<s>
SnapPea	B-Language
is	O
free	B-Application
software	I-Application
designed	O
to	O
help	O
mathematicians	O
,	O
in	O
particular	O
low-dimensional	O
topologists	O
,	O
study	O
hyperbolic	O
3-manifolds	O
.	O
</s>
<s>
Marc	O
Culler	O
,	O
Nathan	O
Dunfield	O
and	O
collaborators	O
have	O
extended	O
the	O
SnapPea	B-Language
kernel	O
and	O
written	O
Python	B-Language
extension	O
modules	O
which	O
allow	O
the	O
kernel	O
to	O
be	O
used	O
in	O
a	O
Python	B-Language
program	I-Language
or	O
in	O
the	O
interpreter	O
.	O
</s>
<s>
They	O
also	O
provide	O
a	O
graphical	O
user	O
interface	O
written	O
in	O
Python	B-Language
which	O
runs	O
under	O
most	O
operating	B-General_Concept
systems	I-General_Concept
(	O
see	O
external	O
links	O
below	O
)	O
.	O
</s>
<s>
The	O
following	O
people	O
are	O
credited	O
in	O
SnapPea	B-Language
2.5.3	O
'	O
s	O
list	O
of	O
acknowledgments	O
:	O
Colin	O
Adams	O
,	O
Bill	O
Arveson	O
,	O
Pat	O
Callahan	O
,	O
Joe	O
Christy	O
,	O
Dave	O
Gabai	O
,	O
Charlie	O
Gunn	O
,	O
Martin	O
Hildebrand	O
,	O
Craig	O
Hodgson	O
,	O
Diane	O
Hoffoss	O
,	O
A	O
.	O
C	B-Language
.	O
Manoharan	O
,	O
Al	O
Marden	O
,	O
Dick	O
McGehee	O
,	O
Rob	O
Meyerhoff	O
,	O
Lee	O
Mosher	O
,	O
Walter	O
Neumann	O
,	O
Carlo	O
Petronio	O
,	O
Mark	O
Phillips	O
,	O
Alan	O
Reid	O
,	O
and	O
Makoto	O
Sakuma	O
.	O
</s>
<s>
The	O
C	B-Language
source	O
code	O
is	O
extensively	O
commented	O
by	O
Jeffrey	O
Weeks	O
and	O
contains	O
useful	O
descriptions	O
of	O
the	O
mathematics	O
involved	O
with	O
references	O
.	O
</s>
<s>
The	O
SnapPeaKernel	O
is	O
released	O
under	O
GNU	B-License
GPL	I-License
2+	O
as	O
is	O
SnapPy	O
.	O
</s>
<s>
At	O
the	O
core	O
of	O
SnapPea	B-Language
are	O
two	O
main	O
algorithms	O
.	O
</s>
<s>
Almost	O
all	O
the	O
other	O
functions	O
of	O
SnapPea	B-Language
rely	O
in	O
some	O
way	O
on	O
one	O
of	O
these	O
decompositions	O
.	O
</s>
<s>
SnapPea	B-Language
inputs	O
data	O
in	O
a	O
variety	O
of	O
formats	O
.	O
</s>
<s>
Given	O
a	O
link	O
diagram	O
,	O
SnapPea	B-Language
can	O
ideally	O
triangulate	O
the	O
link	O
complement	O
.	O
</s>
<s>
Once	O
a	O
suitable	O
ideal	O
triangulation	O
is	O
found	O
,	O
SnapPea	B-Language
can	O
try	O
to	O
find	O
a	O
hyperbolic	O
structure	O
.	O
</s>
<s>
SnapPea	B-Language
uses	O
an	O
iterative	O
method	O
utilizing	O
Newton	O
's	O
method	O
to	O
search	O
for	O
solutions	O
.	O
</s>
<s>
From	O
this	O
description	O
of	O
the	O
hyperbolic	O
structure	O
on	O
a	O
link	O
complement	O
,	O
SnapPea	B-Language
can	O
then	O
perform	O
hyperbolic	O
Dehn	O
filling	O
on	O
the	O
cusps	O
to	O
obtain	O
more	O
hyperbolic	O
3-manifolds	O
.	O
</s>
<s>
SnapPea	B-Language
does	O
this	O
by	O
taking	O
any	O
given	O
slopes	O
which	O
determine	O
certain	O
Dehn	O
filling	O
equations	O
(	O
also	O
explained	O
in	O
Thurston	O
's	O
notes	O
)	O
,	O
and	O
then	O
adjusting	O
the	O
shapes	O
of	O
the	O
ideal	O
tetrahedra	O
to	O
give	O
solutions	O
to	O
these	O
equations	O
and	O
the	O
edge	O
equations	O
.	O
</s>
<s>
SnapPea	B-Language
is	O
usually	O
able	O
to	O
compute	O
the	O
canonical	O
decomposition	O
of	O
a	O
cusped	O
hyperbolic	O
3-manifold	O
from	O
a	O
given	O
ideal	O
triangulation	O
.	O
</s>
<s>
The	O
canonical	O
decomposition	O
allows	O
SnapPea	B-Language
to	O
tell	O
two	O
cusped	O
hyperbolic	O
3-manifolds	O
apart	O
by	O
turning	O
the	O
problem	O
of	O
recognition	O
into	O
a	O
combinatorial	O
question	O
,	O
i.e.	O
</s>
<s>
SnapPea	B-Language
is	O
also	O
able	O
to	O
check	O
if	O
two	O
closed	O
hyperbolic	O
3-manifolds	O
are	O
isometric	O
by	O
drilling	O
out	O
short	O
geodesics	O
to	O
create	O
cusped	O
hyperbolic	O
3-manifolds	O
and	O
then	O
using	O
the	O
canonical	O
decomposition	O
as	O
before	O
.	O
</s>
<s>
The	O
recognition	O
algorithm	O
allow	O
SnapPea	B-Language
to	O
tell	O
two	O
hyperbolic	O
knots	O
or	O
links	O
apart	O
.	O
</s>
<s>
Additionally	O
,	O
from	O
the	O
canonical	O
decomposition	O
,	O
SnapPea	B-Language
is	O
able	O
to	O
:	O
</s>
<s>
SnapPea	B-Language
has	O
several	O
databases	O
of	O
hyperbolic	O
3-manifolds	O
available	O
for	O
systematic	O
study	O
.	O
</s>
