<s>
In	O
computer	B-General_Concept
programming	I-General_Concept
,	O
a	O
scientific	B-Application
programming	I-Application
language	I-Application
can	O
refer	O
to	O
two	O
degrees	O
of	O
the	O
same	O
concept	O
.	O
</s>
<s>
In	O
a	O
wide	O
sense	O
,	O
a	O
scientific	B-Application
programming	I-Application
language	I-Application
is	O
a	B-Language
programming	I-Language
language	I-Language
that	O
is	O
used	O
widely	O
for	O
computational	O
science	O
and	O
computational	O
mathematics	O
.	O
</s>
<s>
In	O
this	O
sense	O
,	O
C/C	O
++	O
and	O
Python	O
can	O
be	O
considered	O
scientific	B-Application
programming	I-Application
languages	I-Application
.	O
</s>
<s>
In	O
a	O
stronger	O
sense	O
,	O
a	O
scientific	B-Application
programming	I-Application
language	I-Application
is	O
one	O
that	O
is	O
designed	O
and	O
optimized	O
for	O
the	O
use	O
of	O
mathematical	O
formula	O
and	O
matrices	B-Architecture
.	O
</s>
<s>
Scientific	B-Application
programming	I-Application
languages	I-Application
in	O
the	O
stronger	O
sense	O
include	O
ALGOL	B-Language
,	O
APL	B-Language
,	O
Fortran	B-Application
,	O
J	B-Language
,	O
Julia	B-Application
,	O
Maple	B-Language
,	O
MATLAB	B-Language
and	O
R	B-Language
.	O
</s>
<s>
Scientific	B-Application
programming	I-Application
languages	I-Application
should	O
not	O
be	O
confused	O
with	O
scientific	O
language	O
in	O
general	O
,	O
which	O
refers	O
loosely	O
to	O
the	O
higher	O
standards	O
in	O
precision	O
,	O
correctness	O
and	O
concision	O
expected	O
from	O
practitioners	O
of	O
the	O
scientific	O
method	O
.	O
</s>
<s>
Scientific	B-Application
programming	I-Application
languages	I-Application
provide	O
facilities	O
to	O
work	O
with	O
linear	B-Language
algebra	I-Language
.	O
</s>
<s>
For	O
example	O
,	O
the	O
following	O
Julia	B-Application
program	O
solves	O
a	O
system	O
of	O
linear	O
equations	O
:	O
</s>
<s>
Working	O
with	O
large	O
vectors	O
and	O
matrices	B-Architecture
is	O
a	O
key	O
feature	O
of	O
these	O
languages	O
,	O
as	O
linear	B-Language
algebra	I-Language
lays	O
the	O
foundation	O
to	O
mathematical	O
optimization	O
,	O
which	O
in	O
turn	O
enables	O
major	O
applications	O
such	O
as	O
deep	B-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
In	O
a	O
scientific	B-Application
programming	I-Application
language	I-Application
,	O
we	O
can	O
compute	O
function	O
optima	O
with	O
a	O
syntax	O
close	O
to	O
mathematical	O
language	O
.	O
</s>
<s>
For	O
instance	O
,	O
the	O
following	O
Julia	B-Application
code	O
finds	O
the	O
minimum	O
of	O
the	O
polynomial	O
.	O
</s>
<s>
In	O
this	O
example	O
,	O
Newton	B-Algorithm
's	I-Algorithm
method	I-Algorithm
for	O
minimizing	O
is	O
used	O
.	O
</s>
<s>
Modern	O
scientific	B-Application
programming	I-Application
languages	I-Application
will	O
use	O
automatic	B-Algorithm
differentiation	I-Algorithm
to	O
compute	O
the	O
gradients	O
and	O
Hessians	O
of	O
the	O
function	O
given	O
as	O
input	O
;	O
cf	O
.	O
</s>
<s>
differentiable	B-Application
programming	I-Application
.	O
</s>
<s>
Older	O
scientific	B-Application
programming	I-Application
languages	I-Application
such	O
as	O
the	O
venerable	O
Fortran	B-Application
would	O
require	O
the	O
programmer	O
to	O
pass	O
,	O
next	O
to	O
the	O
function	O
to	O
be	O
optimized	O
,	O
a	O
function	O
that	O
computes	O
the	O
gradient	O
,	O
and	O
a	O
function	O
that	O
computes	O
the	O
Hessian	O
.	O
</s>
<s>
For	O
instance	O
,	O
convex	O
optimization	O
provides	O
faster	O
computations	O
when	O
the	O
function	O
is	O
convex	O
,	O
quadratic	B-Algorithm
programming	I-Algorithm
provides	O
faster	O
computations	O
when	O
the	O
function	O
is	O
at	O
most	O
quadratic	O
in	O
its	O
variables	O
,	O
and	O
linear	B-Algorithm
programming	I-Algorithm
when	O
the	O
function	O
is	O
at	O
most	O
linear	O
.	O
</s>
