Description
Return one cube-root-of-unity phase power.
Polynomial transformations change coefficient scales or root coordinates under an explicit substitution. Translation, reflection and dilation use different signs, while a single complex phase does not apply a complete root-of-unity filter. The original function’s domain still matters after rational cancellation.
Return one cube-root-of-unity phase power.
When to use this tool
Use Cubic Root Unity Filter Term when checking the stated polynomial transformation or complex-coordinate term.
How to use the tool and how it works
- Enter exponent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read real, imaginary. Use the output convention below.
Return one cube-root-of-unity phase power. Require whole exponent; reduce modulo three, return 1+0i or -1/2 plus/minus sqrt(3)/2 i.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| exponent | Exponent | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| real | Real part of one cube-root-of-unity phase omega^exponent; not a complete filter output. | Required. Finite number. |
| imaginary | Imaginary | Required. Finite number. |
{
"input": {
"exponent": 3
},
"output": {
"real": 1,
"imaginary": 0
}
}Limitations and assumptions
- Negative powers wrap cyclically; this is one phase term, not a complete root-of-unity filter sum or polynomial root solve.
- 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 full transformed expression and explicit variable substitution for complete symbolic equivalence, filtering or root analysis.
References
Similar or alternative tools
- Polynomial Complex Conjugate Root Pair
Return a supplied conjugate root pair.
- Complex Conjugate Root Factor Coefficients
Return ascending monic quadratic coefficients for a supplied conjugate pair.