<s>
In	O
complex	O
analysis	O
,	O
a	O
discipline	O
in	O
mathematics	O
,	O
and	O
in	O
statistical	O
physics	O
,	O
the	O
Asano	B-Algorithm
contraction	I-Algorithm
or	O
Asano	O
–	O
Ruelle	O
contraction	O
is	O
a	O
transformation	O
on	O
a	O
separately	O
affine	O
multivariate	O
polynomial	O
.	O
</s>
<s>
Asano	B-Algorithm
contractions	I-Algorithm
have	O
also	O
been	O
used	O
to	O
study	O
polynomials	O
in	O
graph	O
theory	O
.	O
</s>
<s>
The	O
Asano	B-Algorithm
contraction	I-Algorithm
sends	O
to	O
.	O
</s>
<s>
Asano	B-Algorithm
contractions	I-Algorithm
are	O
often	O
used	O
in	O
the	O
context	O
of	O
theorems	O
about	O
the	O
location	O
of	O
roots	O
.	O
</s>
<s>
Asano	B-Algorithm
contractions	I-Algorithm
can	O
be	O
used	O
in	O
statistical	O
physics	O
to	O
gain	O
information	O
about	O
a	O
system	O
from	O
its	O
subsystems	O
.	O
</s>
<s>
This	O
is	O
because	O
the	O
Asano	B-Algorithm
contraction	I-Algorithm
essentially	O
eliminates	O
all	O
terms	O
where	O
the	O
spins	O
at	O
a	O
site	O
are	O
distinct	O
in	O
the	O
and	O
.	O
</s>
<s>
Ruelle	O
has	O
also	O
used	O
Asano	B-Algorithm
contractions	I-Algorithm
to	O
find	O
information	O
about	O
the	O
location	O
of	O
roots	O
of	O
a	O
generalization	O
of	O
matching	O
polynomials	O
which	O
he	O
calls	O
graph-counting	O
polynomials	O
.	O
</s>
<s>
He	O
then	O
multiplies	O
these	O
symmetric	O
polynomials	O
together	O
and	O
uses	O
Asano	B-Algorithm
contractions	I-Algorithm
to	O
only	O
keep	O
terms	O
where	O
the	O
edge	O
is	O
present	O
at	O
both	O
its	O
endpoints	O
.	O
</s>
<s>
Since	O
the	O
graph-counting	O
polynomial	O
was	O
obtained	O
from	O
these	O
by	O
Asano	B-Algorithm
contractions	I-Algorithm
,	O
most	O
of	O
the	O
remaining	O
work	O
is	O
computing	O
products	O
of	O
these	O
sets	O
.	O
</s>
