x =. 1 2 3 4 5 6 7
   x*x
1 4 9 16 25 36 49
 x */ x
1 2 3 4 5 6 7
2 4 6 8 10 12 14
3 6 9 12 15 18 21
4 8 12 16 20 24 28
5 10 15 20 25 30 35
6 12 18 24 30 36 42
7 14 21 28 35 42 49
  x-/x
0 _1 _2 _3 _4 _5 _6
1 0 _1 _2 _3 _4 _5
2 1 0 _1 _2 _3 _4
3 2 1 0 _1 _2 _3
4 3 2 1 0 _1 _2
5 4 3 2 1 0 _1
6 5 4 3 2 1 0
  x >:/ x
1 0 0 0 0 0 0
1 1 0 0 0 0 0
1 1 1 0 0 0 0
1 1 1 1 0 0 0
1 1 1 1 1 0 0
1 1 1 1 1 1 0
1 1 1 1 1 1 1
 ]n =. x-4
_3 _2 _1 0 1 2 3
  n*/n
 9 6 3 0 _3 _6 _9
 6 4 2 0 _2 _4 _6
 3 2 1 0 _1 _2 _3
 0 0 0 0 0 0 0 
_3 _2 _1 0 1 2 3
_6 _4 _2 0 2 4 6
_9 _6 _3 0 3 6 9
  +/x
28
  */x
5040

  (x-3) * (x-5)
8 3 0 _1 0 3 8
  r =. 8 7 6 5 4 3 2 1 0 _1

ALGEBRA

An Algorithmic Treatment

Kenneth E. Iverson

J translation by Edward Mokurai Cherlin

  ]m =. r =/(x-3)*(x-5)
1 0 0 0 0 0 1
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 1 0 0 0 1 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 1 0 1 0 0
0 0 0 1 0 0 0
  m{' *'
* * * * * * * J * * * * * * ** (1 2 3 4 5 6 - 3) |. j * * * * * * **