Direct function: Difference between revisions

Revision as of 06:47, 9 January 2022

Revision as of 18:17, 9 January 2022

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The significance of this function can be seen as follows:

{{quoteblockquote|Complex numbers can be constructed as ordered pairs of real numbers, similar to how integers can be constructed as ordered pairs of natural numbers and rational numbers as ordered pairs of integers. For complex numbers, {{code|{⍺+0j1×⍵}|apl}} plays the same role as {{code|-|apl}} for integers and {{code|÷|apl}} for rational numbers.<ref name=Hui2016/>{{rp|§8}}}}

Moreover, analogous to that monadic {{code|-⍵|apl}} ⇔ {{code|0-⍵|apl}} (''negate'') and monadic {{code|÷⍵|apl}} ⇔ {{code|1÷⍵|apl}} (''reciprocal''), a monadic definition of the function is useful, effected by specifying a default value of 0 for {{code|⍺|apl}}: if {{code|j←{⍺←0 ⋄ ⍺+0j1×⍵}|apl}}, then {{code|j ⍵|apl}} ⇔ {{code|0 j ⍵|apl}} ⇔ {{code|0+0j1×⍵|apl}}.