polymod — successive division

Break a number into mixed-radix parts in one call — seconds into h/m/s, etc.

.polymod divides a number by a series of moduli in turn, returning the remainder at each step and the final quotient. It's the clean way to convert a total into mixed-radix units.

Time from seconds #

3723.polymod(60, 60) peels off seconds, then minutes, leaving hours: 3 seconds, 2 minutes, 1 hour.

say 3723.polymod(60, 60);

(3 2 1)

The general shape #

Each modulus divides the running quotient; the last element is whatever remains.

say 10.polymod(3);

(1 3)

10 mod 3 is 1 (first element); the quotient 3 is the last.

Notes #

• The result has one more element than the number of moduli — the remainders, then the final quotient.
• Read it low-to-high: with (60, 60) the parts come out seconds, minutes, hours — reverse them for the usual h:m:s display.
• .polymod with an infinite/lazy list of moduli keeps going until the quotient reaches zero, handy for arbitrary-length digit extraction.