sturm-chain

▸ function sturmChain (p: number[]): number[][][]

Defined in euclidean-division-related/double/sturm-chain.ts:33

Returns the Sturm chain for the given polynomial using pseudo remainders with the resulting polynomials given with coefficients as Shewchuk expansions.

  • intermediate calculations use Shewchuk expansions and the final result is given as an array of polynomials with coefficients given densely as an array of Shewchuk expansions from highest to lowest power, e.g. [[5],[-3],[0]] represents the polynomial 5x^2 - 3x

  • see Sturm's Theorem

  • see Pseudo-remainder sequences

example

sturmChain([-3,4,2,-2]); //=> [[[-3],[4],[2],[-2]],[[-9],[8],[2]],[[-204],[138]],[[-1692]]]

Parameters:

NameTypeDescription
pnumber[]a polynomial with coefficients given densely as an array of double precision floating point numbers from highest to lowest power, e.g. [5,-3,0] represents the polynomial 5x^2 - 3x

Returns: number[][][]