JPhrases/FunctionTables

1D. Function Tables

d0=: +/	Addition table
d1=: */	Multiplication table
d2=: >./	Maximum table
d3=: [ by ] over +/	Bordered addition table
d4=: by=: ' '&;@,.@[,.]	Format function
d5=: over=: ({.;}.)@":@,	Format function
m6=: +/~@i.	Addition table on first y integers
m7=: bc=: !/~@i.	Binomial coefficients of order y
a8=: ft=: 1 : 'x/~@i.'	Function table
a9=: bft=: 1 : 'i. by i. over x/~@i.'	Bordered function table (Explicit definition)

The first three phrases produce function tables as illustrated below:

   2 3 5 (d0 ; d1 ; d2) 0 1 2 3 4 5
+----------------------------------------+
|2 3 4 5 6  7|0 2  4  6  8 10|2 2 2 3 4 5|
|3 4 5 6 7  8|0 3  6  9 12 15|3 3 3 3 4 5|
|5 6 7 8 9 10|0 5 10 15 20 25|5 5 5 5 5 5|
+----------------------------------------+

The next produces an addition table bordered by its arguments for easy reading; m6 and m7 produce tables on lists of integers, and the adverb a9 produces a bordered function table:

   2 3 5 d3 0 1 2 3 4 5
+--------------+
| |0 1 2 3 4  5|
+-+------------+
|2|2 3 4 5 6  7|
|3|3 4 5 6 7  8|
|5|5 6 7 8 9 10|
+--------------+

  (m6 ; m7) 5
+-------------------+
|0 1 2 3 4|1 1 1 1 1|
|1 2 3 4 5|0 1 2 3 4|
|2 3 4 5 6|0 0 1 3 6|
|3 4 5 6 7|0 0 0 1 4|
|4 5 6 7 8|0 0 0 0 1|
+-------------------+

   % a9 5
+------------------------+
| |0 1   2         3    4|
+-+----------------------+
|0|0 0   0         0    0|
|1|_ 1 0.5 0.3333333 0.25|
|2|_ 2   1 0.6666667  0.5|
|3|_ 3 1.5         1 0.75|
|4|_ 4   2   1.33333    1|
+-+----------------------+