flo-poly/src/euclidean-division-related/double/prem-sequence-subresultant.ts

A practical, root-focused JavaScript polynomial utility library.

import { ePremSequenceSubresultant as ePremSequenceSubresultant_ } from "../expansion/e-prem-sequence-subresultant.js";

// We *have* to do the below❗ The assignee is a getter❗ The assigned is a pure function❗ Otherwise code is too slow❗
const ePremSequenceSubresultant = ePremSequenceSubresultant_;


/**
 * Returns the subresultant pseudo remainder sequence of a/b with the resulting
 * polynomials given with coefficients as Shewchuk expansions.
 * 
 * * **precondition:** g !== [], i.e. unequal to the zero polynomial.
 * 
 * * Intermediate calculations are done in infinite precision up to
 * overlow (meaning integers can be represented *exactly* up to 
 * `2^1024 === 1797...(300 more digits)...37216`) and may 
 * thus not be applicable to very high degree polynomials (in which case it is 
 * better to use [[bPremSequenceSubresultant]])
 * 
 * * see [*The subresultant polynomial remainder sequence algorithm* by Ruiyuan (Ronnie) Chen, p.10](https://pdfs.semanticscholar.org/2e6b/95ba84e2160748ba8fc310cdc408fc9bbade.pdf)
 * 
 * @param f the polynomial a in the formula a = bq + r; the polynomial is given
 * with coefficients as a dense array of double precision floating point numbers 
 * from highest to lowest power, e.g. `[5,-3,0]` represents the 
 * polynomial `5x^2 - 3x`
 * @param g the polynomial b in the formula a = bq + r;
 * @param sturm if set to true then calculate a Sturm sequence instead
 * 
 * @doc
 */
function premSequenceSubresultant(
        f: number[], 
        g: number[], 
        sturm = false): number[][][] {

    return ePremSequenceSubresultant(
        f.map(c => [c]), 
        g.map(c => [c]), 
        sturm
    );
}


export { premSequenceSubresultant }