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| +

+

+

+ |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| +

+

+

+ | |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| +-+

+ }}}