AdicExpansion

The digits of a $b$ -adic number, written with the infinite end on the left: $\ldots 6667$ for $1/3$ in $\mathbb{Z}_{10}$ , $0.12$ for $7/25$ in $\mathbb{Q}_5$ , $+ O(b^n)$ when capped.

AdicExpansion(x, count?)the first count digits (default 20) as a string

AdicDigits(x, count?)the same digits as a list, LEAST significant first — the only order that lists something with no left end

Typed signatures

Type	Package	Applies
`(value, integer?) -> string`	`numerals`	always

Domain: Numeral systems

Details

The ellipsis marks the infinite left end and is dropped only when nothing hides there: an exact non-negative integer (times $b^v$ )
Digits past the point are the negative-valuation places, prime bases only
Digits $\ge 10$ are bracketed, so base 16 reads …[15][15][15]

Examples

Basic #

In

\mathrm{AdicExpansion}(\mathrm{AdicNumeral}(10, \frac{1}{3}), 8)

Out

\text{…66666667}

the same $1/3$ , 2-adically

In

\mathrm{AdicExpansion}(\mathrm{AdicNumeral}(2, \frac{1}{3}), 8)

Out

\text{…10101011}

as a list, least significant first

In

\mathrm{AdicDigits}(\mathrm{AdicNumeral}(10, \frac{1}{3}), 6)

Out

\bigl\lbrack7, 6, 6, 6, 6, 6\bigr\rbrack

Scope #

$7/25 = 2·5^{-2} + 1·5^{-1}$

In

\mathrm{AdicExpansion}(\mathrm{AdicNumeral}(5, \frac{7}{25}), 8)

Out

\text{0.12}

A plain non-negative integer terminates with no infinite tail

In

\mathrm{AdicExpansion}(\mathrm{AdicNumeral}(10, 42))

Out

\text{42}

$-1$ is the all-9s repeating tail, since $-1=\dots999$ in $\mathbf{Z}_{10}$

In

\mathrm{AdicExpansion}(\mathrm{AdicNumeral}(10, -1), 6)

Out

\text{…999999}

Digits at or above 10 print bracketed, as in $[15]$ for hexadecimal $-1$ 's repeating digit

In

\mathrm{AdicExpansion}(\mathrm{AdicNumeral}(16, -1), 3)

Out

\text{…[15][15][15]}

Digits run least-significant first: $-1$ 's first four 10-adic digits are all 9

In

\mathrm{AdicDigits}(\mathrm{AdicNumeral}(10, -1), 4)

Out

\bigl\lbrack9, 9, 9, 9\bigr\rbrack

About

Examples	8
Checked against	SageMath 2 errorRust 2 error

See also: AdicNumeral, IntegerDigits