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Implement Hermite normal form and associated methods
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ref #43
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frostburn committed Jun 30, 2024
1 parent 721239d commit cf873bb
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97 changes: 88 additions & 9 deletions src/__tests__/basis.spec.ts
Original file line number Diff line number Diff line change
Expand Up @@ -20,7 +20,9 @@ import {
matsub,
matmul,
minor,
transpose,
canonical,
respell,
solveDiophantine,
} from '../basis';
import {
FractionalMonzo,
Expand All @@ -35,6 +37,7 @@ import {
import {dot} from '../number-array';
import {LOG_PRIMES, PRIMES} from '../primes';
import {Fraction} from '../fraction';
import {cokernel, kernel, preimage, transpose} from '../hnf';

const FUZZ = 'FUZZ' in process.env;

Expand Down Expand Up @@ -747,14 +750,6 @@ describe('Determinant', () => {
});

describe('Transpose', () => {
it('transposes a 3x2 matrix', () => {
const mat = [[1, 2], [3], [4, 5]];
expect(transpose(mat)).toEqual([
[1, 3, 4],
[2, 0, 5],
]);
});

it('transposes a 3x2 matrix with rational entries', () => {
const mat = [[1, 0.5], [3], ['2/7', 5]];
expect(
Expand Down Expand Up @@ -826,3 +821,87 @@ describe('Auxiliary matrix methods', () => {
]);
});
});

describe("Sin-tel's example", () => {
it('agrees with temper/example.py', () => {
// 31 & 19
const tMap = [
[19, 30, 44, 53],
[31, 49, 72, 87],
];
// Canonical form
const c = [
[1, 0, -4, -13],
[0, 1, 4, 10],
];
const can = canonical(tMap);
expect(can).toEqual(c);

let commas = transpose(kernel(can));
expect(commas.map(comma => monzoToFraction(comma).toFraction())).toEqual([
'126/125',
'1275989841/1220703125',
]);

commas = lenstraLenstraLovasz(commas).basis;
expect(commas.map(comma => monzoToFraction(comma).toFraction())).toEqual([
'126/125',
'81/80',
]);

const gens = transpose(preimage(can));

expect(gens.map(gen => monzoToFraction(gen).toFraction())).toEqual([
'20253807/9765625',
'3',
]);

const simpleGens = gens.map(gen => respell(gen, commas));

expect(simpleGens.map(gen => monzoToFraction(gen).toFraction())).toEqual([
'2',
'3',
]);
});

it('agrees with temper/example_commas.py', () => {
const commas = ['81/80', '225/224'].map(toMonzo);

expect(commas).toEqual([
[-4, 4, -1],
[-5, 2, 2, -1],
]);

const tMap = cokernel(transpose(commas));
expect(tMap).toEqual([
[1, 0, -4, -13],
[0, 1, 4, 10],
]);
});
});

describe('Diophantine equation solver', () => {
it.skip('solves a diophantine equation', () => {
const A = [
[1, 2, 3],
[-4, 5, 6],
[7, -8, 9],
];
const b = [4, 28, -28];
const solution = solveDiophantine(A, b);
expect(solution).toEqual([-3, 2, 1]);
});

it('converts standard basis commas to subgroup basis monzos (pinkan)', () => {
const subgroup = '2.3.13/5.19/5'.split('.').map(toMonzo);
const commas = ['676/675', '1216/1215'].map(toMonzo);
const subgroupMonzos = solveDiophantine(
transpose(subgroup),
transpose(commas)
);
expect(transpose(subgroupMonzos)).toEqual([
[2, -3, 2, 0],
[6, -5, 0, 1],
]);
});
});
82 changes: 82 additions & 0 deletions src/__tests__/hnf.spec.ts
Original file line number Diff line number Diff line change
@@ -0,0 +1,82 @@
import {describe, it, expect} from 'vitest';
import {antitranspose, hnf, integerDet, transpose} from '../hnf';

describe('Hermite normal form', () => {
it('works on a small matrix', () => {
const A = [
[2, 3, 6, 2],
[5, 6, 1, 6],
[8, 3, 1, 1],
];

const H = hnf(A);

expect(H).toEqual([
[1, 0, 50, -11],
[0, 3, 28, -2],
[0, 0, 61, -13],
]);
});

it('works on a small matrix (bigint)', () => {
const A = [
[2n, 3n, 6n, 2n],
[5n, 6n, 1n, 6n],
[8n, 3n, 1n, 1n],
];

const H = hnf(A);

expect(H).toEqual([
[1n, 0n, 50n, -11n],
[0n, 3n, 28n, -2n],
[0n, 0n, 61n, -13n],
]);
});
});

describe('Integer determinant', () => {
it('works on a small matrix', () => {
const mat = [
[-2, -1, 2],
[2, 1, 4],
[-3, 3, -1],
];
const determinant = integerDet(mat);
expect(determinant).toBe(54);
});

it('works on a small matrix (bigint)', () => {
const mat = [
[-2n, -1n, 2n],
[2n, 1n, 4n],
[-3n, 3n, -1n],
];
const determinant = integerDet(mat);
expect(determinant).toBe(54n);
});
});

describe('Transpose', () => {
it('transposes a 3x2 matrix', () => {
const mat = [[1, 2], [3], [4, 5]];
expect(transpose(mat)).toEqual([
[1, 3, 4],
[2, 0, 5],
]);
});
});

describe('Anti-transpose', () => {
it('anti-transposes a 3x2 matrix', () => {
const mat = [
[1, 2],
[3, 4],
[5, 6],
];
expect(antitranspose(mat)).toEqual([
[6, 4, 2],
[5, 3, 1],
]);
});
});
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