1const chai = require("chai");
  2
  3const bigInt = require("../src/bigint.js");
  4const PolField = require("../src/polfield.js");
  5const ZqField = require("../src/zqfield");
  6
  7const assert = chai.assert;
  8
  9const r  = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
 10
 11describe("Polinomial field", () => {
 12    it("Should compute a multiplication", () => {
 13        const PF = new PolField(new ZqField(r));
 14
 15        const a = [bigInt(1), bigInt(2), bigInt(3)];
 16        const b = [bigInt(1), bigInt(2), bigInt(3)];
 17        const res = PF.mul(a,b);
 18
 19        assert(PF.equals(res, [bigInt(1), bigInt(4), bigInt(10), bigInt(12), bigInt(9)]));
 20    });
 21    it("Should compute a multiplication 2", () => {
 22        const PF = new PolField(new ZqField(r));
 23
 24        const a = [bigInt(5), bigInt(1)];
 25        const b = [bigInt(-5), bigInt(1)];
 26        const res = PF.mul(a,b);
 27
 28        assert(PF.equals(res, [bigInt(-25), bigInt(0), bigInt(1)]));
 29    });
 30    it("Should compute an addition", () => {
 31        const PF = new PolField(new ZqField(r));
 32
 33        const a = [bigInt(5), bigInt(1)];
 34        const b = [bigInt(-5), bigInt(1)];
 35        const res = PF.add(a,b);
 36
 37        assert(PF.equals(res, [bigInt(0), bigInt(2)]));
 38    });
 39    it("Should compute a substraction", () => {
 40        const PF = new PolField(new ZqField(r));
 41
 42        const a = [bigInt(5), bigInt(3), bigInt(4)];
 43        const b = [bigInt(5), bigInt(1)];
 44        const res = PF.sub(a,b);
 45
 46        assert(PF.equals(res, [bigInt(0), bigInt(2), bigInt(4)]));
 47    });
 48    it("Should compute reciprocal", () => {
 49        const PF = new PolField(new ZqField(r));
 50
 51        const a = [bigInt(4), bigInt(1), bigInt(-3), bigInt(-1), bigInt(2),bigInt(1), bigInt(-1), bigInt(1)];
 52        const res = PF._reciprocal(a, 3, 0);
 53
 54        assert(PF.equals(res, [bigInt(12), bigInt(15), bigInt(3), bigInt(-4), bigInt(-3), bigInt(0), bigInt(1), bigInt(1)]));
 55    });
 56    it("Should div2", () => {
 57        const PF = new PolField(new ZqField(r));
 58
 59        // x^6
 60        const a = [bigInt(0), bigInt(0), bigInt(0), bigInt(0), bigInt(0),bigInt(0), bigInt(1)];
 61        // x^5
 62        const b = [bigInt(0), bigInt(0), bigInt(0), bigInt(0), bigInt(0), bigInt(1)];
 63
 64        const res = PF._div2(6, b);
 65        assert(PF.equals(res, [bigInt(0), bigInt(1)]));
 66
 67        const res2 = PF.div(a,b);
 68        assert(PF.equals(res2, [bigInt(0), bigInt(1)]));
 69    });
 70    it("Should div", () => {
 71        const PF = new PolField(new ZqField(r));
 72
 73        const a = [bigInt(1), bigInt(2), bigInt(3), bigInt(4), bigInt(5),bigInt(6), bigInt(7)];
 74        const b = [bigInt(8), bigInt(9), bigInt(10), bigInt(11), bigInt(12), bigInt(13)];
 75
 76        const c = PF.mul(a,b);
 77        const d = PF.div(c,b);
 78
 79        assert(PF.equals(a, d));
 80    });
 81
 82    it("Should div big/small", () => {
 83        const PF = new PolField(new ZqField(r));
 84
 85        const a = [bigInt(1), bigInt(2), bigInt(3), bigInt(4), bigInt(5),bigInt(6), bigInt(7)];
 86        const b = [bigInt(8), bigInt(9)];
 87
 88        const c = PF.mul(a,b);
 89        const d = PF.div(c,b);
 90
 91        assert(PF.equals(a, d));
 92    });
 93    it("Should div random big", () => {
 94        const PF = new PolField(new ZqField(r));
 95
 96        const a = [];
 97        const b = [];
 98        for (let i=0; i<1000; i++) a.push(bigInt(Math.floor(Math.random()*100000) -500000));
 99        for (let i=0; i<900; i++) b.push(bigInt(Math.floor(Math.random()*100000) -500000));
100
101        const c = PF.mul(a,b);
102
103        const d = PF.div(c,b);
104
105        assert(PF.equals(a, d));
106    }).timeout(10000);
107    it("Should evaluate and zero", () => {
108        const PF = new PolField(new ZqField(r));
109        const p = [PF.F.neg(bigInt(2)), bigInt(1)];
110        const v = PF.eval(p, bigInt(2));
111        assert(PF.F.equals(v, bigInt(0)));
112    });
113    it("Should create lagrange polynomial minmal", () => {
114        const PF = new PolField(new ZqField(r));
115
116        const points=[];
117        points.push([bigInt(1), bigInt(1)]);
118        points.push([bigInt(2), bigInt(2)]);
119        points.push([bigInt(3), bigInt(5)]);
120
121        const p=PF.lagrange(points);
122
123        for (let i=0; i<points.length; i++) {
124            const v = PF.eval(p, points[i][0]);
125            assert(PF.F.equals(v, points[i][1]));
126        }
127    });
128    it("Should create lagrange polynomial", () => {
129        const PF = new PolField(new ZqField(r));
130
131        const points=[];
132        points.push([bigInt(1), bigInt(2)]);
133        points.push([bigInt(2), bigInt(-2)]);
134        points.push([bigInt(3), bigInt(0)]);
135        points.push([bigInt(4), bigInt(453345)]);
136
137        const p=PF.lagrange(points);
138
139        for (let i=0; i<points.length; i++) {
140            const v = PF.eval(p, points[i][0]);
141            assert(PF.F.equals(v, points[i][1]));
142        }
143    });
144
145});