Mixed Radix Next Digits

Advance a mixed-radix tuple forward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.

Description

Advance a mixed-radix tuple forward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.

A mixed-radix successor carries across position-specific radices. It can advance a product-space index without enumeration.

When to use this tool

Advance a mixed-radix tuple forward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.

Prepare the supplied digits, radices fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter digits, radices. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.digits. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Encode valid aligned digits/radices, add one and decode if below the product of radices. At the final vector return null.^[1]

Input field	Meaning and representation	Accepted input
digits	digits.	List of finite numbers; at most 128 entries
radices	radices.	List of finite numbers; at most 128 entries

Output field	Interpretation
result	Object containing the named outputs below.
result.digits	The digits list in the ordering and representation described above.

json

{
  "input": {
    "digits": [
      0,
      2
    ],
    "radices": [
      2,
      3
    ]
  },
  "output": {
    "result": {
      "digits": [
        1,
        0
      ]
    }
  }
}

Limitations and assumptions

Radices range from 1 to one million. The rightmost digit is least significant; there is no cyclic wraparound.
All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.

Alternative or Complementary methods

Retain the universe size, subset size and ordering convention with a rank. Use rank/unrank pairs from the same convention and distinguish subset masks from lexicographic indexes.

References

Tool behavior and example: Mixed Radix Next Digits — tool.io

Similar or alternative tools

Mixed Radix Previous Digits
Advance a mixed-radix tuple backward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.
Mixed Radix Digit Decoder
Decode a zero-based exact integer index into mixed-radix digits most-significant lane first; out-of-range indexes do not wrap.