Description
Return a linear-linear resultant.
Polynomial coefficients encode powers in a chosen order, with zeros, multiplicities and leading terms carrying different meanings. Local coefficient identities and necessary divisibility conditions can be checked without finding every root or proving a proposed factorization. Floating-point comparisons use the exact supplied values unless an explicit tolerance is provided.
Return a linear-linear resultant.
When to use this tool
Use Resultant Linear Linear Term when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter a, b, c, d. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read resultant. Use the output convention below.
Return a linear-linear resultant. Require a and c nonzero; resultant = a*d-b*c for a*x+b and c*x+d.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Finite number. |
| b | B | Required. Finite number. |
| c | C | Required. Finite number. |
| d | D | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| resultant | Resultant | Required. Finite number. |
{
"input": {
"a": 2,
"b": 3,
"c": 4,
"d": 5
},
"output": {
"resultant": -2
}
}Limitations and assumptions
- Exact zero indicates the algebraic shared-root condition under these inputs; no numerical tolerance, root solve or higher-degree resultant 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 a complete symbolic or numerically appropriate polynomial method for root finding, full factorization and robust treatment of near-degenerate coefficients.
References
Similar or alternative tools
- Polynomial Double Root Coefficient Constraint
Check exact quadratic double-root discriminant.
- Binomial Square Cross Term Tool
Calculate binomial square cross term from explicit caller-supplied inputs.