Description
Check a rational-root denominator necessary condition.
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.
Check a rational-root denominator necessary condition.
When to use this tool
Use Rational Root Denominator Divisibility when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter leading, denominator. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read divides. Inspect divides before interpreting the associated values.
Check a rational-root denominator necessary condition. Require nonzero whole leading and positive whole denominator; divides tests leading mod denominator == 0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leading | Leading | Required. Safe integer. |
| denominator | Denominator | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| divides | Whether the proposed denominator divides the leading integer coefficient; a necessary condition only, not a complete rational-root test. | Required. Boolean. |
{
"input": {
"leading": 12,
"denominator": 3
},
"output": {
"divides": true
}
}Limitations and assumptions
- This alone does not establish a root; candidate fractions must be reduced and the other rational-root conditions and polynomial evaluation remain separate.
- 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
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