should be printed when defining a user function or an alias, or installing a symbol from the library.
The default value is 0 (off).