Expand description
Elimination: polynomials in several variables over the rationals, held sparse, and their resultants.
A resultant eliminates one variable from two polynomials: it vanishes exactly where they share a root in that variable (or both leading coefficients vanish). The norm of a polynomial whose coefficients are algebraic numbers is a tower of resultants against their minimal polynomials, and the projection of a cylindrical decomposition is built from them.
The resultant is computed by evaluation and interpolation. Specializing every other variable at a
point where neither polynomial’s leading coefficient in the eliminated variable vanishes commutes
with taking the resultant, and the resultant’s degree in each other variable is bounded by the
degrees of the two polynomials, so the resultant in v of polynomials in n variables is
interpolated, one variable at a time, from resultants of polynomials in one.
Structs§
- Polynomial
- A polynomial in variables numbered from 0, with rational coefficients. No coefficient is zero, so equal polynomials are structurally equal.