Roots p.  1 1 0 兜Α

   p. c   «  (m;r)
   p.p.c  «  c
狦 e 8じ 獶璽俱计秖玥 p.<c,.e 眔 单兜Α玒计:
   (p. <c,.e)&p.  «  (<c,.e)&p. 
  Τ贺摸玒计计籔 兜Α (玒计籔计杆痻皚)
     c p. x  «  +/c*x^i.#c
 (m;r) p. x  «  m * */x-r
    (<r)&p.  «  (1;r)&p.
(<c,.e)p.<y  «  c+/ .*e*/ .(^~)y
ㄤい m 秖; c r  秖┪秖τ e 8秖┪痻皚ㄏ眔 ($e)-:(#c),(#y)秖 y 硄盽extended
 

   p. 1 0 0 1
+-+-----------------------------+
|1|_1 0.5j0.866025 0.5j_0.866025|
+-+-----------------------------+

   ]mr=: p. c=: 0 16 _12 2     Multiplier/Roots from玒计
+-+-----+
|2|4 2 0|
+-+-----+

   x=: 0 1 2 3 4 5
   (c p. x), ((<c,.i.4)p. x), (mr p. x),: 2*(x-4)*(x-2)*(x-0)
0 6 0 _6 0 30
0 6 0 _6 0 30
0 6 0 _6 0 30
0 6 0 _6 0 30

   c=: 1 3 3 1
   c p. x
1 8 27 64 125 216
   (x+1)^3
1 8 27 64 125 216

   bc=: !~/~i.5                Binomial玒计
   bc;(bc p./ x);((i.5) ^~/ x+1)
+---------+--------------------+--------------------+
|1 0 0 0 0|1  1  1   1   1    1|1  1  1   1   1    1|
|1 1 0 0 0|1  2  3   4   5    6|1  2  3   4   5    6|
|1 2 1 0 0|1  4  9  16  25   36|1  4  9  16  25   36|
|1 3 3 1 0|1  8 27  64 125  216|1  8 27  64 125  216|
|1 4 6 4 1|1 16 81 256 625 1296|1 16 81 256 625 1296|
+---------+--------------------+--------------------+

   c&p. d. 1 x                 First 旧ㄧ计of 兜Α
3 12 27 48 75 108

   (<1 _1 ,. 5 0) p. 3         玒计/ Exponents
242
              
   _1 0 0 0 0 1 p. 3
242
              
   p. <1 _1 ,. 5 0             玒计/ Exponents to玒计
_1 0 0 0 0 1

   c=: _1 1 2 3 [ e=: 4 2$2 1 1 1 1 2 0 2
   c,.e                        玒计/ Exponents
_1 2 1
 1 1 1
 2 1 2
 3 0 2
                  
   (<c,.e) p. <y=:2.5 _1       Multinomial
11.75

   c +/ .* e */ .(^~) y
11.75
Note that (<c,.e)p.<y is a "proper" multinomial only if だ of e are all 獶璽俱计s. In general powers are not so limited, as weighted sum of square root籔4-th root:
   ] t=: <2 3,.1r2 1r4
+-----+
|2 1r2|
|3 1r4|
+-----+

   (t p. 16), +/ 2 3 * 16 ^ 1r2 1r4
14 14
variant p.!.s is a 辫琿 兜Α; it differs from p. in that its ﹚竡is based upon辫琿 ^!.s instead of on ^ (power).


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