純粋・応用数学・数学隣接分野（含むガロア理論）12

>>183
�@=-1

�B*�B=(2η　-η^3-2η^2)�D
�B*�D=(2η^2-η　-2η^4)�F
�B*�F=(2η　-η^3-2η^2)�H
�B*�H=11

�D*�B=(2η^2-η　-2η^4)�F
�D*�D=(2η^2-η　-2η^4)�H
�D*�F=11
�D*�H=(2η^4-η^2-2η^3)�B

�F*�B=(2η　-η^3-2η^2)�H
�F*�D=11
�F*�F=(2η^3-η^4-2η　)�B
�F*�H=(2η^3-η^4-2η　)�D

�H*�B=11
�H*�D=(2η^4-η^2-2η^3)�B
�H*�F=(2η^3-η^4-2η　)�D
�H*�H=(2η^4-η^2-2η^3)�F

�B^5
=�B^3�D(2η-η^3-2η^2)
=�B^2�F(2η^2-η-2η^4)(2η-η^3-2η^2)
=�B　�H(2η-η^3-2η^2)(2η^2-η-2η^4)(2η-η^3-2η^2)
=11(2η-η^3-2η^2)(2η^2-η-2η^4)(2η-η^3-2η^2)

�D^5
=�D^3�H(2η^2-η-2η^4)
=�D^2�B(2η^4-η^2-2η^3)(2η^2-η-2η^4)
=�D�F(2η^2-η-2η^4)(2η^4-η^2-2η^3)(2η^2-η-2η^4)
=11(2η^2-η-2η^4)(2η^4-η^2-2η^3)(2η^2-η-2η^4)

�F^5
=�F^3�B(2η^3-η^4-2η)
=�F^2�H(2η-η^3-2η^2)(2η^3-η^4-2η)
=�F　�D(2η^3-η^4-2η)(2η-η^3-2η^2)(2η^3-η^4-2η)
=11(2η^3-η^4-2η)(2η-η^3-2η^2)(2η^3-η^4-2η)

�H^5
=�H^3�F(2η^4-η^2-2η^3)
=�H^2�D(2η^3-η^4-2η)(2η^4-η^2-2η^3)
=�H�B(2η^4-η^2-2η^3)(2η^3-η^4-2η)(2η^4-η^2-2η^3)
=11(2η^4-η-2η^3)(2η^3-η^4-2η)(2η^4-η^2-2η^3)

(2η-η^3-2η^2)(2η^4-η^2-2η^3)
=(4+1+4-2η^3+2η-4η-4η^4-2η^2+2η^2)
=(4+1+4-2η^3-2η-2η^2-2η^4)
=11

(2η^3-η^4+2η)(2η^2-η-2η^4)
=(4+1+4-2η^4+2η^3-4η^3-4η^2-2η^+2η^2)
=(4+1+4-2η^4-2η^3-2η^2-2η)
=11