Description
Calculate the signed unit-term balance in an alternating prefix.
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.
Calculate the signed unit-term balance in an alternating prefix.
When to use this tool
Use it for alternating prefix balance when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter length, firstPositive. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read balance. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Return zero for an even alternating prefix length and plus or minus one for an odd length according to firstPositive. Length must be a nonnegative safe integer.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| length | Length | Required. Safe integer; minimum 0. |
| firstPositive | First Positive | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| balance | Balance | Required. Safe integer. |
{
"input": {
"length": 5,
"firstPositive": true
},
"output": {
"balance": 1
}
}Limitations and assumptions
- The result is the balance of unit signs, not the sum of arbitrarily sized alternating terms. No sequence values are supplied or generated.
- 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 alternating prefix balance, 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
- Alternating Series Next Term Bound
Form a one-sided next-term enclosure for a supplied alternating-series partial sum.
- Affine Recurrence Two Step Constant
Return the coefficients obtained by composing a supplied affine recurrence twice.