Description
Return determinant=previous*next-current² for three supplied terms.
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 determinant=previous*next-current² for three supplied terms.
When to use this tool
Use Second Order Recurrence State Determinant 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 previous, current, next. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read determinant. Use the output convention below.
Return determinant=previous*next-current² for three supplied terms.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| previous | Previous | Required. Finite number. |
| current | Current | Required. Finite number. |
| next | Next | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| determinant | Determinant | Required. Finite number. |
{
"input": {
"previous": 1,
"current": 2,
"next": 3
},
"output": {
"determinant": -1
}
}Limitations and assumptions
- This is a local algebraic term. Zero does not establish a complete recurrence, nonzero significance, or a global sequence property, and cancellation can affect near-zero results.
- 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
- Second Order Recurrence Characteristic Product
For a_n = firstCoefficient*a_(n-1)+secondCoefficient*a_(n-2), return characteristic-root sum and product.
- Lucas Recurrence One State Update
Parse current, previous, p, and q as bounded exact decimal integers and return next=p*current-q*previous as decimal text.