Constants
The form of a numeric constant defined and illustrated in
Part I
is elaborated by the use of further letters, as in 2r3
for two-thirds, 2p1 for two π, and 2e3p1
for 2000 π.
The complete scheme of numeric constants obeys the following hierarchy:
| . | The decimal point is obeyed first |
| _ | The negative sign is obeyed next |
| e | Exponential (scientific) notation |
| ad ar j | Complex (magnitude and angle) in degrees or radians; Complex number |
| p x | Numbers based on pi (o.1) and on Euler’s number (the exponential ^1) |
| b | Base value (using a to z for 10 to 35) |
Moreover, digits with a trailing x denote an extended
precision integer, and digits followed by an r followed by
further digits denote a rational number.
See Section II G.
For example, 2.3 denotes two and three-tenths and _2.3
denotes its negation; but _2j3 denotes a complex number with
real part _2 and imaginary part 3 , not
the negation of the complex number 2j3 .
Furthermore, symbols at the same level of the hierarchy cannot be
used together: 1p2x3 is an ill-formed number.
The following lists illustrate the main points:
2.3e2 2.3e_2 2j3 230 0.023 2j3 2p1 1p_1 6.28319 0.31831 1x2 2x1 1x_1 7.38906 5.43656 0.367879 2e2j_2e2 2e2j2p1 2ad45 2ar0.785398 200j_200 628.319j6.28319 1.41421j1.41421 1.41421j1.41421 16b1f 10b23 _10b23 1e2b23 2b111.111 31 23 _17 203 7.875
Negative integers following p and x indicate the use
of reciprocals. For example, 2p_2 is two divided
by π squared,
and 2x_2 is two divided by the square of Euler’s number.