Description
Map between ascending and descending coefficient indexes.
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.
Map between ascending and descending coefficient indexes.
When to use this tool
Use Polynomial Descending Ascending Index Pair when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter degree, index. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read oppositeIndex. Use the output convention below.
Map between ascending and descending coefficient indexes. Require whole degree 0..1e6 and index within [0,degree]; oppositeIndex = degree-index.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| degree | Degree | Required. Safe integer; minimum 0; maximum 1000000. |
| index | Index | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| oppositeIndex | Opposite Index | Required. Safe integer. |
{
"input": {
"degree": 5,
"index": 1
},
"output": {
"oppositeIndex": 4
}
}Limitations and assumptions
- This maps one index without checking an actual coefficient array or its effective polynomial degree.
- 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
- Palindromic Polynomial Middle Index
Return a polynomial coefficient array's middle-position convention.
- Reciprocal Polynomial Coefficient Index
Return reciprocal-polynomial coefficient position.