The 3-basis

basis3 = {1, {σ1, σ2, σ3}, {σ1σ2, σ2σ3, σ3σ1}, σ1σ2σ3} ;

basis3//MatrixForm

( {{1}, {{σ1, σ2, σ3}}, {{σ1σ2, σ2σ3, σ3σ1}}, {σ1σ2σ3}} )

b3 = {1, {σ1, σ2, σ3}, {iσ1, iσ2, iσ3}, i} ;

b3//MatrixForm

( {{1}, {{σ1, σ2, σ3}}, {{iσ1, iσ2, iσ3}}, {i}} )

n3 = 8 ;

a3 = {a0, {ax, ay, az}, {aix, aiy, aiz}, ai} ; b3 = {b0, {bx, by, bz}, {bix, biy, biz}, bi} ;

a3v = {0, {ax, ay, az}, {0, 0, 0}, 0} ;

 b3v = {0, {bx, by, bz}, {0, 0, 0}, 0} ;

c3v = {0, {cx, cy, cz}, {0, 0, 0}, 0} ;

a3bi = {0, {0, 0, 0}, {aix, aiy, aiz}, 0} ; b3bi = {0, {0, 0, 0}, {bix, biy, biz}, 0} ;


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