|
Download
|
|
|
e1
|
e2
|
e1
|
e1
|
e2
|
e2
|
e2
|
-e1
|
Multiplication of two numbers
![](corr/2/1.jpg)
requires 4 multiplications and 2 additions of real numbers.
Use of formula:
![](corr/2/2.jpg)
requires 3 multiplications and 5 additions.
B) System of double numbers.
|
e1
|
e2
|
e1
|
e1
|
e2
|
e2
|
e2
|
e1
|
Multiplication of two numbers
![](corr/2/3.jpg)
requires 4 multiplications and 2 additions of real numbers.
It is expedient to move to isomorphic system with multiplication table:
|
E1
|
E2
|
E1
|
E1
|
0
|
E2
|
0
|
E2
|
where multiplication is carried out by formula:
![](corr/2/4.jpg)
Isomorphism between these systems is defined by formulae:
![]() |
![]() |
![](corr/2/7.jpg)
![](corr/2/8.jpg)
![](corr/2/9.jpg)
Thus, multiplication with the use of this system, even taking into account direct and reverse transitions, requires only 2 multiplications on real numbers, and 2 additions.
2. Systems of dimension 3.
Isomorphism between the system of triplex numbers of Lyusha T and direct sum of real and complex numbers
with multiplication tables has the following form:
![](corr/2/11.jpg)
|
e1
|
e2
|
e3
|
|
|
|
E1
|
E2
|
E3
|
e1
|
e1
|
e2
|
e3
|
|
|
E1
|
E1
|
0
|
0
|
e2
|
e2
|
(e3 – e2)/2
|
–e2
|
|
|
E2
|
0
|
E2
|
E3
|
e3
|
e3
|
–e2
|
e1
|
|
|
E3
|
0
|
E3
|
–E2
|
![](corr/2/12.jpg)
![](corr/2/13.jpg)
![](corr/2/14.jpg)
![](corr/2/15.jpg)
![](corr/2/16.jpg)
![](corr/2/17.jpg)
Evidently, multiplication in the system of triplex numbers of Lyusha T requires 10 multiplications and 1 addition in the system of real numbers, and in
system, taking into account direct and reverse transitions, multiplication requires only 4 multiplications and 7 additions.
![](corr/2/18.jpg)
3. Systems of dimension 4.
Isomorphism between the systems of quadriplex
and bycomplex
numbers with multiplication tables:
![](corr/2/19.jpg)
![](corr/2/20.jpg)
e1
|
e2
|
e3
|
e4
|
E1
|
E2
|
E3
|
E4
|
|||
e1
|
e1
|
e2
|
e3
|
e4
|
E1
|
E1
|
E2
|
0
|
0
|
|
e2
|
e2
|
-e1
|
e4
|
- e3
|
E2
|
E2
|
- E1
|
0
|
0
|
|
e3
|
e3
|
e4
|
- e1
|
- e2
|
E3
|
0
|
0
|
E3
|
E4
|
|
e4
|
e4
|
- e3
|
- e2
|
e1
|
E4
|
0
|
0
|
E4
|
- E3
|
is defined by formulae:
![](corr/2/21.jpg)
![](corr/2/22.jpg)
![](corr/2/23.jpg)
![](corr/2/24.jpg)
![](corr/2/25.jpg)
![](corr/2/26.jpg)
Evidently, multiplication in the system of quadriplex numbers requires 16 multiplications and 12 additions in the system of real numbers, and in the system of bycomplex numbers
, taking into account direct and reverse transitions, multiplication requires only 6 multiplications and 14 additions.
![](corr/2/27.jpg)