Description
Find an alternating sequence's sign relative to a supplied reference index.
Sequence calculations depend on the reference index, common difference or ratio, and whether a domain uses exact integers or real-valued arithmetic. Alternation depends on index parity; modular arithmetic chooses a representative in a fixed residue interval. A supplied local rule is not discovered from data and need not establish a complete recurrence or prediction model.
Find an alternating sequence's sign relative to a supplied reference index.
When to use this tool
Use Alternating Sequence Sign At Index when you already have index, referenceIndex, referenceSign and need to find an alternating sequence's sign relative to a supplied reference index.
How to use the tool and how it works
- Enter index, referenceIndex, referenceSign. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sign. Use the output convention below.
Require signed safe whole indices and referenceSign exactly -1 or 1. Exact BigInt index-difference parity preserves the sign when even and negates it when odd.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| index | Index | Required. Safe integer. |
| referenceIndex | Reference Index | Required. Safe integer. |
| referenceSign | Exactly +1 or -1; phase reference for the alternating sign. | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sign | Sign | Required. Safe integer. |
{
"input": {
"index": 5,
"referenceIndex": 2,
"referenceSign": 1
},
"output": {
"sign": -1
}
}Limitations and assumptions
- This determines only a sign under an alternating model, not term magnitudes or a complete recurrence.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete sequence definition and initial conditions for recurrence analysis. Choose exact integer or rational arithmetic when large indices or exact terms matter; local reference shifts and residue operations do not discover a generating rule.
References
Similar or alternative tools
- Finite Sequence Endpoint Parity
Compare endpoint-index parity and calculate inclusive sequence length.
- Recurrence Term Modulus Step
Calculate one exact modular affine recurrence step.