/*
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* Copyright 2007 ZXing authors
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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/*namespace com.google.zxing.common.reedsolomon {*/
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import AbstractGenericGF from './AbstractGenericGF';
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import System from '../../util/System';
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import IllegalArgumentException from '../../IllegalArgumentException';
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/**
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* <p>Represents a polynomial whose coefficients are elements of a GF.
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* Instances of this class are immutable.</p>
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*
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* <p>Much credit is due to William Rucklidge since portions of this code are an indirect
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* port of his C++ Reed-Solomon implementation.</p>
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*
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* @author Sean Owen
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*/
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export default class GenericGFPoly {
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/**
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* @param field the {@link GenericGF} instance representing the field to use
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* to perform computations
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* @param coefficients coefficients as ints representing elements of GF(size), arranged
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* from most significant (highest-power term) coefficient to least significant
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* @throws IllegalArgumentException if argument is null or empty,
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* or if leading coefficient is 0 and this is not a
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* constant polynomial (that is, it is not the monomial "0")
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*/
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constructor(field, coefficients) {
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if (coefficients.length === 0) {
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throw new IllegalArgumentException();
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}
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this.field = field;
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const coefficientsLength = coefficients.length;
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if (coefficientsLength > 1 && coefficients[0] === 0) {
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// Leading term must be non-zero for anything except the constant polynomial "0"
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let firstNonZero = 1;
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while (firstNonZero < coefficientsLength && coefficients[firstNonZero] === 0) {
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firstNonZero++;
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}
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if (firstNonZero === coefficientsLength) {
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this.coefficients = Int32Array.from([0]);
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}
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else {
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this.coefficients = new Int32Array(coefficientsLength - firstNonZero);
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System.arraycopy(coefficients, firstNonZero, this.coefficients, 0, this.coefficients.length);
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}
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}
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else {
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this.coefficients = coefficients;
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}
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}
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getCoefficients() {
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return this.coefficients;
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}
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/**
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* @return degree of this polynomial
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*/
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getDegree() {
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return this.coefficients.length - 1;
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}
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/**
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* @return true iff this polynomial is the monomial "0"
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*/
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isZero() {
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return this.coefficients[0] === 0;
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}
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/**
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* @return coefficient of x^degree term in this polynomial
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*/
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getCoefficient(degree /*int*/) {
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return this.coefficients[this.coefficients.length - 1 - degree];
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}
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/**
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* @return evaluation of this polynomial at a given point
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*/
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evaluateAt(a /*int*/) {
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if (a === 0) {
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// Just return the x^0 coefficient
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return this.getCoefficient(0);
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}
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const coefficients = this.coefficients;
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let result;
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if (a === 1) {
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// Just the sum of the coefficients
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result = 0;
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for (let i = 0, length = coefficients.length; i !== length; i++) {
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const coefficient = coefficients[i];
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result = AbstractGenericGF.addOrSubtract(result, coefficient);
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}
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return result;
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}
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result = coefficients[0];
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const size = coefficients.length;
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const field = this.field;
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for (let i = 1; i < size; i++) {
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result = AbstractGenericGF.addOrSubtract(field.multiply(a, result), coefficients[i]);
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}
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return result;
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}
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addOrSubtract(other) {
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if (!this.field.equals(other.field)) {
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throw new IllegalArgumentException('GenericGFPolys do not have same GenericGF field');
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}
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if (this.isZero()) {
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return other;
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}
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if (other.isZero()) {
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return this;
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}
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let smallerCoefficients = this.coefficients;
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let largerCoefficients = other.coefficients;
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if (smallerCoefficients.length > largerCoefficients.length) {
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const temp = smallerCoefficients;
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smallerCoefficients = largerCoefficients;
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largerCoefficients = temp;
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}
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let sumDiff = new Int32Array(largerCoefficients.length);
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const lengthDiff = largerCoefficients.length - smallerCoefficients.length;
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// Copy high-order terms only found in higher-degree polynomial's coefficients
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System.arraycopy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
