forked from kalmar/DALGLI0
Compare commits
3 Commits
| Author | SHA1 | Date | |
|---|---|---|---|
| 210e91191b | |||
| 488d8468cd | |||
| ee015fbb9d |
@ -1,87 +0,0 @@
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const rl = require('readline').createInterface({
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input: process.stdin,
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output: process.stdout
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});
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//zapytanie o wartosc n
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rl.question('n? ', n => {
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n = parseInt(n);
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//sprawdzenie czy n na pewno jest liczba
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if (isNaN(n)) throw Error('Must be Number');
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// deklarowanie slownikow dla poszczegolnych elementow(aby się nie powtorzyly)
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let elOdw = new Dictionary();
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let dzielZero = new Dictionary();
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let elNil = new Dictionary();
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let elIden = new Dictionary();
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//#region dodanie trywalnych
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dzielZero.add(0, 0);
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elNil.add(0, 0);
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elIden.add(0, 0);
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//#endregion
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for (let y = 0; y < n; y++) {
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//#region Obliczanie elementow Idenpotetnych
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if (Math.pow(y, 2) % n == y) {
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elIden.add(y, y);
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}
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//#endregion
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for (let x = 0; x < n; x++) {
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//#region obliczanie elementow Nilpotetnych
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if (Math.pow(y, x) % n == 0) {
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elNil.add(y, y);
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}
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//#endregion
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//#region Obliczanie elementow odwracalnych'
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if (x >= y && (x * y) % n == 1) {
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elOdw.add(x, x);
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elOdw.add(y, y);
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}
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//#endregion
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//#region obliczanie dzielnikow zera
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if (x >= y && x != 0 && y != 0 && (x * y) % n == 0) {
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dzielZero.add(x, x);
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dzielZero.add(y, y);
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}
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//#endregion
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}
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}
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//wypisanie obliczonych wartosci wartosci
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console.log([
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elOdw.getValues(),
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dzielZero.getValues(),
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elNil.getValues(),
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elIden.getValues()
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]);
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//zamkniecie połaczenia z input/output
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rl.close();
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});
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function NWD(a, b) {
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return b ? NWD(b, a % b) : a;
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}
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// klasa słownika
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class Dictionary {
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constructor() {
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this.elements = {};
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}
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add(key, value) {
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this.elements[key] = value;
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}
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remove(key, value) {
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delete this.elements[key];
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}
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getKeys() {
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let keys = [];
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for (let key in this.elements) {
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keys.push(key);
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}
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return keys;
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}
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getValues() {
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let values = [];
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for (let key in this.elements) {
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values.push(this.elements[key]);
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}
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return values;
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}
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}
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@ -1,22 +0,0 @@
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let Polynomial = require('./polynomial.js');
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let mul, div, gcd;
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let n = parseInt(process.argv[2]);
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let p1 = JSON.parse(process.argv[3].replace(/'/g, '"'));
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let p2 = JSON.parse(process.argv[4].replace(/'/g, '"'));
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let f = new Polynomial.Class(n, p1);
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let g = new Polynomial.Class(n, p2);
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mul = Polynomial.multiply(f, g).coefficients;
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try {
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div = Polynomial.divide(f, g).coefficients
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} catch (e) {
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console.log(e)
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}
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try {
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gcd = Polynomial.gcd(f, g).coefficients;
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} catch (e) {
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console.log(e);
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}
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console.log([mul, div, gcd])
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97
03-CRC.md
Normal file
97
03-CRC.md
Normal file
@ -0,0 +1,97 @@
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## Zadanie
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Napisać program, który dla wiadomości `M` w formie tekstowej ASCII (tj. `8` bitów na znak):
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1. utworzy FCS (*Frame Check Sequence*) długości `16` bitów zgodnie z algorytmem **D-1.1**;
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- INPUT: `M` - tablica znaków ASCII długości `n-2`;
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- OUTPUT: `N` - tablica 8-bitowych liczb (`unsigned char`) długości `n`, która zawiera oryginalną wiadomość `M` na pierwszych `n-2` miejscach, zaś ostatnie dwa zawierają FCS.
