flo-poly/src/basic/expansion/e-subtract.ts

A practical, root-focused JavaScript polynomial utility library.

import { eDiff as eDiff_ } from "big-float-ts";
import { eRemoveLeadingZeros as eRemoveLeadingZeros_ } from "./e-remove-leading-zeros.js";

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


/** 
 * Returns the exact result (bar underflow / overflow) of subtracting the 
 * second polynomial from the first (both with coefficients given as Shewchuk 
 * floating point expansions); (p1 - p2).
 * 
 * @param p1 minuend; the polynomial from which will be subtracted; a polynomial 
 * with coefficients given densely as Shewchuk floating point expansions
 * from highest to lowest power, e.g. `[[5],[-3],[0]]` represents the 
 * polynomial `5x^2 - 3x`
 * @param p2 subtrahend; the polynomial that will be subtracted
 * 
 * @example
 * ```typescript
 * eSubtract([[2],[3]],[[4],[4]]); //=> [[-2], [-1]]
 * ```
 * 
 * @doc
 */
function eSubtract(p1: number[][], p2: number[][]): number[][] {
	// Initialize result array  
	const d1 = p1.length-1;
	const d2 = p2.length-1;
	const Δd = d1 - d2;
	
	const Δd1 = Δd < 0 ? +Δd : 0;
	const Δd2 = Δd > 0 ? -Δd : 0;
	
	const d = Math.max(d1, d2);
	
	// Add coefficients
	const result = [];
	for (let i=0; i<d+1; i++) {
		const c1 = p1[i+Δd1] || [0];
		const c2 = p2[i+Δd2] || [0];
		result.push(eDiff(c1, c2));  
	}
	
	// Ensure the result is a valid polynomial representation
	return eRemoveLeadingZeros(result);
}


export { eSubtract }