MixedRadixNumerals

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

Wolfram's own MixedRadix, mapped through for the transpiler and the oracle but not yet written up here.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageMixedRadix✓↗

MixedRadixNumerals(...)Wolfram's own MixedRadix, mapped through for the transpiler and the oracle but not yet written up here.

Typed signatures

Type	Package	Applies
(list<integer>) -> value	numerals	always

Domain: Wolfram

Examples

Basic #

Digits for 571 in radices 12, 9, 6, with the top digit unbounded

live ↗

In$\mathrm{IntegerDigits}(571, \mathrm{MixedRadixNumerals}(\bigl\lbrack12, 9, 6\bigr\rbrack))$Out$\bigl\lbrack10, 5, 1\bigr\rbrack$

Scope #

Four digits needed for 1024 with radices 6, 4, 2

live ↗

In$\mathrm{IntegerLength}(1\,024, \mathrm{MixedRadixNumerals}(\bigl\lbrack6, 4, 2\bigr\rbrack))$Out$4$

Digits of 534 for radices 15, 10, 5

live ↗

In$\mathrm{IntegerDigits}(534, \mathrm{MixedRadixNumerals}(\bigl\lbrack15, 10, 5\bigr\rbrack))$Out$\bigl\lbrack10, 6, 4\bigr\rbrack$

FromDigits inverts the digit expansion above

live ↗

In$\mathrm{FromDigits}(\bigl\lbrack10, 6, 4\bigr\rbrack, \mathrm{MixedRadixNumerals}(\bigl\lbrack15, 10, 5\bigr\rbrack))$Out$534$

Reversing the digits of 1024 and reading them back gives 25

live ↗

In$\mathrm{IntegerReverse}(1\,024, \mathrm{MixedRadixNumerals}(\bigl\lbrack6, 4, 2\bigr\rbrack))$Out$25$

Applications #

A long prime-radix expansion of a million

live ↗

In$\mathrm{IntegerDigits}(1\,000\,000, \mathrm{MixedRadixNumerals}(\bigl\lbrack19, 17, 13, 11, 7, 5, 3, 2\bigr\rbrack))$Out$\bigl\lbrack1, 16, 3, 9, 6, 1, 2, 0\bigr\rbrack$

A factorial-style base gives digits of 437 in radices 6 down to 1

live ↗

In$\mathrm{IntegerDigits}(437, \mathrm{MixedRadixNumerals}(\bigl\lbrack6, 5, 4, 3, 2, 1\bigr\rbrack))$Out$\bigl\lbrack3, 3, 0, 2, 1, 0\bigr\rbrack$

Properties #

The leading digit may exceed its radix when the number is too big, here 19

live ↗

In$\mathrm{IntegerDigits}(100\,000, \mathrm{MixedRadixNumerals}(\bigl\lbrack10, 9, 8, 7\bigr\rbrack))$Out$\bigl\lbrack19, 8, 3, 5, 5\bigr\rbrack$

With equal radices of 10 it is ordinary decimal

live ↗

In$\mathrm{IntegerDigits}(4\,237, \mathrm{MixedRadixNumerals}(\bigl\lbrack10, 10, 10, 10\bigr\rbrack))$Out$\bigl\lbrack4, 2, 3, 7\bigr\rbrack$

Radices 10, 8, 6, 4, 2 give five digits

live ↗

In$\mathrm{IntegerDigits}(2\,135, \mathrm{MixedRadixNumerals}(\bigl\lbrack10, 8, 6, 4, 2\bigr\rbrack))$Out$\bigl\lbrack5, 4, 2, 3, 1\bigr\rbrack$

Ten thousand seconds as hours, minutes, seconds: 2 h 46 m 40 s

live ↗

In$\mathrm{IntegerDigits}(10\,000, \mathrm{MixedRadixNumerals}(\bigl\lbrack24, 60, 60\bigr\rbrack))$Out$\bigl\lbrack2, 46, 40\bigr\rbrack$

The round trip: 2 h 46 m 40 s is 10000 seconds

live ↗

In$\mathrm{FromDigits}(\bigl\lbrack2, 46, 40\bigr\rbrack, \mathrm{MixedRadixNumerals}(\bigl\lbrack24, 60, 60\bigr\rbrack))$Out$10\,000$

About

Examples	12
Checked against	Wolfram Language 12 agree
Crosswalk	Wolfram Language