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2. pozwoli sprawdzić, czy dana ramka (tj. wiadomość + FCS) zawiera poprawną treść (zgodnie z **D-1.2**;
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- INPUT: `N` - tablica 8-bitowych liczb (`unsigned char`) długości `n` (np. w formacie hex)
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- OUTPUT: `true` jeśli dwie ostatnie liczby tablicy `N` odpowiadają FCS wiadomości `M = N[0:n-2]` (interpretowanej jako tablica typu `char`), `false` w przeciwnym wypadku;
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UWAGA: Program w punkcie **2** powinien być w stanie zweryfikować output z punktu **1**!
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Źródło: [Report: Telemetry Summary of Concept and Rationale](http://mtc-m16c.sid.inpe.br/col/sid.inpe.br/mtc-m18@80/2009/07.15.17.25/doc/CCSDS%20100.0-G-1.pdf), CCSDS 100.0-G-1 Report Concerning Space.
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### Warunki punktacji
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* program musi być typu wsadowego, tj. uruchamiany z linii komend;
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* program musi się działać (i kompilować) na serwerze [LTS](https://laboratoria.wmi.amu.edu.pl/en/uslugi/serwer-terminalowy/lts)
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* implementacja bazowa (korzystająca z dzielenia wielomianów) jest warta 1 punkt;
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* każda zmiana która wpływa na szybkość musi być skomentowana i opisana bardzo dokładnie (co zrobiliśmy, dlaczego (i jak) wpływa to na szybkość i dlaczego wynik matematycznie jest taki sam);
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* najszybsza implementacja dostaje 2 pkt; najwolniejsza 1; reszta rozłożona liniowo;
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* dwie kategorie szybkości:
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- języki statycznie kompilowane (C, C++, java,...) oraz języki JIT;
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- języki interpretowane (python, lua,...);
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UWAGA: **NIE** przyjmuję squashed pulls (z jednym commitem), zwłaszcza jeśli chodzi o wersję działającą szybko.
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### Termin
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21.06.2018
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### Dodatkowe informacje
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Funkcja, którą omawialiśmy, to tzw. CRC-16-CCITT, czyli [16-bit Cyclic Redundancy Check](https://en.wikipedia.org/wiki/Cyclic_redundancy_check). Funkcje tego typu , są uzywane we wszystkich ramkach [komunikacji](https://en.wikipedia.org/wiki/Cyclic_redundancy_check#Polynomial_representations_of_cyclic_redundancy_checks), od USB, przez Ethernet, Bluetooth, Wifi, GSM, na standardach dźwięku i obrazu (MPEG, PNG) i dyskach twadrdych (SATA) kończąc.
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#### Implementacja referencyjna
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```c
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static unsigned short crc_table[256] = {
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0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50a5,
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0x60c6, 0x70e7, 0x8108, 0x9129, 0xa14a, 0xb16b,
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0xc18c, 0xd1ad, 0xe1ce, 0xf1ef, 0x1231, 0x0210,
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0x3273, 0x2252, 0x52b5, 0x4294, 0x72f7, 0x62d6,
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0x9339, 0x8318, 0xb37b, 0xa35a, 0xd3bd, 0xc39c,
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0xf3ff, 0xe3de, 0x2462, 0x3443, 0x0420, 0x1401,
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0x64e6, 0x74c7, 0x44a4, 0x5485, 0xa56a, 0xb54b,
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0x8528, 0x9509, 0xe5ee, 0xf5cf, 0xc5ac, 0xd58d,
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0x3653, 0x2672, 0x1611, 0x0630, 0x76d7, 0x66f6,
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0x5695, 0x46b4, 0xb75b, 0xa77a, 0x9719, 0x8738,
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0xf7df, 0xe7fe, 0xd79d, 0xc7bc, 0x48c4, 0x58e5,
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0x6886, 0x78a7, 0x0840, 0x1861, 0x2802, 0x3823,
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0xc9cc, 0xd9ed, 0xe98e, 0xf9af, 0x8948, 0x9969,
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0xa90a, 0xb92b, 0x5af5, 0x4ad4, 0x7ab7, 0x6a96,
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0x1a71, 0x0a50, 0x3a33, 0x2a12, 0xdbfd, 0xcbdc,
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0xfbbf, 0xeb9e, 0x9b79, 0x8b58, 0xbb3b, 0xab1a,
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0x6ca6, 0x7c87, 0x4ce4, 0x5cc5, 0x2c22, 0x3c03,
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0x0c60, 0x1c41, 0xedae, 0xfd8f, 0xcdec, 0xddcd,
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0xad2a, 0xbd0b, 0x8d68, 0x9d49, 0x7e97, 0x6eb6,
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0x5ed5, 0x4ef4, 0x3e13, 0x2e32, 0x1e51, 0x0e70,
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0xff9f, 0xefbe, 0xdfdd, 0xcffc, 0xbf1b, 0xaf3a,
