Description
Return effective ascending-polynomial degree under a supplied tolerance.
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 effective ascending-polynomial degree under a supplied tolerance.
When to use this tool
Use Algebra: Polynomial Effective Degree Tolerance when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter coefficients, tolerance. 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 effective ascending-polynomial degree under a supplied tolerance. Require nonempty coefficients and tolerance >= 0; remove high terms while abs(coefficient) <= tolerance, degree may reach -1, removedHighTerms counts omissions.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficients | Coefficients | Required. Array of finite number. Implementation limit: 128 items. |
| tolerance | Nonnegative absolute coefficient cutoff; magnitudes equal to the tolerance are removed. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the returned operation-specific members listed below. | Required. Object. |
| result.effectiveDegree | Highest remaining ascending-power index, or -1 if all coefficients are removed. | Calculated result member: number. |
| result.removedHighTerms | Removed High Terms | Calculated result member: number. |
{
"input": {
"coefficients": [
1,
2,
1e-8
],
"tolerance": 1e-7
},
"output": {
"result": {
"effectiveDegree": 1,
"removedHighTerms": 1
}
}
}Limitations and assumptions
- Tolerance is an absolute caller-selected cutoff, not symbolic zero or an approximation-error guarantee.
- 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
- Polynomial Even Odd Part Coefficient
Build the monomial coefficient array at that exponent, partition it without reindexing powers, and select the requested parity coefficient; the opposite parity returns zero.
- Algebra: Polynomial Horner Stage
Return one Horner accumulator stage.