Description
Return sign of a product from bases and exponent parities.
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 sign of a product from bases and exponent parities.
When to use this tool
Use Monomial Sign From Exponent Parities when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter bases, exponents. 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 sign. Use the output convention below.
Return sign of a product from bases and exponent parities. Require aligned bases/nonnegative whole exponents; ignore zero exponents, any zero base with positive exponent makes sign zero, negative bases flip sign for odd powers.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| bases | Bases | Required. Array of finite number; maximum items 256. |
| exponents | Exponents | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sign | Sign | Required. Safe integer. |
{
"input": {
"bases": [
-2,
3
],
"exponents": [
3,
2
]
},
"output": {
"sign": -1
}
}Limitations and assumptions
- Zero powers contribute identity, including a supplied zero base; no magnitude, coefficient or full polynomial is evaluated.
- 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
- Algebra: Monomial Square Exponent Parity Mask
Return exponent parity flags and a variable-part square predicate.
- Monomial Radical Exponent Divisibility
Check variable exponents for exact radical extraction.