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0x9f59, 0x8f78, 0x9188, 0x81a9, 0xb1ca, 0xa1eb,
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0xd10c, 0xc12d, 0xf14e, 0xe16f, 0x1080, 0x00a1,
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0x30c2, 0x20e3, 0x5004, 0x4025, 0x7046, 0x6067,
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0x83b9, 0x9398, 0xa3fb, 0xb3da, 0xc33d, 0xd31c,
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0xe37f, 0xf35e, 0x02b1, 0x1290, 0x22f3, 0x32d2,
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0x4235, 0x5214, 0x6277, 0x7256, 0xb5ea, 0xa5cb,
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0x95a8, 0x8589, 0xf56e, 0xe54f, 0xd52c, 0xc50d,
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0x34e2, 0x24c3, 0x14a0, 0x0481, 0x7466, 0x6447,
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0x5424, 0x4405, 0xa7db, 0xb7fa, 0x8799, 0x97b8,
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0xe75f, 0xf77e, 0xc71d, 0xd73c, 0x26d3, 0x36f2,
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0x0691, 0x16b0, 0x6657, 0x7676, 0x4615, 0x5634,
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0xd94c, 0xc96d, 0xf90e, 0xe92f, 0x99c8, 0x89e9,
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0xb98a, 0xa9ab, 0x5844, 0x4865, 0x7806, 0x6827,
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0x18c0, 0x08e1, 0x3882, 0x28a3, 0xcb7d, 0xdb5c,
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0xeb3f, 0xfb1e, 0x8bf9, 0x9bd8, 0xabbb, 0xbb9a,
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0x4a75, 0x5a54, 0x6a37, 0x7a16, 0x0af1, 0x1ad0,
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0x2ab3, 0x3a92, 0xfd2e, 0xed0f, 0xdd6c, 0xcd4d,
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0xbdaa, 0xad8b, 0x9de8, 0x8dc9, 0x7c26, 0x6c07,
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0x5c64, 0x4c45, 0x3ca2, 0x2c83, 0x1ce0, 0x0cc1,
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0xef1f, 0xff3e, 0xcf5d, 0xdf7c, 0xaf9b, 0xbfba,
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0x8fd9, 0x9ff8, 0x6e17, 0x7e36, 0x4e55, 0x5e74,
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0x2e93, 0x3eb2, 0x0ed1, 0x1ef0
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};
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unsigned short CRCCCITT(unsigned char *data, size_t length)
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{
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size_t count;
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unsigned int crc = 0xffff;
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unsigned int temp;
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for (count = 0; count < length; ++count)
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{
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temp = (*data++ ^ (crc >> 8)) & 0xff;
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crc = crc_table[temp] ^ (crc << 8);
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}
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return (unsigned short)(crc);
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}
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```
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@ -1,20 +0,0 @@
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const crc = require("./crc.js");
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const message = process.argv[3];
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const flag = process.argv[2];
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switch (flag) {
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case '-e':
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console.log(crc.encode(message).encoded);
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break;
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case '-d':
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let fcs = JSON.parse(process.argv[4].replace(/'/g, '"'));
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console.log(crc.decode(message, fcs));
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break;
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case '-t':
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let res = crc.encode(message);
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console.log(res.encoded);
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console.log(crc.decode(message, res.FCS))
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break;
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default:
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throw "incorect flag"
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}
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48
04-Ilorazy-pierścienia-wielomianów.md
Normal file
48
04-Ilorazy-pierścienia-wielomianów.md
Normal file
@ -0,0 +1,48 @@
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|
## Zadanie
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Napisać program, który dla pierścienia `ℤ/nℤ[x]/(f = a₀ + a₁x¹+ ...+ aₖxᵏ)` znajdzie wszystkie
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1. elementy odwracalne,
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2. dzielniki zera,
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3. elementy nilpotentne,
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4. elementy idempotentne.
