Description
Return exponent parity flags and a variable-part square predicate.
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 exponent parity flags and a variable-part square predicate.
When to use this tool
Use Algebra: Monomial Square Exponent Parity Mask when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter exponents. 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 exponent parity flags and a variable-part square predicate. Require exponents whole 0..1e6; oddExponentMask flags odd entries, squareMonomial requires every exponent even.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| exponents | 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.oddExponentMask | Odd Exponent Mask | Calculated result member: array. |
| result.squareMonomial | All supplied variable exponents are even; numerical coefficient squarehood is not tested. | Calculated result member: boolean. |
{
"input": {
"exponents": [
2,
3
]
},
"output": {
"result": {
"oddExponentMask": [
false,
true
],
"squareMonomial": false
}
}
}Limitations and assumptions
- Empty input passes; coefficient sign/perfect-square status is not checked, so the flag concerns only the supplied variable part.
- 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 Sign From Exponent Parities
Return sign of a product from bases and exponent parities.
- Monomial Radical Exponent Divisibility
Check variable exponents for exact radical extraction.