Description
Return mirror=length-1-index and fixed when it equals index.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Return mirror=length-1-index and fixed when it equals index.
When to use this tool
Use Sequence Symmetric Index Pair Map when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter length, index. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read mirror, fixed. Inspect fixed before interpreting the associated values.
Return mirror=length-1-index and fixed when it equals index. Require positive integer length and a bounded zero-based index.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| length | Length | Required. Safe integer; minimum 1. |
| index | Zero-based index unless the mechanics explicitly state otherwise. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| mirror | Zero-based reversal partner. | Required. Safe integer. |
| fixed | Fixed | Required. Boolean. |
{
"input": {
"length": 5,
"index": 1
},
"output": {
"mirror": 3,
"fixed": false
}
}Limitations and assumptions
- This is reversal-index mapping, not reversal of actual data. Only an odd-length list has a fixed central position, and no external indexing convention is inferred.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Recurrence Companion State Index Map
Return shiftEntry one only for row>0 and column=row-1, and coefficientRow for row zero.
- Sequence: Periodic Index Quotient Remainder
Decompose a signed sequence index into floor quotient and nonnegative within-period phase, retaining negative cycle numbers.