Mixed Radix Total Size
Return exact mixed-radix product size as decimal integer text; an empty digit tuple has one possible state.
Description
Return exact mixed-radix product size as decimal integer text; an empty digit tuple has one possible state.
The size of a mixed-radix product space is the product of its position-specific radix counts.
When to use this tool
Return exact mixed-radix product size as decimal integer text; an empty digit tuple has one possible state.
- Prepare the supplied 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 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.size. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Require every radix to be an integer from 1 to one million. Multiply with exact integers and return size as decimal text.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| radices | radices. | List of finite numbers; at most 128 entries |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.size | The size value under the stated formula or text convention. |
{
"input": {
"radices": [
2,
3,
4
]
},
"output": {
"result": {
"size": "24"
}
}
}Limitations and assumptions
- An empty radix list has size one. No vectors are enumerated and no probability distribution is assumed.
- 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
Similar or alternative tools
- 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.
- Mixed Radix Digit Encoder
Encode bounded mixed-radix digits most-significant lane first into exact integer text; every radix is positive and every digit must fit.