digits

Returns the digits of an integer or a rational number.

Syntax

• digits(x[, n[, mode]])

  • x is an integer or a rational number

  • n is a non-negative integer

  • mode is either "fractional" or "significant"

Description

• If x is an integer, then digits(x) returns the digits of x as a list with the MSD first.

  All digits are exact.

• If x is a rational number, then digits(x, n, mode) returns the digits of x in a structure with one member, int, for the integer part and another member, frac, for the fractional part. Each member is a list of digits with the MSD first.

  If mode = "fractional", all integral digits are returned and up to n fractional digits (trailing, insignificant, zeroes are not included).

  If mode = "significant", then the n most significant digits are returned, except for trailing zeros. Notice that not all integral digits might be returned.

  If omitted, n defaults to 64 and mode to "fractional".

  All digits are exact. No rounding takes place.

• If x is a real or complex number, an attempt is made to convert it to an integer (preferably) or an approximate rational number, and then proceed with the result of that conversion. Unless x happens to be an integer or a rational number, the resulting digits may not be exact.

Examples

digits(521341)

5
2
1
3
4
1

#digits(1852616517806850212)

19

digits(1/613)

int: (0)
frac: (0, 0, 1, 6, 3, 1, 3, 2, 1, 3, 7, 0, 3, 0, 9, 9, 5, 1, 0, 6, 0, 3, 5, 8, 8, 9, 0, 7, 0, 1, 4, 6, 8, 1, 8, 9, 2, 3, 3, 2, 7, 8, 9, 5, 5, 9, 5, 4, 3, 2, 3, 0, 0, 1, 6, 3, 1, 3, 2, 1, 3, 7, 0, 3)

sort(frequencies(digits(1/123456789, 1E6).frac))

(0, 100177)
(1, 99612)
(2, 100115)
(3, 100281)
(4, 100006)
(5, 100022)
(6, 99586)
(7, 99791)
(8, 100175)
(9, 100235)

sort(frequencies(compute(RandomInt(1000000)^2, n, 1, 1000000) @ digits @ first))

(1, 192164)
(2, 146925)
(3, 123873)
(4, 109158)
(5, 98564)
(6, 90439)
(7, 84566)
(8, 79092)
(9, 75219)