FORMAL REALIZABILITY THEORY — II 565 



D-D by »Si , *Si ; • • • ; Sn , S„ , where here the r^ pair is the intersection 

 Avith D-D of the leads to the r^'' terminal pair of N^*\ In each case we 

 orient the pair T, T' or S, S' so that the primed (negative) terminal is 

 on the lead to the primed terminal of N or N^*'. 

 Let the 2«-tiiplc 



[tti , a2 , • ■ ■ , ttn , bi , bo , ■ ■ ■ , bn] (2) 



represent the currents into the terminals of Mad in the order 



Tl , To , • ■ • , Tn , Si , • • ■ , On • 



Then we may interpret 



[«!,•••, dn] (3) 



as a vector in K expressed in the coordinate frame introduced for Fig. 5, 

 and also 



[&!,•••, bn] (4) 



as a vector in K in the same frame. That is, any current vector into 

 Mad can be written as an ordered pair 



/h , k2 (5) 



where each k, e K, with the convention that such a pair determines a 

 2«--tuple (2) from the ?i-tuples (3) of fci and (4) of ki . 

 We shall WTite the ordered pair (5) in the form 



A-i e ^-2 . (6) 



Because we have K represented in the special way 



K = J e Ki , 



where J is the subspace spanned by n-tuples (3) in which the last n-m 

 components vanish (this is (1) of 4.5) we can further split the 2n-tuple 

 (2) into 



(ii e A) © (J2 @ ^2), (7) 



where ji ej, (i eKi , i = 1, 2, and in (6) 



A-.- = ji @ ii . (8) 



Formulas dual to those of (2) through (8) of course hold for voltage 

 (2rt)-tuples. Let K^ be the space of current 2n-tuples (2) (or (7)) and 

 V^ the space of voltage (2n)-tuples 



[ei , 62 ,'••, t'„ , /i ,•••,/„] = (ui © ^i) © (W2 © ^2) 



