Description
Return one affine fixed-point denominator and degeneracy flag.
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 affine fixed-point denominator and degeneracy flag.
When to use this tool
Use Affine Fixed Point Denominator when checking the stated polynomial transformation or complex-coordinate term.
How to use the tool and how it works
- Enter coefficient. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read denominator, degenerate. Inspect degenerate before interpreting the associated values.
Return one affine fixed-point denominator and degeneracy flag. denominator = 1-coefficient, degenerate means coefficient exactly one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficient | Coefficient | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| denominator | Denominator | Required. Finite number. |
| degenerate | coefficient=1; without an intercept this tool cannot distinguish no fixed point from every point fixed. | Required. Boolean. |
{
"input": {
"coefficient": 0.8
},
"output": {
"denominator": 0.19999999999999996,
"degenerate": false
}
}Limitations and assumptions
- The constant term is absent, so a degenerate flag cannot distinguish no fixed points from every point being fixed.
- 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
- Affine Inverse Constant Coefficient
Return constant coefficient of an affine inverse.
- Polynomial Affine Input Shift Root Coordinate
Transform a root coordinate under affine input substitution.