<s>
Within	O
computer	O
engineering	O
and	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
computer	O
for	O
operations	O
with	O
(	O
mathematical	O
)	O
functions	O
(	O
unlike	O
the	O
usual	O
computer	O
)	O
operates	O
with	O
functions	O
at	O
the	O
hardware	B-Architecture
level	O
(	O
i.e.	O
</s>
<s>
Among	O
the	O
operations	O
of	O
this	O
computing	O
machine	O
were	O
the	O
functions	O
addition	O
,	O
subtraction	O
and	O
multiplication	O
,	O
functions	O
comparison	O
,	O
the	O
same	O
operations	O
between	O
a	O
function	O
and	O
a	O
number	O
,	O
finding	O
the	O
function	O
maximum	O
,	O
computing	O
indefinite	B-Algorithm
integral	I-Algorithm
,	O
computing	O
definite	B-Algorithm
integral	I-Algorithm
of	O
derivative	B-Algorithm
of	O
two	O
functions	O
,	O
derivative	B-Algorithm
of	O
two	O
functions	O
,	O
shift	O
of	O
a	O
function	O
along	O
the	O
X-axis	O
etc	O
.	O
</s>
<s>
By	O
its	O
architecture	B-General_Concept
this	O
computing	O
machine	O
was	O
(	O
using	O
the	O
modern	O
terminology	O
)	O
a	O
vector	B-Operating_System
processor	I-Operating_System
or	O
array	B-Operating_System
processor	I-Operating_System
,	O
a	O
central	B-General_Concept
processing	I-General_Concept
unit	I-General_Concept
(	O
CPU	O
)	O
that	O
implements	O
an	O
instruction	O
set	O
containing	O
instructions	O
that	O
operate	O
on	O
one-dimensional	O
arrays	O
of	O
data	O
called	O
vectors	O
.	O
</s>
<s>
In	O
it	O
there	O
has	O
been	O
used	O
the	O
fact	O
that	O
many	O
of	O
these	O
operations	O
may	O
be	O
interpreted	O
as	O
the	O
known	O
operation	O
on	O
vectors	O
:	O
addition	O
and	O
subtraction	O
of	O
functions	O
-	O
as	O
addition	O
and	O
subtraction	O
of	O
vectors	O
,	O
computing	O
a	O
definite	B-Algorithm
integral	I-Algorithm
of	O
two	O
functions	O
derivative	B-Algorithm
—	O
as	O
computing	O
the	O
vector	O
product	O
of	O
two	O
vectors	O
,	O
function	O
shift	O
along	O
the	O
X-axis	O
–	O
as	O
vector	O
rotation	O
about	O
axes	O
,	O
etc	O
.	O
</s>
<s>
And	O
so	O
the	O
mentioned	O
operations	O
with	O
functions	O
are	O
performed	O
as	O
unique	O
computer	O
operations	O
with	O
such	O
codes	O
on	O
a	O
"	O
single	O
"	O
arithmetic	B-General_Concept
unit	I-General_Concept
.	O
</s>
<s>
Addition	O
of	O
positional	O
codes	O
of	O
one-variable	O
functions	O
is	O
also	O
associated	O
with	O
the	O
carry	B-Algorithm
transfer	O
to	O
higher	O
digits	O
according	O
to	O
the	O
scheme	O
:	O
</s>
<s>
is	O
written	O
in	O
the	O
-digit	O
of	O
summary	O
code	O
,	O
and	O
the	O
carry	B-Algorithm
from	O
the	O
given	O
digit	O
is	O
carried	O
into	O
-digit	O
and	O
—	O
digit	O
.	O
</s>
<s>
is	O
written	O
into	O
—	O
digit	O
of	O
the	O
resulting	O
code	O
,	O
and	O
carry	B-Algorithm
from	O
the	O
given	O
digit	O
is	O
transferred	O
into	O
the	O
-digit	O
and	O
-digit	O
.	O
</s>
<s>
So	O
the	O
derivation	B-Algorithm
of	O
triangular	O
codes	O
of	O
a	O
function	O
consists	O
in	O
determining	O
the	O
triangular	O
code	O
of	O
the	O
partial	O
derivative	B-Algorithm
and	O
its	O
multiplication	O
by	O
the	O
known	O
triangular	O
code	O
of	O
the	O
derivative	B-Algorithm
.	O
</s>
<s>
The	O
derivation	B-Algorithm
method	O
consists	O
of	O
organizing	O
carries	O
from	O
mk-digit	O
into	O
(	O
m+1	O
,	O
k	O
)	O
-digit	O
and	O
into	O
(	O
m-1	O
,	O
k	O
)	O
-digit	O
,	O
and	O
their	O
summing	O
in	O
the	O
given	O
digit	O
is	O
performed	O
in	O
the	O
same	O
way	O
as	O
in	O
one-digit	O
addition	O
.	O
</s>
<s>
At	O
the	O
addition	O
of	O
the	O
codes	O
the	O
carry	B-Algorithm
extends	O
to	O
four	O
digits	O
and	O
hence	O
.	O
</s>
<s>
At	O
the	O
codes	O
addition	O
the	O
carry	B-Algorithm
extends	O
on	O
a-dimensional	O
cube	O
,	O
containing	O
digits	O
,	O
and	O
hence	O
.	O
</s>
