Description
Return rational zero order and a pole flag.
Local polynomial and rational-function behavior depends on the order of zeros and poles and on the sign of the leading term. Canceling equal local orders differs from evaluating an undefined original expression; a zero placeholder for a pole must be read with its finite/defined flag.
Return rational zero order and a pole flag.
When to use this tool
Use Rational Function Zero Order From Orders when checking the stated local order, leading behavior or limit convention.
How to use the tool and how it works
- Enter numeratorOrder, denominatorOrder. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read zeroOrder, pole. Inspect pole before interpreting the associated values.
Return rational zero order and a pole flag. Require nonnegative whole numerator/denominator orders; zeroOrder = max(0,numerator-denominator), pole means denominator order is larger.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| numeratorOrder | Numerator Order | Required. Safe integer; minimum 0. |
| denominatorOrder | Denominator Order | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| zeroOrder | Zero Order | Required. Safe integer. |
| pole | Pole | Required. Boolean. |
{
"input": {
"numeratorOrder": 3,
"denominatorOrder": 1
},
"output": {
"zeroOrder": 2,
"pole": false
}
}Limitations and assumptions
- Orders are supplied local vanishing orders; no polynomial factorization, coefficients, limit or complete singularity is independently 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
Use the complete function, original domain and an appropriate symbolic limit or asymptotic analysis for a full mathematical conclusion.
References
Similar or alternative tools
- Rational Function Pole Order From Orders
Return rational pole order and removable flag.
- Rational Pole Removal Limit Coefficient
Return a rational-function local limit from supplied orders and leading terms.