<s>
Fermat	B-Language
(	O
named	O
after	O
Pierre	O
de	O
Fermat	B-Language
)	O
is	O
a	O
freeware	B-License
program	O
developed	O
by	O
Prof	O
.	O
Robert	O
H	O
.	O
Lewis	O
of	O
Fordham	O
University	O
.	O
</s>
<s>
It	O
is	O
a	O
computer	B-General_Concept
algebra	I-General_Concept
system	I-General_Concept
,	O
in	O
which	O
items	O
being	O
computed	O
can	O
be	O
integers	O
(	O
of	O
arbitrary	O
size	O
)	O
,	O
rational	O
numbers	O
,	O
real	O
numbers	O
,	O
complex	O
numbers	O
,	O
modular	O
numbers	O
,	O
finite	O
field	O
elements	O
,	O
multivariable	O
polynomials	O
,	O
rational	O
functions	O
,	O
or	O
polynomials	O
modulo	O
other	O
polynomials	O
.	O
</s>
<s>
Fermat	B-Language
does	O
not	O
do	O
simplification	O
of	O
transcendental	O
functions	O
or	O
symbolic	B-Algorithm
integration	I-Algorithm
.	O
</s>
<s>
A	O
session	O
with	O
Fermat	B-Language
usually	O
starts	O
by	O
choosing	O
rational	O
or	O
modular	O
"	O
mode	O
"	O
to	O
establish	O
the	O
ground	O
field	O
(	O
or	O
ground	O
ring	O
)	O
as	O
or	O
.	O
</s>
<s>
The	O
polynomial	B-Algorithm
gcd	I-Algorithm
procedures	O
,	O
which	O
call	O
each	O
other	O
in	O
a	O
highly	O
recursive	O
manner	O
,	O
are	O
about	O
7000	O
lines	O
of	O
code	O
.	O
</s>
<s>
Fermat	B-Language
has	O
extensive	O
built-in	O
primitives	O
for	O
array	O
and	O
matrix	O
manipulations	O
,	O
such	O
as	O
submatrix	O
,	O
sparse	B-Algorithm
matrix	I-Algorithm
,	O
determinant	O
,	O
normalize	B-Algorithm
,	O
column	O
reduce	O
,	O
row	O
echelon	O
,	O
Smith	O
normal	O
form	O
,	O
and	O
matrix	O
inverse	O
.	O
</s>
<s>
It	O
is	O
consistently	O
faster	O
than	O
some	O
well	O
known	O
computer	B-General_Concept
algebra	I-General_Concept
systems	I-General_Concept
,	O
especially	O
in	O
multivariate	O
polynomial	B-Algorithm
gcd	I-Algorithm
.	O
</s>
<s>
The	O
basic	O
data	O
item	O
in	O
Fermat	B-Language
is	O
a	O
multivariate	O
rational	O
function	O
or	O
quolynomial	O
.	O
</s>
<s>
To	O
implement	O
(	O
most	O
)	O
finite	O
fields	O
,	O
the	O
user	O
finds	O
an	O
irreducible	O
monic	O
polynomial	O
in	O
a	O
symbolic	O
variable	O
,	O
say	O
and	O
commands	O
Fermat	B-Language
to	O
mod	O
out	O
by	O
it	O
.	O
</s>
<s>
With	O
Windows	B-Application
10	O
,	O
and	O
thanks	O
to	O
Bogdan	O
Radu	O
,	O
it	O
is	O
now	O
possible	O
(	O
May	O
2021	O
)	O
to	O
run	O
Fermat	B-Language
Linux	B-Application
natively	O
on	O
Windows	B-Application
.	O
</s>
<s>
Fermat	B-Language
was	O
last	O
updated	O
on	O
20	O
May	O
2020	O
(	O
Mac	O
and	O
Linux	B-Application
;	O
latest	O
Windows	B-Application
version	O
:	O
1	O
November	O
2011	O
)	O
.	O
</s>
<s>
In	O
an	O
earlier	O
version	O
,	O
called	O
FFermat	O
(	O
Float	B-Algorithm
Fermat	B-Language
)	O
,	O
the	O
basic	O
number	O
type	O
is	O
floating	B-Algorithm
point	I-Algorithm
numbers	I-Algorithm
of	O
18	O
digits	O
.	O
</s>
<s>
That	O
version	O
allows	O
for	O
numerical	O
computing	O
techniques	O
,	O
has	O
extensive	O
graphics	O
capabilities	O
,	O
no	O
sophisticated	O
polynomial	B-Algorithm
gcd	I-Algorithm
algorithms	O
,	O
and	O
is	O
available	O
only	O
for	O
Mac	B-Application
OS	I-Application
9	O
.	O
</s>
<s>
Fermat	B-Language
was	O
originally	O
written	O
in	O
Pascal	B-Application
for	O
a	O
DEC	B-Device
VAX	I-Device
,	O
then	O
for	O
the	O
classic	B-Application
Mac	I-Application
OS	I-Application
during	O
1985	O
–	O
1996	O
.	O
</s>
<s>
It	O
was	O
ported	O
to	O
Microsoft	B-Application
Windows	I-Application
in	O
1998	O
.	O
</s>
<s>
In	O
2003	O
it	O
was	O
translated	O
into	O
C	B-Language
and	O
ported	O
to	O
Linux	B-Application
(	O
Intel	O
machines	O
)	O
and	O
Unix	B-Application
(	O
Sparc/Sun	O
)	O
.	O
</s>
<s>
It	O
is	O
about	O
98,000	O
lines	O
of	O
C	B-Language
code	O
.	O
</s>
<s>
The	O
FFermat	O
and	O
(	O
old	O
)	O
Windows	B-Application
Fermat	B-Language
Pascal	B-Application
source	O
code	O
have	O
been	O
made	O
available	O
to	O
the	O
public	O
under	O
a	O
restrictive	O
license	O
.	O
</s>
