Description
Return translation removing a cubic quadratic term.
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 translation removing a cubic quadratic term.
When to use this tool
Use Depressed Cubic Shift Coordinate when checking the stated polynomial transformation or complex-coordinate term.
How to use the tool and how it works
- Enter a, b. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read translation. Use the output convention below.
Return translation removing a cubic quadratic term. Require a != 0; translation = -b/(3*a), interpreted as x = newVariable+translation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Finite number. |
| b | B | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| translation | -b/(3*a), used in x=t+translation for the supplied cubic coefficients. | Required. Finite number. |
{
"input": {
"a": 2,
"b": 12
},
"output": {
"translation": -2
}
}Limitations and assumptions
- This is one substitution coordinate, not the full depressed cubic, root solve or coefficient validation.
- 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 Affine Input Shift Root Coordinate
Transform a root coordinate under affine input substitution.
- Polynomial Coefficient Binomial Shift Term
Return one binomial-shift coefficient contribution.