Description
Return leading coefficient and effective degree after shared normalization.
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 leading coefficient and effective degree after shared normalization.
When to use this tool
Use Algebra: Polynomial Leading Nonzero Coefficient when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter coefficients. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return leading coefficient and effective degree after shared normalization. The shared helper normalizes the supplied coefficient array, then this tool reads its final coefficient and degree, using degree -1 for the zero polynomial.1
The shared coefficient normalizer removes exact high-power zeros under ascending-power order and preserves the zero polynomial as [0]. This tool reads the normalized last entry and length to report the leading coefficient and local degree convention.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficients | Ascending-power coefficients; only exact trailing high-power zeros are removed. | Required. Array of finite number. Implementation limit: 128 items. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the returned operation-specific members listed below. | Required. Object. |
| result.leadingCoefficient | Leading Coefficient | Calculated result member: number. |
| result.degree | Normalized coefficient length minus one; the preserved [0] zero polynomial reports degree -1. | Calculated result member: number. |
{
"input": {
"coefficients": [
1,
2,
0
]
},
"output": {
"result": {
"leadingCoefficient": 2,
"degree": 1
}
}
}Limitations and assumptions
- The coefficient-order and normalization convention follow the shared helper; no root solving, tolerance or symbolic simplification is performed.
- Outputs are nested inside result. 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
- Algebra: Polynomial Effective Degree Tolerance
Return effective ascending-polynomial degree under a supplied tolerance.
- Polynomial Root Zero Multiplicity From Prefix
Return zero-root multiplicity from ascending coefficients.