*/b=:2 7 1 8 2 8 1792 <./b 1 >./b 8The verb resulting from the application of an adverb may (like a primitive verb) have both monadic and dyadic cases; due to its two uses, the adverb / is called either insert or table. In the present instance of / the dyadic case produces a table. For example:
2 3 5 +/ 0 1 2 3 2 3 4 5 3 4 5 6 5 6 7 8The verbs over=:({.;}.)@":@, and by=:' '&;@,.@[,.] can be entered as utilities (for use rather than for immediate study), and can clarify the interpretation of function tables such as the addition table produced above. For example:
a=: 2 3 5 b=: 0 1 2 3 a by b over a +/ b +++  0 1 2 3 +++ 22 3 4 5 33 4 5 6 55 6 7 8 +++ b by b over b </ b +++  0 1 2 3 +++ 00 1 1 1 10 0 1 1 20 0 0 1 30 0 0 0 +++
Exercises
3.1  Enter d=: i.5 and the sentences st=: d/d
and pt=: d^/d to produce function tables for subtraction
and power.

3.2  Make tables for further functions from previous sections,
including the relations < and = and > and
lesserof and greaterof.

3.3  Apply the verbs . and : to various tables,
and try to state what they do.

3.4  The transpose function : changes the
subtraction table, but appears to have no effect on the multiplication table.
State the property of those functions whose tables remain unchanged
when transposed. Answer: They are commutative 
3.5  Enter d by d over d!/d and state the definition
of the dyad ! . Answer: ! is the binomial coefficient or outof function; 3!5 is the number of ways that three things can be chosen from five. 