Discriminant Resultant Calculator
Compute exact degree-general integer polynomial discriminant from signed derivative resultant divided by leading coefficient; constant-first degree 1–12, no separate cubic/quartic aliases or real-root-count inference.
Description
A polynomial discriminant vanishes when the polynomial has a repeated root over the complex numbers.
A polynomial discriminant vanishes when the polynomial has a repeated root over the complex numbers. Its sign alone does not provide a general real-root count.1
Compute exact degree-general integer polynomial discriminant from signed derivative resultant divided by leading coefficient; constant-first degree 1–12, no separate cubic/quartic aliases or real-root-count inference.
When to use Discriminant Resultant Calculator
Use this tool to compute exact degree-general integer polynomial discriminant from signed derivative resultant divided by leading coefficient; constant-first degree 1–12, no separate cubic/quartic aliases or real-root-count inference.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Discriminant Resultant Calculator and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter coefficients using the field table and calculation rules, then run the tool.
- Read exactPolynomialDiscriminant, hasRepeatedComplexRoot. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| coefficients | Coefficients | list of number | Required |
Enter constant-first integer coefficients, magnitudes ≤one million, for effective degree 1–12. Trim high-degree zeros, compute the exact derivative resultant with BigInt and return a decimal discriminant string plus a zero-result repeated-root flag.
discriminant = (−1)^(n(n−1)/2) resultant(P,P′)/leading coefficient Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| exactPolynomialDiscriminant | Exact polynomial discriminant | string |
| hasRepeatedComplexRoot | Has repeated complex root | boolean |
{
"input": {
"coefficients": [
-1,
0,
1
]
},
"output": {
"exactPolynomialDiscriminant": "4",
"hasRepeatedComplexRoot": false
}
}Limitations and assumptions
Constant and zero polynomials are rejected. Roots and their locations are not solved.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Sylvester Resultant Calculator: Compute exact integer resultant by fraction-free Sylvester determinant for constant-first integer polynomials of degree ≤12; zero polynomial returns zero resultant. Nonzero constants have no common roots. For a complementary task, use Polynomial GCD Calculator: Exact polynomial GCD over rational coefficients from bounded integer input, normalized monic; zero result is ["0"], rational coefficients are exact decimal numerator/denominator strings.
References
-
Discriminant Resultant Calculator — tool.io
Similar or alternative tools
- Sylvester Resultant Calculator
Compute exact integer resultant by fraction-free Sylvester determinant for constant-first integer polynomials of degree ≤12; zero polynomial returns zero resultant. Nonzero constants have no common roots.
- Polynomial GCD Calculator
Exact polynomial GCD over rational coefficients from bounded integer input, normalized monic; zero result is ["0"], rational coefficients are exact decimal numerator/denominator strings.