<s>
In	O
mathematics	O
,	O
the	O
Poincaré	B-Algorithm
residue	I-Algorithm
is	O
a	O
generalization	O
,	O
to	O
several	B-Architecture
complex	I-Architecture
variables	I-Architecture
and	O
complex	O
manifold	O
theory	O
,	O
of	O
the	O
residue	B-Algorithm
at	O
a	O
pole	O
of	O
complex	O
function	O
theory	O
.	O
</s>
<s>
If	O
we	O
recover	O
the	O
classical	O
residue	B-Algorithm
construction	O
.	O
</s>
<s>
When	O
Poincaré	O
first	O
introduced	O
residues	B-Algorithm
he	O
was	O
studying	O
period	O
integrals	O
of	O
the	O
form	O
for	O
where	O
was	O
a	O
rational	O
differential	O
form	O
with	O
poles	O
along	O
a	O
divisor	O
.	O
</s>
<s>
Then	O
,	O
he	O
gave	O
a	O
formula	O
for	O
computing	O
this	O
residue	B-Algorithm
aswhich	O
are	O
both	O
cohomologous	O
forms	O
.	O
</s>
<s>
which	O
we	O
call	O
the	O
residue	B-Algorithm
.	O
</s>
<s>
Notice	O
if	O
we	O
restrict	O
to	O
the	O
case	O
,	O
this	O
is	O
just	O
the	O
standard	O
residue	B-Algorithm
from	O
complex	O
analysis	O
(	O
although	O
we	O
extend	O
our	O
meromorphic	O
-form	O
to	O
all	O
of	O
.	O
</s>
<s>
There	O
is	O
a	O
simple	O
recursive	O
method	O
for	O
computing	O
the	O
residues	B-Algorithm
which	O
reduces	O
to	O
the	O
classical	O
case	O
of	O
.	O
</s>
