e-num-roots-in-range
▸ function eNumRootsInRange
(p: number[][], a: number[], b: number[]): number
Defined in roots/descartes/expansion/e-num-roots-in-range.ts:38
Returns the exact number of distinct real roots in the open interval (a,b) of the given polynomial - subject to floating point underflow / overflow of intermediate calculations.
- From Wikipedia: "In the case of a non-square-free polynomial, if neither a nor b is a multiple root of p, then V(a) − V(b) is the number of distinct real roots of P".
example
const p = [[1], [1], [-64], [236], [-240]];
eNumRootsInRange(p,-20,-11); //=> 0
eNumRootsInRange(p,-11,-9); //=> 1
eNumRootsInRange(p,-11,3.5); //=> 3
eNumRootsInRange(p,-11,5); //=> 4
Parameters:
| Name | Type | Description |
|---|---|---|
p | number[][] | a polynomial 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 |
a | number[] | a lower bound given as a Shewchuk expansion |
b | number[] | an upper bound |
Returns: number