threeform               package:onion               R Documentation

_V_a_r_i_o_u_s _n_o_n-_f_i_e_l_d _d_i_a_g_n_o_s_t_i_c_s

_D_e_s_c_r_i_p_t_i_o_n:

     Diagnostics of non-field behaviour: threeform, associator,
     commutator

_U_s_a_g_e:

     threeform(x1, x2, x3)
     associator(x1, x2, x3)
     commutator(x1, x2)

_A_r_g_u_m_e_n_t_s:

x1,x2,x3: onionic vectors

_D_e_t_a_i_l_s:

     The threeform is defined as 'Re(x1 * (Conj(x2) * x3) - x3 *
     (Conj(x2) * x1))/2';

     the associator is '(x1 * x2) * x3 - x1 * (x2 * x3)';

     the commutator is 'x1 * x2 - x2 * x1'.

_V_a_l_u_e:

     Returns an octonionic vector.

_A_u_t_h_o_r(_s):

     Robin K. S. Hankin

_E_x_a_m_p_l_e_s:

     x <- roct(7) ; y <- roct(7) ; z <- roct(7)
     associator(x,y,z)

