\title{Appendix D : Summary of available Constants}

In this appendix we give the list of predefined constants available in the
PARI library. 

{\obeylines\parskip=0pt plus 1pt
\hbox{}
{\bf gzero (zero)} see 4.1.1.
{\bf gun (un)} see 4.1.1.
{\bf gdeux (deux)} see 4.1.1.
{\bf ghalf (lhalf)} see 4.1.1.
{\bf gi} see 4.1.1.
{\bf polun[] (lpolun[])} see 4.1.1.
{\bf polx[] (lpolx[])} see 4.1.1.}

{\bf geuler}. This is Euler's constant, and is in the heap, {\it not\/}
in the PARI stack. It is not initialized, and if you want to use it you must
call {\bf consteuler}(prec) ( see 3.3.19.).

{\bf gpi}. This is the number pi, and is in the heap, {\it not\/}
in the PARI stack. It is not initialized, and if you want to use it you must
call {\bf constpi}(prec) (see 3.3.33.).

{\bf bern}(i). This is the $2i$-th Bernoulli number ($B_0=1$, $B_2=1/6$,
$B_4=-1/30$, etc\dots) The Bernoulli numbers are
in the heap and {\it not\/} in the PARI stack, and are not initialized.
To initialize them you must use the function {\bf mpbern} which has the following
syntax:

{\tt void mpbern(long n, long prec);}

The effect of this function is to create the even numbered Bernoulli numbers up
to $B_{2n-2}$ {\bf as real numbers} of precision {\tt prec}. They can then be used with
the macro {\bf bern}($i$). Note that this is not a function but simply an abbreviation,
hence care must be taken that $i$ is inside the right bounds (i.e. $0\le i\le n-1$)
before using it, since no checking is done in PARI itself.

Finally, one has access to a table of (differences of) primes through the
pointer {\bf diffptr}. This is used as follows: after {\tt init} has been
called, this table is initialized with the differences of primes up to $500000$
(default which can trivially be changed by calling {\tt init} with different
arguments, see 4.1.1). Then one declares {\tt byteptr $d$=diffptr;}, where $d$ is
the name of the pointer that one uses. This will point to the first difference
in the table, i.e. 2. To get to the next difference, just do {\tt $d$++}.

In addition, some single or double-precision real numbers are predefined,
and their list is in the file {\tt gencom.h}


\vfill\eject
