<s>
In	O
quantum	O
geometry	O
or	O
noncommutative	O
geometry	O
a	O
quantum	B-Algorithm
differential	I-Algorithm
calculus	I-Algorithm
or	O
noncommutative	O
differential	O
structure	O
on	O
an	O
algebra	O
over	O
a	O
field	O
means	O
the	O
specification	O
of	O
a	O
space	O
of	O
differential	O
forms	O
over	O
the	O
algebra	O
.	O
</s>
<s>
Correspondingly	O
,	O
a	O
first	O
order	O
quantum	B-Algorithm
differential	I-Algorithm
calculus	I-Algorithm
means	O
at	O
least	O
the	O
following	O
:	O
</s>
<s>
In	O
the	O
Connes	O
approach	O
a	O
more	O
fundamental	O
object	O
is	O
a	O
replacement	O
for	O
the	O
Dirac	O
operator	O
in	O
the	O
form	O
of	O
a	O
spectral	B-Algorithm
triple	I-Algorithm
,	O
and	O
an	O
exterior	O
algebra	O
can	O
be	O
constructed	O
from	O
this	O
data	O
.	O
</s>
