Description
Return a Schwarzian expression from supplied derivatives.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Return a Schwarzian expression from supplied derivatives.
When to use this tool
Use Scalar Schwarzian From Derivatives when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter first, second, third. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read schwarzian. Use the output convention below.
Return a Schwarzian expression from supplied derivatives. Require first != 0; schwarzian = third/first-(3/2)*(second/first)².1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number. |
| second | Second | Required. Finite number. |
| third | Third | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| schwarzian | Schwarzian | Required. Finite number. |
{
"input": {
"first": 2,
"second": 4,
"third": 6
},
"output": {
"schwarzian": -3
}
}Limitations and assumptions
- Derivatives must come from the same sufficiently differentiable function and variable; no function or analytic property is verified.
- 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
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
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