Description
Return a variable-part divisibility witness.
A monomial combines a coefficient with variable exponents. Ordinary nonnegative exponents and signed Laurent exponents have different domains; exponent-vector divisibility and greatest-common-factor rules describe the variable part unless coefficients are explicitly included. Zero coefficients and absent variables need separate flags.
Return a variable-part divisibility witness.
When to use this tool
Use Algebra: Monomial Divisibility Witness when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter divisorExponents, dividendExponents. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return a variable-part divisibility witness. Require aligned exponent vectors whole 0..1e6; firstFailureIndex locates the first divisor exponent greater than dividend exponent, divides means no failure and index -1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| divisorExponents | Divisor Exponents | Required. Array of finite number. Implementation limit: 128 items. |
| dividendExponents | Dividend Exponents | Required. Array of finite number. Implementation limit: 128 items. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the returned operation-specific members listed below. | Required. Object. |
| result.divides | Divides | Calculated result member: boolean. |
| result.firstFailureIndex | Zero-based first variable with divisor exponent greater than dividend, or -1 when divides=true. | Calculated result member: number. |
{
"input": {
"divisorExponents": [
2,
1
],
"dividendExponents": [
3,
0
]
},
"output": {
"result": {
"divides": false,
"firstFailureIndex": 1
}
}
}Limitations and assumptions
- Empty aligned vectors pass; coefficients and domain restrictions are not checked, so this is not arbitrary polynomial divisibility.
- Outputs are nested inside result. 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 the complete coefficient domain and variable assumptions for symbolic simplification, full monomial divisibility or algebraic-domain conclusions.
References
Similar or alternative tools
- Monomial Radical Exponent Divisibility
Check variable exponents for exact radical extraction.
- Algebra: Monomial Gcd Exponent Vector
Return variable-part monomial GCD exponents.