Index Permutation Composition
Compose index permutations by applying first then second to each index; composition convention is explicit and operand lengths must agree.
Description
Compose index permutations by applying first then second to each index; composition convention is explicit and operand lengths must agree.
Permutation composition needs an explicit direction because reversing the order can change the result.
When to use this tool
Compose index permutations by applying first then second to each index; composition convention is explicit and operand lengths must agree.
- Prepare the supplied first, second 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 first, second. 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.permutation. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate equal-size permutations and return second[first[j]] for every index j: apply first, then second.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| first | first. | List of finite numbers; at most 128 entries |
| second | second. | List of finite numbers; at most 128 entries |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.permutation | The permutation list in the ordering and representation described above. |
{
"input": {
"first": [
2,
0,
1
],
"second": [
1,
0,
2
]
},
"output": {
"result": {
"permutation": [
2,
1,
0
]
}
}
}Limitations and assumptions
- Both inputs map indexes to images. This convention must be retained when comparing with libraries that use a different composition or reorder-array convention.
- Except in the diagnostic validator, a permutation must contain each integer from zero through length minus one exactly once. Lists contain at most 128 entries.
- 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
Keep the index-to-image convention and composition direction explicit. A rank, cycle table, reorder-index list and inverse map encode different operations even when their entries are all integers.
References
Similar or alternative tools
- Index Permutation Cycle Table
Decompose an index permutation into disjoint cycles, including fixed points and starting each cycle at its smallest unseen index.
- Index Permutation Fixed Points
List all fixed input indexes of a validated complete permutation in ascending original order.