<s>
Examples	O
include	O
linear	B-Architecture
transformations	I-Architecture
of	O
vector	O
spaces	O
and	O
geometric	B-Algorithm
transformations	I-Algorithm
,	O
which	O
include	O
projective	B-Algorithm
transformations	I-Algorithm
,	O
affine	B-Algorithm
transformations	I-Algorithm
,	O
and	O
specific	O
affine	B-Algorithm
transformations	I-Algorithm
,	O
such	O
as	O
rotations	O
,	O
reflections	B-Algorithm
and	O
translations	B-Algorithm
.	O
</s>
<s>
When	O
such	O
a	O
narrow	O
notion	O
of	O
transformation	O
is	O
generalized	O
to	O
partial	B-Algorithm
functions	I-Algorithm
,	O
then	O
a	O
partial	O
transformation	O
is	O
a	O
function	O
f	O
:	O
A	O
→	O
B	O
,	O
where	O
both	O
A	O
and	O
B	O
are	O
subsets	O
of	O
some	O
set	O
X	O
.	O
</s>
<s>
The	O
set	O
of	O
all	O
transformations	O
on	O
a	O
given	O
base	O
set	O
,	O
together	O
with	O
function	B-Application
composition	I-Application
,	O
forms	O
a	O
regular	O
semigroup	O
.	O
</s>
<s>
For	O
a	O
finite	O
set	O
of	O
cardinality	B-Application
n	O
,	O
there	O
are	O
nn	O
transformations	O
and	O
(	O
n+1	O
)	O
n	O
partial	O
transformations	O
.	O
</s>
