Description
Return one formal monomial partial derivative.
A monomial combines a coefficient with variable exponents. Ordinary nonnegative exponents and signed Laurent exponents have different domains; exponent-vector divisibility and greatest-common-factor rules describe the variable part unless coefficients are explicitly included. Zero coefficients and absent variables need separate flags.
Return one formal monomial partial derivative.
When to use this tool
Use Algebra: Monomial Variable Partial Term when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter coefficient, exponents, variableIndex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return one formal monomial partial derivative. Require exponents whole 0..1e6 and valid variableIndex; coefficient multiplies selected power, decrement that exponent only when power > 0, zero flags absent power or zero original coefficient.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficient | Coefficient | Required. Finite number. |
| exponents | Exponents | Required. Array of finite number. Implementation limit: 128 items. |
| variableIndex | Variable Index | Required. Safe integer. Calculation range: 0 through exponents.length - 1, inclusive. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the returned operation-specific members listed below. | Required. Object. |
| result.coefficient | Coefficient | Calculated result member: number. |
| result.exponents | Exponents | Calculated result member: array. |
| result.zero | True when differentiated exponent or supplied coefficient is zero; inspect before using returned exponent-vector placeholder. | Calculated result member: boolean. |
{
"input": {
"coefficient": 3,
"exponents": [
2,
1
],
"variableIndex": 0
},
"output": {
"result": {
"coefficient": 6,
"exponents": [
1,
1
],
"zero": false
}
}
}Limitations and assumptions
- When selected power is zero, the original exponent vector is retained as an encoding placeholder; inspect zero before interpreting the returned term.
- Outputs are nested inside result. 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 complete coefficient domain and variable assumptions for symbolic simplification, full monomial divisibility or algebraic-domain conclusions.
References
Similar or alternative tools
- Algebra: Monomial Variable Degree Label
Return a requested variable's supplied exponent.
- Monomial Absent Variable Indicator
Return support absence and listing status for one variable.