<s>
PARI/GP	B-Language
is	O
a	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
with	O
the	O
main	O
aim	O
of	O
facilitating	O
number	O
theory	O
computations	O
.	O
</s>
<s>
Versions	O
2.1.0	O
and	O
higher	O
are	O
distributed	O
under	O
the	O
GNU	B-License
General	I-License
Public	I-License
License	I-License
.	O
</s>
<s>
It	O
runs	O
on	O
most	O
common	O
operating	B-General_Concept
systems	I-General_Concept
.	O
</s>
<s>
The	O
PARI/GP	B-Language
system	O
is	O
a	O
package	O
that	O
is	O
capable	O
of	O
doing	O
formal	O
computations	O
on	O
recursive	O
types	O
at	O
high	O
speed	O
;	O
it	O
is	O
primarily	O
aimed	O
at	O
number	O
theorists	O
.	O
</s>
<s>
The	O
PARI/GP	B-Language
system	O
consists	O
of	O
the	O
following	O
standard	O
components	O
:	O
</s>
<s>
PARI	O
is	O
a	O
C	B-Language
library	B-Library
,	O
allowing	O
for	O
fast	O
computations	O
,	O
and	O
which	O
can	O
be	O
called	O
from	O
a	O
high-level	O
language	O
application	O
(	O
for	O
instance	O
,	O
written	O
in	O
C	B-Language
,	O
C++	B-Language
,	O
Pascal	B-Application
,	O
Fortran	B-Application
,	O
Perl	B-Language
,	O
or	O
Python	B-Language
)	O
.	O
</s>
<s>
gp	O
is	O
an	O
easy-to-use	O
interactive	O
command	B-Application
line	I-Application
interface	I-Application
giving	O
access	O
to	O
the	O
PARI	O
functions	O
.	O
</s>
<s>
It	O
functions	O
as	O
a	O
sophisticated	O
programmable	O
calculator	O
which	O
contains	O
most	O
of	O
the	O
control	O
instructions	O
of	O
a	O
standard	O
language	O
like	O
C	B-Language
.	O
GP	O
is	O
the	O
name	O
of	O
gp	O
's	O
scripting	O
language	O
which	O
can	O
be	O
used	O
to	O
program	O
gp	O
.	O
</s>
<s>
Also	O
available	O
is	O
gp2c	O
,	O
the	O
GP-to-C	O
compiler	O
,	O
which	O
compiles	O
GP	O
scripts	O
into	O
the	O
C	B-Language
language	I-Language
and	O
transparently	O
loads	O
the	O
resulting	O
functions	O
into	O
gp	O
.	O
</s>
<s>
PARI/GP	B-Language
performs	O
arbitrary	B-Algorithm
precision	I-Algorithm
calculations	O
(	O
e.g.	O
,	O
the	O
significand	B-Algorithm
can	O
be	O
millions	O
of	O
digits	O
long	O
—	O
and	O
billions	O
of	O
digits	O
on	O
64-bit	B-Device
machines	O
)	O
.	O
</s>
<s>
It	O
also	O
allows	O
computations	O
with	O
matrices	B-Architecture
,	O
polynomials	O
,	O
power	O
series	O
,	O
algebraic	O
numbers	O
and	O
implements	O
many	O
special	O
functions	O
.	O
</s>
<s>
PARI/GP	B-Language
comes	O
with	O
its	O
own	O
built-in	O
graphical	O
plotting	B-Application
capability	O
.	O
</s>
<s>
PARI/GP	B-Language
has	O
some	O
symbolic	O
manipulation	O
capability	O
,	O
e.g.	O
,	O
multivariate	O
polynomial	O
and	O
rational	O
function	O
handling	O
.	O
</s>
<s>
It	O
also	O
has	O
some	O
formal	O
integration	O
and	O
differentiation	B-Algorithm
capabilities	O
.	O
</s>
<s>
PARI/GP	B-Language
can	O
be	O
compiled	O
with	O
GMP	B-Application
(	O
GNU	B-Application
Multiple	I-Application
Precision	I-Application
Arithmetic	I-Application
Library	I-Application
)	O
providing	O
faster	O
computations	O
than	O
PARI/GP	B-Language
'	O
s	O
native	O
arbitrary-precision	B-Algorithm
kernel	O
.	O
</s>
<s>
PARI/GP	B-Language
'	O
s	O
progenitor	O
was	O
a	O
program	O
named	O
Isabelle	O
,	O
an	O
interpreter	O
for	O
higher	O
arithmetic	O
,	O
written	O
in	O
1979	O
by	O
Henri	O
Cohen	O
and	O
François	O
Dress	O
at	O
the	O
Université	O
Bordeaux	O
1	O
.	O
</s>
<s>
PARI/GP	B-Language
was	O
originally	O
developed	O
in	O
1985	O
by	O
a	O
team	O
led	O
by	O
Henri	O
Cohen	O
at	O
Laboratoire	O
A2X	O
and	O
is	O
now	O
maintained	O
by	O
Karim	O
Belabas	O
at	O
the	O
Université	O
Bordeaux	O
1	O
with	O
the	O
help	O
of	O
many	O
volunteer	O
contributors	O
.	O
</s>
<s>
The	O
name	O
PARI	O
is	O
a	O
pun	O
about	O
the	O
project	O
's	O
early	O
stages	O
when	O
the	O
authors	O
started	O
to	O
implement	O
a	O
library	B-Library
for	O
"	O
Pascal	B-Application
ARIthmetic	O
"	O
in	O
the	O
Pascal	B-Application
programming	I-Application
language	I-Application
(	O
although	O
they	O
quickly	O
switched	O
to	O
C	B-Language
)	O
,	O
and	O
after	O
"	O
pari	O
de	O
Pascal	B-Application
"	O
(	O
Pascal	B-Application
's	O
Wager	O
)	O
.	O
</s>
<s>
The	O
trailing	O
C	B-Language
was	O
eventually	O
dropped	O
.	O
</s>
