(Ä-operation) in (Fm, FΔm) representations
Å-operation in (Fm, FΔm) representations
4) F m ( a i ⊗ a j ) = 〈 m ( a i , a j ) 〉 = 〈 m ( a i ) , m ( a j ) 〉
F m ( a i ⊗ a i ) = F m ( a i ) = m ( a i )
1) F m ( a i ⊕ a j ) = F m ( a i ) + F m ( a j ) = m ( a i ) + m ( a j )
F m ( a i ⊕ a i ) = F m ( a i ) + F m ( a i ) = m ( a i ) + m ( a i ) = 2 m ( a i )
2) F Δ m ( a i ⊗ a j ) = 0
F Δ m ( a i ⊗ a j ) ⊕ ≠ 0
with ( a i ⊗ a j ) ⊕ = ( a i ⊗ a j ) ⊕ a k
2) F Δ m ( a ⊕ b ⊕ c ) = F Δ m ( a ) + F Δ m ( b ) + F Δ m ( c ) + F Δ m ( a ⊕ _ b ) a b + F Δ m ( a ⊕ _ c ) a c + F Δ m ( b ⊕ _ c ) b c
3) F Δ m ( a i ⊗ a j ) ⊕ = F Δ m ( a i )
F Δ m ( ( a i ⊗ a j ) ⊕ a k ) = F Δ m ( ( a i ) ⊕ a k )
3) F Δ m [ ( a i ⊕ a j ) ⊕ a k ] = F Δ m [ ( a i ⊕ a k ) ⊕ ( a j ⊕ a k ) ]
4) F m [ ( a i 1 ⊗ a j 2 ) ⊕ ( a i 2 ⊗ a j 1 ) ] = F m [ 2 ( a i ⊗ a j ) 12 ]
4) F Δ m [ ( a i ⊗ a j ) ⊕ ( a k ⊗ a r ) ] = F Δ m [ ( a i ⊗ a j ) ⊕ ( a k ) ] + F Δ m [ ( a i ⊗ a j ) ⊕ ( a r ) ]
5) F Δ m ( 2 a i ⊗ a j ) = F Δ m ( 2 ( a i ⊗ a j ) )
F Δ m ( n ( a i ⊗ a j ) ⊕ m ( a k ⊗ a r ) ) = ( n × m ) F Δ m ( ( a i ⊗ a j ) ⊕ ( a k ⊗ a r ) )
6) F Δ m [ a i ⊕ a j ] + F Δ m [ a i ⊕ a k ] = F Δ m [ a i ⊕ ( a j + a k ) ]