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- INPUT: `n [a₀,a₁,...,aₖ]`
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- OUTPUT: lista zawierająca cztery powyższe listy elementów (wielomianów, podanych jako listy współczynników)
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### Przykłady:
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|
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||||||
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1. `ℤ/2ℤ[x]/(x² + x + 1)`, który jest ciałem, tzn. `0` jest jedynym elementem nilpotentnym i jedynym dzielnikiem zera:
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* INPUT: `2 [1,1,1]`
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* OUTPUT:
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||||||
|
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||||||
|
```shell
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|
[
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|
[[1], [0,1], [0,1], [1,1]], # odwracalne
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[[0]], # dzielniki zera
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[[0]], # nilpotenty
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[[1]] # idempotenty
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|
]
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|
```
|
||||||
|
|
||||||
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1. `ℤ/5ℤ[x]/(2x³ + 2x² + x + 1)`
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* INPUT: `3, [1,1,2,2]`
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|
* OUTPUT:
|
||||||
|
|
||||||
|
```sh
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||||||
|
[
|
||||||
|
[[1], [2], [0, 1], [0, 2], [0, 0, 1], [1, 0, 1], [2, 1, 1], [2, 2, 1], [0, 0, 2], [2, 0, 2], [1, 1, 2], [1, 2, 2]], # odwracalne
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||||||
|
[[0], [1, 1], [2, 1], [1, 2], [2, 2], [2, 0, 1], [0, 1, 1], [1, 1, 1], [0, 2, 1], [1, 2, 1], [1, 0, 2], [0, 1, 2], [2, 1, 2], [0, 2, 2], [2, 2, 2]], # dzielniki zera
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[[0], [2, 0, 1], [1, 0, 2]], # nilpotenty
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||||||
|
[[0], [1], [1, 2, 1], [0, 1, 2]] # idempotenty
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||||||
|
]
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||||||
|
```
|
||||||
|
|
||||||
|
### Warunki punktacji
|
||||||
|
* program musi być typu wsadowego, tj. uruchamiany z linii komend;
|
||||||
|
* program musi się działać (i kompilować) na serwerze [LTS](https://laboratoria.wmi.amu.edu.pl/en/uslugi/serwer-terminalowy/lts)
|
||||||
|
|
||||||
|
UWAGA: **NIE** przyjmuję squashed pulls (z jednym commitem)
|
||||||
|
|
||||||
|
### Termin
|
||||||
|
28.06.2018
|
||||||
117
crc.js
117
crc.js
@ -1,117 +0,0 @@
|
|||||||
const Polynomial = require('./polynomial.js');
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|
||||||
|
|
||||||
const L = new Polynomial.Class(2, new Array(16).fill(1));
|
|
||||||
const X16 = new Polynomial.Class(2, [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]); //jako ze można to od razu wymnożyć
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|
||||||
const G = new Polynomial.Class(2, [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]); //jako ze można to od razu wymnożyć
|
|
||||||
|
|
||||||
const to_bin = a => {
|
|
||||||
var result = "";
|
|
||||||
for (var i = 0; i < a.length; i++) {
|
|
||||||
var bin = a[i].charCodeAt().toString(2);
|
|
||||||
result += Array(8 - bin.length + 1).join("0") + bin;
|
|
||||||
}
|
|
||||||
return result;
|
|
||||||
}
|
|
||||||
const to_ascii = a => {
|
|
||||||
a = a.join('');
|
|
||||||
a = parseInt(a, 2);
|
|
||||||
//nie znalazłem innego sposobu w js na osiągniecie tego efektu..
