Description
Return a polynomial coefficient array's middle-position convention.
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 a polynomial coefficient array's middle-position convention.
When to use this tool
Use Palindromic Polynomial Middle Index when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter degree. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read middleIndex, uniqueMiddle. Inspect uniqueMiddle before interpreting the associated values.
Return a polynomial coefficient array's middle-position convention. Require nonnegative whole degree; middleIndex = floor(degree/2), uniqueMiddle means even degree.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| degree | Degree | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| middleIndex | Middle Index | Required. Safe integer. |
| uniqueMiddle | True for even degree; palindromic coefficient symmetry is not checked. | Required. Boolean. |
{
"input": {
"degree": 6
},
"output": {
"middleIndex": 3,
"uniqueMiddle": true
}
}Limitations and assumptions
- For odd degree the output is the lower of two middle indexes; palindromic coefficients or an actual array are not checked.
- 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 Descending Ascending Index Pair
Map between ascending and descending coefficient indexes.
- Reciprocal Polynomial Coefficient Index
Return reciprocal-polynomial coefficient position.