<s>
In	O
mathematics	O
,	O
Schubert	B-Algorithm
calculus	I-Algorithm
is	O
a	O
branch	O
of	O
algebraic	O
geometry	O
introduced	O
in	O
the	O
nineteenth	O
century	O
by	O
Hermann	O
Schubert	O
,	O
in	O
order	O
to	O
solve	O
various	O
counting	O
problems	O
of	O
projective	O
geometry	O
(	O
part	O
of	O
enumerative	O
geometry	O
)	O
.	O
</s>
<s>
The	O
phrase	O
"	O
Schubert	B-Algorithm
calculus	I-Algorithm
"	O
is	O
sometimes	O
used	O
to	O
mean	O
the	O
enumerative	O
geometry	O
of	O
linear	O
subspaces	O
,	O
roughly	O
equivalent	O
to	O
describing	O
the	O
cohomology	O
ring	O
of	O
Grassmannians	O
,	O
and	O
sometimes	O
used	O
to	O
mean	O
the	O
more	O
general	O
enumerative	O
geometry	O
of	O
nonlinear	O
varieties	O
.	O
</s>
<s>
Even	O
more	O
generally	O
,	O
"	O
Schubert	B-Algorithm
calculus	I-Algorithm
"	O
is	O
often	O
understood	O
to	O
encompass	O
the	O
study	O
of	O
analogous	O
questions	O
in	O
generalized	O
cohomology	O
theories	O
.	O
</s>
<s>
Lifted	O
from	O
the	O
Grassmannian	O
,	O
which	O
is	O
a	O
homogeneous	O
space	O
,	O
to	O
the	O
general	O
linear	O
group	O
that	O
acts	O
on	O
it	O
,	O
similar	O
questions	O
are	O
involved	O
in	O
the	O
Bruhat	O
decomposition	O
and	O
classification	O
of	O
parabolic	O
subgroups	O
(	O
by	O
block	B-Algorithm
matrix	I-Algorithm
)	O
.	O
</s>
<s>
Schubert	B-Algorithm
calculus	I-Algorithm
can	O
be	O
constructed	O
using	O
the	O
Chow	O
ring	O
of	O
the	O
Grassmannian	O
where	O
the	O
generating	O
cycles	O
are	O
represented	O
by	O
geometrically	O
meaningful	O
data	O
.	O
</s>
<s>
It	O
can	O
be	O
shown	O
these	O
classes	O
generate	O
the	O
Chow	O
ring	O
,	O
and	O
the	O
associated	O
intersection	O
theory	O
is	O
called	O
Schubert	B-Algorithm
calculus	I-Algorithm
.	O
</s>
<s>
Note	O
given	O
a	O
sequence	O
the	O
Schubert	B-Algorithm
class	I-Algorithm
is	O
typically	O
denoted	O
as	O
just	O
.	O
</s>
<s>
In	O
the	O
special	O
case	O
,	O
there	O
is	O
an	O
explicit	O
formula	O
of	O
the	O
product	O
of	O
with	O
an	O
arbitrary	O
Schubert	B-Algorithm
class	I-Algorithm
given	O
byNote	O
.	O
</s>
<s>
Schubert	B-Algorithm
calculus	I-Algorithm
can	O
be	O
used	O
to	O
find	O
the	O
number	O
of	O
lines	O
on	O
a	O
Cubic	O
surface	O
.	O
</s>
