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Octonion Algebra Multiplication Tables

​
μ
1
μ
2
μ
3
symbolic coefficients
highlight negative coefficients
u
1
u
2
u
3
u
4
u
5
u
6
u
7
u
8
u
2
3
u
1
-
u
4
-3
u
3
-
u
6
-3
u
5
u
8
3
u
7
u
3
u
4
3
u
1
3
u
2
-
u
7
-
u
8
-3
u
5
-3
u
6
u
4
3
u
3
-3
u
2
-9
u
1
-
u
8
-3
u
7
3
u
6
9
u
5
u
5
u
6
u
7
u
8
5
u
1
5
u
2
5
u
3
5
u
4
u
6
3
u
5
u
8
3
u
7
-5
u
2
-15
u
1
-5
u
4
-15
u
3
u
7
-
u
8
3
u
5
-3
u
6
-5
u
3
5
u
4
-15
u
1
15
u
2
u
8
-3
u
7
3
u
6
-9
u
5
-5
u
4
15
u
3
-15
u
2
45
u
1
Multiplication tables for Cayley's octonion numbers incorporate three scalar coefficients. Modify these coefficients to change the resulting positions of negative coefficients.
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