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12. Reading and Writing
Translating to and from a known language provides useful beginning exercises in learning a new one. The following provides examples.
Cover the right side of the page and make a serious attempt to translate the sentences on the left to English; that is, state succinctly in English what the verb defined by each sentence does. Use any available aids, including the dictionary and experimentation on the computer:

`f1=: <:` | Decrement (monad); Less or equal
`f2=: f1&9` | Less or equal 9
`f3=: f2 *. >:&2` | Interval test 2 to 9 (inclusive)
`f4=: f3 *. <. = ]` | In 2 to 9 and integer
`f5=: f3 +. <. = ]` | In 2 to 9 or integer
`g1=: %&1.8` | Divide by 1.8
`g2=: g1^:_1` | Multiply by 1.8
`g3=: -&32` | Subtract 32
`g4=: g3^:_1` | Add 32
`g5=: g1@g3` | Celsius from Fahrenheit
`g6=: g5^:_1` | Fahrenheit from Celsius
`h1=: >./` | Maximum over list (monad)
`h2=: h1-<./` | Spread. Try`h2 b` with the parabola:`b=:(-&2 * -&3) -:i.12`
`h3=: h1@]-i.@[*h2@]%<:@[` | Grid. Try`10 h3 b`
`h4=: h3 <:/ ]` | Barchart. Try`10 h4 b`
`h5=: {&' *' @ h4` | Barchart. Try`10 h5 b`

After entering the foregoing definitions, enter each verb name alone to display its definition, and learn to interpret the resulting displays. To see several forms of display, first enter`9!:3 (2 4 5)` .
Cover the left side of the page, and translate the English definitions on the right back into J.

Exercises

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,sp-LS)` | 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` .

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