<s>
Chebfun	B-Application
is	O
a	O
free/open	B-Application
-source	I-Application
software	O
system	O
written	O
in	O
MATLAB	B-Language
for	O
numerical	O
computation	O
with	O
functions	O
of	O
a	O
real	O
variable	O
.	O
</s>
<s>
It	O
is	O
based	O
on	O
the	O
idea	O
of	O
overloading	O
MATLAB	B-Language
's	O
commands	O
for	O
vectors	O
and	O
matrices	O
to	O
analogous	O
commands	O
for	O
functions	O
and	O
operators	O
.	O
</s>
<s>
Thus	O
,	O
for	O
example	O
,	O
whereas	O
the	O
SUM	O
command	O
in	O
MATLAB	B-Language
adds	O
up	O
the	O
elements	O
of	O
a	O
vector	O
,	O
the	O
SUM	O
command	O
in	O
Chebfun	B-Application
evaluates	O
a	O
definite	O
integral	O
.	O
</s>
<s>
Similarly	O
the	O
backslash	O
command	O
in	O
MATLAB	B-Language
becomes	O
a	O
Chebfun	B-Application
command	O
for	O
solving	O
differential	O
equations	O
.	O
</s>
<s>
The	O
mathematical	O
basis	O
of	O
Chebfun	B-Application
is	O
numerical	O
algorithms	O
involving	O
piecewise	O
polynomial	O
interpolants	O
and	O
Chebyshev	O
polynomials	O
,	O
and	O
this	O
is	O
where	O
the	O
name	O
"	O
Cheb	O
"	O
comes	O
from	O
.	O
</s>
<s>
The	O
package	O
aims	O
to	O
combine	O
the	O
feel	O
of	O
symbolic	O
computing	O
systems	O
like	O
Maple	B-Language
and	O
Mathematica	B-Language
with	O
the	O
speed	O
of	O
floating-point	O
numerics	O
.	O
</s>
<s>
The	O
Chebfun	B-Application
project	O
is	O
based	O
in	O
the	O
Mathematical	O
Institute	O
at	O
the	O
University	O
of	O
Oxford	O
and	O
was	O
initiated	O
in	O
2002	O
by	O
Lloyd	O
N	O
.	O
Trefethen	O
and	O
his	O
student	O
Zachary	O
Battles	O
.	O
</s>
<s>
Chebfun2	O
,	O
a	O
software	O
system	O
that	O
extends	O
Chebfun	B-Application
to	O
two	O
dimensions	O
,	O
was	O
made	O
publicly	O
available	O
on	O
the	O
4th	O
of	O
March	O
2013	O
.	O
</s>
