12.1 
These exercises are grouped by topic and organized
like the section, with programs that are first to be read
and then to be rewritten. However, a reader already familiar
with a given topic might begin by writing.
A. Properties of numbers
pn=: >:@i. 
Positive numbers (e.g. pn 9) 
rt=: pn / pn 
Remainder table 
dt=: 0&=@rt 
Divisibility table 
nd=: +/@dt 
Number of divisors 
prt=: 2&=@nd 
Prime test 
prsel=: prt # pn 
Prime select 
N=: >:@pn 
Numbers greater than 1 
rtt=: ,@(N */ N) 
Ravelled times table 
aprt=: .@(N e. rtt) 
Alternative test and selection
(primes do not occur in the times table for N) 
apsel=: aprt # N 

pfac=: q: 
Prime factors 
first=: p:@i. 
First primes 
B. Coordinate Geometry
Do experiments on the vector (or point) p=: 3 4
and the triangle represented by the
table tri=: 3 2$ 3 4 6 5 7 2
L=: %:@:(+/)@:*:"1 
Length of vector (See rank in the dictionary
or in Section 20 of the Introduction) 
LR=:L"1 
Length of rows in table 
disp=: ]  1&. 
Displacement between rows 
LS=: LR@disp 
Lengths of sides of figure 
sp=: :@(+/)@LS 
Semiperimeter (try sp tri) 
H=: %:@(*/)@(sp,spLS) 
Heron's formula for area 
det=: / . * 
Determinant (See dictionary) 
SA=: det@(,.&0.5) 
Signed area. Try SA@. 
sa=:det@(],.%@!@<:@#) 
General signed volume; try on the tetrahedron 
tet=:?4 3$9 
as well as on the triangle tri . 
