Description
Return zero-root multiplicity from ascending coefficients.
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 zero-root multiplicity from ascending coefficients.
When to use this tool
Use Polynomial Root Zero Multiplicity From Prefix when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter ascendingCoefficients. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read multiplicity, identicallyZero. Inspect identicallyZero before interpreting the associated values.
Return zero-root multiplicity from ascending coefficients. Require nonempty array; multiplicity is the first nonzero coefficient index, or zero placeholder with identicallyZero true when all zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ascendingCoefficients | Ascending Coefficients | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| multiplicity | Leading ascending-power zero count when nonzero polynomial; zero placeholder for the identically zero polynomial. | Required. Safe integer. |
| identicallyZero | Identically Zero | Required. Boolean. |
{
"input": {
"ascendingCoefficients": [
0,
0,
3,
2
]
},
"output": {
"multiplicity": 2,
"identicallyZero": false
}
}Limitations and assumptions
- An identically zero polynomial has no finite zero-root multiplicity here; no tolerance, other roots or factorization is computed.
- 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
- Polynomial Zero Coefficient Run
Return the exact-zero coefficient run from a supplied start.
- Algebra: Polynomial Leading Nonzero Coefficient
Return leading coefficient and effective degree after shared normalization.