Description
Partition p(x) into same-width even-power and odd-power coefficient vectors, with p=even+odd under ascending-power convention.
A coefficient list here is constant-first: index j multiplies x to power j. Thus [1, 2, 3] represents 1 + 2x + 3x². Trailing list zeros are high-power zeros; stored length can differ from mathematical degree, and the zero polynomial needs a separate degree convention.
Partition p(x) into same-width even-power and odd-power coefficient vectors, with p=even+odd under ascending-power convention.
When to use this tool
Use this tool to partition p(x) into same-width even-power and odd-power coefficient vectors, with p=even+odd under ascending-power convention.
How to use the tool and how it works
- Enter coefficients using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.even, result.odd. Use the ordering, boundary rules and absence conditions described below.
Return two coefficient lists of the original length, zeroing odd powers in even and even powers in odd.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficients | Nonempty coefficients in ascending power order [constant, x, x², ...]. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.even | Original-length list retaining even-power coefficients and zeroing odd powers. |
| result.odd | Original-length list retaining odd-power coefficients and zeroing even powers. |
{
"input": {
"coefficients": [
1,
2,
3
]
},
"output": {
"result": {
"even": [
1,
0,
3
],
"odd": [
0,
2,
0
]
}
}
}Limitations and assumptions
- Powers remain at their original indexes; the lists are not compacted or degree-normalized.
- Coefficient lists use ascending powers and ordinary floating-point arithmetic. Nonempty input is required; individual operations impose tighter size limits. The tool does not attach or check physical units for x and its coefficients.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Check coefficient order before importing data from another algebra library. Use separate root-finding or symbolic algebra methods when an operation requires more than the stated coefficient transformation.
References
Similar or alternative tools
- Polynomial Antiderivative Coefficient List
Integrate ascending-power polynomial coefficients with an explicitly supplied integration constant; bounded number arithmetic, no symbolic rational simplification.
- Polynomial Coefficient Convolution Product
Multiply two ascending-power polynomial coefficient lists by convolution and normalize high-power exact zeros; no FFT or symbolic integer arithmetic.