Information Technology Reference
In-Depth Information
Chapter 5
Index Matrices with Function-Type of Elements
F
Let the set of all used functions be
.
The research over IMs with function-type of elements has two cases:
•
each function of set
has one argument and it is exactly
x
(i.e., it is not possible
that one of the functions has argument
x
and another function has argument
y
)—let
us mark the set of these functions by
F
1
F
x
;
•
each function of set
has one argument, but that argument might be different for
the different functions or the different functions of set
F
F
have different numbers
of arguments.
Here, we discuss the two cases, simultaneously.
5.1 Definition of the Index Matrix with Function-Type
of Elements
The IM with Function-type of Elements (IMFE) has the form (see [15])
l
1
...
l
j
...
l
n
k
1
f
k
1
,
l
1
...
f
k
1
,
l
j
...
f
k
1
,
l
n
.
.
.
.
.
. . .
...
[
K
,
L
,
{
f
k
i
,
l
j
}] ≡
,
k
i
f
k
i
,
l
1
...
f
k
i
,
l
j
...
f
k
i
,
l
n
.
.
.
.
.
. . .
...
k
m
f
k
m
,
l
1
...
f
k
m
,
l
j
...
f
k
m
,
l
n
where
K
={
k
1
,
k
2
,...,
k
m
}
,
L
={
l
1
,
l
2
,...,
l
n
}
,for1
≤
i
≤
m
,
and 1
≤
j
≤
n
:
1
x
.
The IMFE has this form independently of the form of its elements. They can be
functions from
f
k
i
,
l
j
∈
F
1
x
having one, exactly determined argument (e.g.,
x
), as well as
functions with a lot of arguments. The set of
n
-argument functions will be marked
by
F
n
.
F
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