Description
Fill an ascending array of length maximumDegree + 1 with zeros and assign the supplied coefficients.
A polynomial or rational expression has coefficients, an evaluation rule, and a domain. An algebraically reduced rational form can extend across a removed hole, so evaluating that form does not by itself restore the original expression's domain.
Fill an ascending array of length maximumDegree + 1 with zeros and assign the supplied coefficients.
When to use this tool
Use Polynomial Missing Degree Padding when you need one bounded polynomial representation or rational-evaluation component.
How to use the tool and how it works
- Enter degrees, coefficients, maximumDegree. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ascendingCoefficients. Use the output convention below.
Require aligned unique degrees and coefficients with each degree within maximumDegree 0-255. Fill an ascending array of length maximumDegree + 1 with zeros and assign the supplied coefficients.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| degrees | Degrees | Required. Array of safe integer; maximum items 256. |
| coefficients | Coefficients | Required. Array of finite number; maximum items 256. |
| maximumDegree | Maximum Degree | Required. Safe integer; minimum 0; maximum 255. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ascendingCoefficients | Ascending Coefficients | Required. Array of finite number; maximum items 256. |
{
"input": {
"degrees": [
3,
0,
1
],
"coefficients": [
2,
7,
-4
],
"maximumDegree": 4
},
"output": {
"ascendingCoefficients": [
7,
-4,
0,
2,
0
]
}
}Limitations and assumptions
- This pads missing degrees without combining duplicates, normalizing leading coefficients, inferring degree, or simplifying a polynomial.
- 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
Track the original domain and verify any claimed cancellation or equivalence before using the reduced expression.
References
Similar or alternative tools
- Polynomial Coefficient Decimal Scale Label
Parse a signed decimal coefficient token with optional fraction and exponent.
- Recurrence Step Boundary Label
Classify requestedIndex before initialIndex as before-sequence, within the next order positions as initial-condition, and later as recurrence-step.