Description
Return one binomial-shift coefficient contribution.
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 binomial-shift coefficient contribution.
When to use this tool
Use Polynomial Coefficient Binomial Shift Term when checking the stated polynomial transformation or complex-coordinate term.
How to use the tool and how it works
- Enter coefficient, sourcePower, targetPower, shift. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Return one binomial-shift coefficient contribution. Require whole sourcePower 0..128 and targetPower within it; compute C(source,target), contribution = coefficient*C*shift^(source-target).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficient | Coefficient | Required. Finite number. |
| sourcePower | Source Power | Required. Safe integer; minimum 0; maximum 128. |
| targetPower | Target Power | Required. Safe integer; minimum 0. |
| shift | Shift in x→x+shift; this is one binomial coefficient contribution, not the entire transformed coefficient. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | Contribution | Required. Finite number. |
{
"input": {
"coefficient": 2,
"sourcePower": 3,
"targetPower": 1,
"shift": 2
},
"output": {
"contribution": 24
}
}Limitations and assumptions
- This is one source monomial's contribution under x to x+shift; binomial arithmetic uses floating point and a complete transformed polynomial is not summed.
- 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 Affine Substitution Leading Coefficient
Return leading coefficient under affine input substitution.