Description
Select the coefficient of a supplied monomial in the even- or odd-power part of a polynomial.
A polynomial separates into an even-power part and an odd-power part, whose sum is the original polynomial. Coefficients keep their power indices; choosing a part suppresses coefficients of the opposite parity rather than shifting their positions.
Select the coefficient of a supplied monomial in the even- or odd-power part of a polynomial.
When to use this tool
Use Polynomial Even Odd Part Coefficient when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter coefficient, exponent, requestedPart. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read selectedCoefficient. Use the output convention below.
Select the coefficient of a supplied monomial in the even- or odd-power part of a polynomial. Require a whole exponent in the declared range 0..255 and requestedPart even or odd. Build the monomial coefficient array at that exponent, partition it without reindexing powers, and select the requested parity coefficient; the opposite parity returns zero. The delegated validator additionally limits the constructed array to 128 entries, so execution currently accepts only exponents 0..127; values 128..255 fail despite the outer schema.1
The even/odd partition calculation retains original power positions and replaces the opposite parity by zeros. This tool constructs the single supplied monomial and returns its selected parity coefficient.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficient | Signed coefficient of the supplied single monomial. | Required. Finite number. |
| exponent | Outer schema allows whole exponents 0..255, but delegated execution accepts only 0..127; values 128..255 produce an input error. | Required. Safe integer; minimum 0; maximum 255. |
| requestedPart | Exactly even or odd; coefficients keep their original power positions. | Required. Text; one of "even", "odd"; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| selectedCoefficient | Supplied coefficient when exponent parity matches requestedPart; zero for the opposite parity. | Required. Finite number. |
{
"input": {
"coefficient": 7,
"exponent": 3,
"requestedPart": "odd"
},
"output": {
"selectedCoefficient": 7
}
}Limitations and assumptions
- This selects one coefficient, not a complete polynomial decomposition. The effective 0..127 execution range is narrower than the declared schema.
- 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.
- Polynomial Derivative Constant Coefficient
Return a polynomial derivative's constant coefficient.