∨ — Real-imag / Or

Function. Keys: Alt-9. Ranks: 0 monadic, 0 0 dyadic

∨Y gives real/imaginary pairs along a new last axis. Y is a numeric array.

∨3j4              ⍝ 3 4
∨3j4 1j2          ⍝ [3 4⋄1 2]
∨1r3              ⍝ 1r3 0ₓ

X∨Y gives GCD; on Booleans, OR. Pervasive.

0 0 1 1∨0 1 0 1   ⍝ 0 1 1 1
12ₓ∨18ₓ            ⍝ 6ₓ
∨/0 0 1            ⍝ 1

Includes rational and complex GCD. Inputs are finite. Empty reduction identity: zero, or $f on Booleans.

For approximate real inputs, GCD reconstructs the ratio of their magnitudes using continued fractions. It chooses the first convergent equal to that ratio within the comparison tolerance. Integer convergents are computed exactly. The result is the larger magnitude divided by the convergent’s numerator. Exact inputs use exact GCD. Complex inputs use Gaussian-integer Euclidean iteration.

Inverse

∨⁻¹Y rebuilds complex numbers from the real and imaginary pairs on the last axis of Y.

∨⁻¹3 4   ⍝ 3j4