Description
Return support absence and listing status for one variable.
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 support absence and listing status for one variable.
When to use this tool
Use Monomial Absent Variable Indicator when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter variables, exponents, requestedVariable. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read absentFromSupport, listed, exponent. Inspect absentFromSupport, listed before interpreting the associated values.
Return support absence and listing status for one variable. Require aligned unique variable names/nonnegative whole exponents; absentFromSupport means exponent zero, listed independently reports name membership, absent names return exponent zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| variables | Variables | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| exponents | Exponents | Required. Array of safe integer; maximum items 256. |
| requestedVariable | Requested Variable | Required. Text; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| absentFromSupport | True for an unlisted variable or an explicitly listed zero exponent. | Required. Boolean. |
| listed | Listed | Required. Boolean. |
| exponent | Exponent | Required. Safe integer. |
{
"input": {
"variables": [
"x",
"y"
],
"exponents": [
2,
0
],
"requestedVariable": "y"
},
"output": {
"absentFromSupport": true,
"listed": true,
"exponent": 0
}
}Limitations and assumptions
- A listed zero-power variable is still absent from support; no polynomial parsing, coefficient or semantic variable resolution is performed.
- 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.
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.
- Algebra: Monomial Variable Partial Term
Return one formal monomial partial derivative.