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∧ — Polar / And

Function. Keys: Alt-0. Hanzi: 极/且 (極/且). Ranks: 0 monadic, 0 0 dyadic

∧Y gives a magnitude and an angle for each number in Y, along a new last axis. Angles are in radians.

∧0j2              ⍝ [2 1π2]
∧3j4              ⍝ 5 0.9272952180016122

An exact number keeps an exact magnitude beside its float angle. Where integers wrap, under static kinds or at a fixed width, an integer’s magnitude and angle are both floats, at the width that ÷ gives the integer.

X∧Y gives LCM; on Booleans, AND. Pervasive.

0 0 1 1∧0 1 0 1   ⍝ 0 0 0 1
4ₓ∧6ₓ              ⍝ 12ₓ
∧/1 1 0            ⍝ 0

Includes rational and complex LCM. Inputs are finite. Empty reduction identity: one, or $t on Booleans.

Inverse

∧⁻Y rebuilds complex numbers from the magnitude and angle pairs on the last axis of Y.

∧⁻[2 π0.5]   ⍝ 0j2