Root
A polynomial root is a value in the relevant number system at which the polynomial evaluates to zero.
Geometry for Programmers
A polynomial root is a value of the variable at which the polynomial evaluates to zero.
- How it is used
- Locates zero values of polynomial equations and identifies x-axis intersections, extrema, and interpolation oscillations.
- How deep it goes
- Defines roots geometrically, classifies root counts by degree, and links derivative roots to extrema; it stops short of root-solving algorithms.
- Examples
- Uses factored cubics, linear graphs, quadratic parabolas, cubic graphs, and interpolating polynomials with increasing oscillations.
- What you can do after
- Evaluate polynomial graphs by identifying their roots, possible root counts, and relationships between derivative roots and extrema.
Elliptic Curve Cryptography for Developers
A polynomial root is a value in the relevant algebraic structure that satisfies a polynomial equation by making it equal to zero.
- How it is used
- Uses roots to factor Hilbert class polynomials modulo a prime and construct finite-field extension elements.
- How deep it goes
- Explains direct linear and quadratic solutions plus recursive higher-degree splitting, while deferring complete implementation details.
- Examples
- Uses Hilbert class polynomials, zero-root division, linear and quadratic equations, and x² + 13x + 1 modulo 1187.
- What you can do after
- Apply modular factorization procedures to isolate roots and represent extension-field elements through irreducible polynomial equations.
Read how Elliptic Curve Cryptography for Developers explains root →
Related concepts
- Hilbert class polynomialproduced by · A Hilbert class polynomial is a polynomial whose roots are j-invariants associated with elliptic curves having complex multiplication by a specified imaginary quadratic order.
- polynomial functionproduced by · A polynomial function is a function expressible as a finite sum of constant multiples of nonnegative integer powers of one or more variables.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.