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for (let i = lengthDiff; i < largerCoefficients.length; i++) {
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sumDiff[i] = AbstractGenericGF.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
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}
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return new GenericGFPoly(this.field, sumDiff);
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}
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multiply(other) {
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if (!this.field.equals(other.field)) {
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throw new IllegalArgumentException('GenericGFPolys do not have same GenericGF field');
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}
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if (this.isZero() || other.isZero()) {
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return this.field.getZero();
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}
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const aCoefficients = this.coefficients;
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const aLength = aCoefficients.length;
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const bCoefficients = other.coefficients;
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const bLength = bCoefficients.length;
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const product = new Int32Array(aLength + bLength - 1);
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const field = this.field;
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for (let i = 0; i < aLength; i++) {
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const aCoeff = aCoefficients[i];
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for (let j = 0; j < bLength; j++) {
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product[i + j] = AbstractGenericGF.addOrSubtract(product[i + j], field.multiply(aCoeff, bCoefficients[j]));
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}
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}
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return new GenericGFPoly(field, product);
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}
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multiplyScalar(scalar /*int*/) {
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if (scalar === 0) {
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return this.field.getZero();
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}
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if (scalar === 1) {
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return this;
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}
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const size = this.coefficients.length;
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const field = this.field;
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const product = new Int32Array(size);
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const coefficients = this.coefficients;
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for (let i = 0; i < size; i++) {
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product[i] = field.multiply(coefficients[i], scalar);
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}
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return new GenericGFPoly(field, product);
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}
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multiplyByMonomial(degree /*int*/, coefficient /*int*/) {
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if (degree < 0) {
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throw new IllegalArgumentException();
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}
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if (coefficient === 0) {
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return this.field.getZero();
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}
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const coefficients = this.coefficients;
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const size = coefficients.length;
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const product = new Int32Array(size + degree);
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const field = this.field;
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for (let i = 0; i < size; i++) {
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product[i] = field.multiply(coefficients[i], coefficient);
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}
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return new GenericGFPoly(field, product);
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}
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divide(other) {
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if (!this.field.equals(other.field)) {
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throw new IllegalArgumentException('GenericGFPolys do not have same GenericGF field');
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}
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if (other.isZero()) {
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throw new IllegalArgumentException('Divide by 0');
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}
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const field = this.field;
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let quotient = field.getZero();
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let remainder = this;
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const denominatorLeadingTerm = other.getCoefficient(other.getDegree());
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const inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
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while (remainder.getDegree() >= other.getDegree() && !remainder.isZero()) {
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const degreeDifference = remainder.getDegree() - other.getDegree();
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const scale = field.multiply(remainder.getCoefficient(remainder.getDegree()), inverseDenominatorLeadingTerm);
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const term = other.multiplyByMonomial(degreeDifference, scale);
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const iterationQuotient = field.buildMonomial(degreeDifference, scale);
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quotient = quotient.addOrSubtract(iterationQuotient);
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remainder = remainder.addOrSubtract(term);
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}
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return [quotient, remainder];
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}
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/*@Override*/
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toString() {
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let result = '';
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for (let degree = this.getDegree(); degree >= 0; degree--) {
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let coefficient = this.getCoefficient(degree);
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if (coefficient !== 0) {
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if (coefficient < 0) {
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result += ' - ';
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coefficient = -coefficient;
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}
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else {
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if (result.length > 0) {
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result += ' + ';
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}
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}
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if (degree === 0 || coefficient !== 1) {
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const alphaPower = this.field.log(coefficient);
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if (alphaPower === 0) {
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result += '1';
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}
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else if (alphaPower === 1) {
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result += 'a';
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}
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else {
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result += 'a^';
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result += alphaPower;
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}
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}
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if (degree !== 0) {
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if (degree === 1) {
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result += 'x';
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}
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else {
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result += 'x^';
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result += degree;
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}
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}
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}
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}
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return result;
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}
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}
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