Description
Return the coefficients obtained by composing a supplied affine recurrence twice.
A sequence rule specifies how terms relate. Checking one transition, advancing a recurrence, and bounding an infinite tail answer different questions. A calculation from supplied coefficients assumes that rule; it does not infer it from observations.
Return the coefficients obtained by composing a supplied affine recurrence twice.
When to use this tool
Use it for affine recurrence two step constant when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter multiplier, offset. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read twoStepMultiplier, twoStepOffset. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Compose x -> multiplier*x+offset twice and return twoStepMultiplier = multiplier squared and twoStepOffset = offset*(multiplier+1).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| multiplier | Multiplier | Required. Finite number. |
| offset | Offset | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| twoStepMultiplier | Two Step Multiplier | Required. Finite number. |
| twoStepOffset | Two Step Offset | Required. Finite number. |
{
"input": {
"multiplier": 2,
"offset": 3
},
"output": {
"twoStepMultiplier": 4,
"twoStepOffset": 9
}
}Limitations and assumptions
- This returns coefficients of the composed affine rule rather than evaluating a state. No stability or convergence guarantee follows from the coefficient calculation.
- The field tables describe structural bounds; the mechanics also state cross-field requirements. Malformed input shapes, disallowed keys, and invalid domains cause input errors. Results must remain finite and within the declared output contract. A successful false flag or zero placeholder is distinct from an error.
- Numeric arithmetic uses binary floating point. Exact comparisons have no hidden tolerance or decimal rounding; negative zero is exported as zero. Decimal-text integer operations retain the exactness specifically stated above.
Alternative or Complementary methods
For affine recurrence two step constant, check the source records and the supplied rule before comparing the result with another method. Use exact integer or symbolic arithmetic when a numerical equality is insufficient.
References
Similar or alternative tools
- Bounded Recurrence Zero Input Step
Advance one multiplicative recurrence step and clamp it to supplied bounds.
- Arithmetic Progression Modular Residue Step
Advance a numeric residue by a supplied difference under floating-point modulo arithmetic.