Domain eXtensions for Dyalog APL.

Installation

⎕FIX the APL source file.

Usage

Use the operator dx to extend the domain of any monadic or dyadic function.

      {~⍵} 2 3 4 0
DOMAIN ERROR
      {~⍵}2 3 4 0
       ∧
      {~⍵}dx 2 3 4 0
0 0 0 1

Features

Glyph	Extension
~	Extended, behaves like 0=
⍭	New, dfns.pco
√	New, ⍺-th root (by default ⍺=2)
<	Extended, monadic decrement.
>	Extended, monadic increment.
⍛	New, reverse compose.
⍢	New, Round towards closest ⍺, defaulting to ⍺=1
⍍	New, Matrix multiplication, identity matrix of size..
…	New, Adam Brudzewsky's Range
⍙	New, Iverson's monadic dot product (e.g. -⍙× - determinant)
∧	Extended, monadic sorts ascending
∨	Extended, monadic sorts descending
⍗	New, inverse a function
⍐	New, iterate infintely
φ	New, fibonacci numbers
⍦	New, middle function
⍁	New, diagonal function (extract all diagonals of a matrix)
⍮	New, pair ({⍺ ⍵}) or constant (monadic)
Φ	New, Euler's totient
⍲	Extended, monadic - prefixes of a vector
⍱	Extended, monadic - suffixes of a vector
=	Extended, monadic checks if all elements are equal
⍡	New, filter operator
⊤	Extended, ⊥⍣¯1 with ⍺=10 by default
⌂	New, the dx operator accessible to the code

Example usage of the middle function:

      3⍦⍳7
4
      2⍦⍳7
3 4 5
      1⍦⍳7
2 3 4 5 6
      1⍦⍳8
2 3 4 5 6 7
      ¯1⍦⍳8
4 5
      ¯2⍦⍳8
3 4 5 6
      ¯3⍦⍳8
2 3 4 5 6 7

Quirks & Bugs

• The left operand to dx must be a dfn, either inline or named.

Additional credits

Dzaima: a better pmat implementation
Adam Brudzewsky: Range implementation