Description
Classify rational order at infinity from supplied degrees.
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.
Classify rational order at infinity from supplied degrees.
When to use this tool
Use Rational Function Infinity Order when checking the stated local order, leading behavior or limit convention.
How to use the tool and how it works
- Enter numeratorDegree, denominatorDegree. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read order, classification. Use the output convention below.
Classify rational order at infinity from supplied degrees. Require nonnegative whole degrees; order = denominatorDegree-numeratorDegree, positive labels zero, negative pole, zero finite-nonzero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| numeratorDegree | Numerator Degree | Required. Safe integer; minimum 0. |
| denominatorDegree | Denominator Degree | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| order | denominatorDegree-numeratorDegree; positive means a zero at infinity, negative means a pole. | Required. Safe integer. |
| classification | Classification | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"numeratorDegree": 2,
"denominatorDegree": 4
},
"output": {
"order": 2,
"classification": "zero"
}
}Limitations and assumptions
- This assumes nonzero actual leading coefficients and valid effective degrees; no polynomial normalization or limit magnitude is computed.
- 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 Leading Term Sign
Return rational leading sign at a supplied infinity direction.
- Rational Function Pole Order From Orders Tool
Compute rational function pole order from orders from explicit bounded inputs.