Description
Return cubic pairwise root-product sum.
Polynomial coefficients encode powers in a chosen order, with zeros, multiplicities and leading terms carrying different meanings. Local coefficient identities and necessary divisibility conditions can be checked without finding every root or proving a proposed factorization. Floating-point comparisons use the exact supplied values unless an explicit tolerance is provided.
Return cubic pairwise root-product sum.
When to use this tool
Use Cubic Vieta Pairwise Root Sum when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter leading, linear. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read pairwiseSum. Use the output convention below.
Return cubic pairwise root-product sum. Require leading != 0; pairwiseSum = linear/leading.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leading | Leading | Required. Finite number. |
| linear | Linear | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| pairwiseSum | Pairwise Sum | Required. Finite number. |
{
"input": {
"leading": 2,
"linear": 12
},
"output": {
"pairwiseSum": 6
}
}Limitations and assumptions
- The linear input is the x coefficient of the cubic; roots, actual degree and the remaining coefficients are not solved or verified.
- 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 a complete symbolic or numerically appropriate polynomial method for root finding, full factorization and robust treatment of near-degenerate coefficients.
References
Similar or alternative tools
- Cubic Vieta Root Product Sign
Return cubic root product and sign.
- Quadratic Root Sum Scale Residual
Return scaled expected quadratic root sum and residual.