Point Notation

Overview

Base Point Notation: e.g., 16b10FFFFas a shorthand for 16⊥1 0 15 15 15 15 15. Euler Point Notation: e.g., 2x3 as a shorthand for 2e3 or 2×(*1)*3 Pi Point Notation: e.g., 2p3 as a shorthand for 2π3 or 2×(○1)*3 Rational Point Notation: e.g., 2r3 as a shorthand for 2÷3 as a rational number Decimal Point Notation: e.g., 2.5 as a shorthand for 2½ or 2+5÷10 Exponential Point Notation: e.g., 2e3 as a shorthand for 2•103 or 2×10*3

Base, Euler, Pi, and Rational Point Notations are extensions to the familiar Decimal Point Notation as well as Exponential Point or Scientific Notation methods of entering numeric constants. Thanks to the designers of J for these clever ideas.

Base Point Notation

This notation makes it easy to enter numeric constants in an arbitrary base.

The number to the left of the b is the base of the number system for the characters to the right of the b. The base may be represented in several ways including integers, Exponential, Decimal, Pi, Euler, and Rational Point Notation, but not Base Point Notation.

For example, 1e3b111 is the same as 1000b111.

Note that the base may also be negative as in ¯1b0z or fractional as in 0.1b1234.

The characters to the right of the b may range from 0-9 or a-z where the latter range is a way of representing numbers from 10-35 in a single character. The uppercase letters (A-Z) have the same values as the corresponding lowercase case letters and may be used instead of or intermixed with them.

For example, 10bzzZ is the same as 10⊥35 35 35 35, and 1r2b111 is the same as 0.5b111.

Euler Point Notation

This notation allows you to enter numeric constants that are in the form of the product of a multiplier and e (the base of the natural logarithms) raised to an exponent, that is, Me^E or M×(*1)*E. The numbers to the left (multiplier) and right (exponent) of the x may be represented in several ways including integers, Decimal, Exponential, or Rational Point Notation, but not Base, Pi, or Euler Point Notation.

For example, 1e2x1.1 is the same as 100x1.1, and 1r2x1.1e2 is the same as 0.5x110.

Both the multiplier and exponent may be negative and/or fractional as in ¯1e2x¯3.3.

Pi Point Notation

This notation allows you to enter numeric constants that are in the form of the product of a multiplier and π raised to an exponent, that is, Mπ^E or M×(○1)*E. The numbers to the left (multiplier) and right (exponent) of the p may be represented in several ways including integers, Decimal, Exponential, or Rational Point Notation, but not Base, Euler, or Pi Point Notation.

For example, 1e2p1.1 is the same as 100p1.1, and 1r2p1.1e2 is the same as 0.5p110.

Both the multiplier and exponent may be negative and/or fractional as in ¯1e2p¯3.3.

Rational Point Notation

This notation allows you to enter fractions as rational numbers and have them be retained as rational numbers. The implementation of this feature is woefully incomplete — in fact, the only place this notation is allowed is as an argument to Base, Euler, or Pi Point Notation.