Description
Normalize a descending coefficient array to monic form.
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.
Normalize a descending coefficient array to monic form.
When to use this tool
Use Monic Polynomial Coefficient Scale 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 coefficients. Use the output convention below.
Normalize a descending coefficient array to monic form. Require nonempty coefficients and first coefficient nonzero; divide every coefficient by the first.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficients | Descending-power coefficient array; divide by its first, nonzero leading coefficient. | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coefficients | Descending-power coefficient array; divide by its first, nonzero leading coefficient. | Required. Array of finite number; maximum items 256. |
{
"input": {
"coefficients": [
2,
4,
6
]
},
"output": {
"coefficients": [
1,
2,
3
]
}
}Limitations and assumptions
- This helper treats the first entry as leading, unlike ascending-array helpers; no zero trimming, root solving or symbolic exact arithmetic is supplied.
- 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 Derivative Constant Coefficient
Return a polynomial derivative's constant coefficient.
- 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.