Ⓠ — FactorⓆN: sorted prime factors, with multiplicity. J’s q: family. Positive integral input; exact integer results.
Ⓠ700 ⍝ 2x 2x 5x 5x 7x
Ⓠ1 ⍝ 0⍴0x
Ⓠ⍣¯1⊢Ⓠ700 ⍝ 700x
Inverse: product. KⓆN selects exponents or a factor table.
| K | Result |
|---|---|
| Nonnegative integer | Exponents of the first K primes; remaining factors are omitted |
∞ |
Exponents through the largest factor |
| Negative integer | Last \|K distinct factors and their exponents, in two rows |
¯∞ |
Complete two-row factor/exponent table |
2Ⓠ700 ⍝ 2x 0x
∞Ⓠ700 ⍝ 2x 0x 2x 1x
¯2Ⓠ700 ⍝ 2 2⍴5x 7x 2x 1x
¯∞Ⓠ700 ⍝ 2 3⍴2x 5x 7x 2x 2x 1x
0Ⓠ700 ⍝ 0⍴0x
¯∞Ⓠ1 ⍝ 2 0⍴0x
Scalar cells; results assemble with fill. Large factors follow Prime’s probable-prime policy.
DOMAIN: nonpositive/non-integral N; non-integral finite K.