|
|
||||||
// if (a < 126) //ponieważ wieksze liczby nie należą do typowego Ascii//porzucone ze wzgledu na decode
|
|
||||||
return String.fromCharCode(a);
|
|
||||||
// else {
|
|
||||||
// return "0x" + a.toString(16);
|
|
||||||
// // return "\\x" + a.toString(16); //escape \ nie wiem czemu dobrze nie działą i i tak wypisuje \\
|
|
||||||
// }
|
|
||||||
|
|
||||||
|
|
||||||
}
|
|
||||||
const mod8format = array => {
|
|
||||||
while (array.length % 8 != 0) {
|
|
||||||
array.push(0);
|
|
||||||
}
|
|
||||||
return array;
|
|
||||||
}
|
|
||||||
|
|
||||||
const fcs = m => {
|
|
||||||
let bits = m.map(to_bin); //message in binary
|
|
||||||
bits = bits.join('').split('').reverse(); //reverse binary decoded message
|
|
||||||
let M = new Polynomial.Class(2, bits);
|
|
||||||
let fcs = Polynomial.multiply(X16, M);
|
|
||||||
|
|
||||||
fcs = Polynomial.add(fcs,
|
|
||||||
Polynomial.multiply(
|
|
||||||
Polynomial.Mono(m.length * 8, 1, 2),
|
|
||||||
L
|
|
||||||
)
|
|
||||||
)
|
|
||||||
fcs = Polynomial.divide(fcs, G);
|
|
||||||
for (let i = 0; i < 16 - fcs.coefficients.length; i++) fcs.coefficients.push(0);
|
|
||||||
fcs.coefficients.reverse();
|
|
||||||
return fcs.coefficients;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
const check = m => {
|
|
||||||
|
|
||||||
let bits = m.map(to_bin); //message in binary
|
|
||||||
bits = bits.join('').split('').reverse(); //reverse binary decoded message
|
|
||||||
|
|
||||||
let fcs = Polynomial.Mono(bits.length, 1, 2);
|
|
||||||
|
|
||||||
|
|
||||||
let C = new Polynomial.Class(2, bits);
|
|
||||||
C = Polynomial.multiply(X16, C);
|
|
||||||
C.coefficients = mod8format(C.coefficients);
|
|
||||||
let S = Polynomial.add(
|
|
||||||
C,
|
|
||||||
Polynomial.multiply(
|
|
||||||
fcs,
|
|
||||||
L
|
|
||||||
)
|
|
||||||
)
|
|
||||||
|
|
||||||
S = Polynomial.divide(S, G)
|
|
||||||
if (S.coefficients.length === 0) {
|
|
||||||
return true;
|
|
||||||
} else
|
|
||||||
return false;
|
|
||||||
}
|
|
||||||
|
|
||||||
function encode(m) {
|
|
||||||
m = m.split('');
|
|
||||||
let res = fcs(m);
|
|
||||||
|
|
||||||
let f1 = [];
|
|
||||||
let f2 = [];
|
|
||||||
for (let i = 0; i < res.length; i++) {
|
|
||||||
if (i < 8) {
|
|
||||||
f1.push(res[i]);
|
|
||||||
} else {
|
|
||||||
f2.push(res[i]);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
f1 = to_ascii(f1);
|
|
||||||
f2 = to_ascii(f2);
|
|
||||||
m.push(f1);
|
|
||||||
m.push(f2);
|
|
||||||
return {
|
|
||||||
encoded: m,
|
|
||||||
FCS: [f1, f2]
|
|
||||||
|
|
||||||
};
|
|
||||||
|
|
||||||
}
|
|
||||||
|
|
||||||
exports.encode = encode;
|
|
||||||
|
|
||||||
function decode(m, fcs) {
|
|
||||||
m = m.split('');
|
|
||||||
to_check = fcs;
|
|
||||||
for (let char in fcs) {
|
|
||||||
m.push(fcs[char]);
|
|
||||||
}
|
|
||||||
return check(m)
|
|
||||||
|
|
||||||
}
|
|
||||||
exports.decode = decode;
|
|
||||||
180
polynomial.js
180
polynomial.js
@ -1,180 +0,0 @@
|
|||||||
class Polynomial {
|
|
||||||
constructor(mod, coefArray) {
|
|
||||||
this.mod = mod;
|
|
||||||
this.degree = (coefArray.length - 1);
|
|
||||||
|
|
||||||
this.coefficients = Array.from(coefArray); //zeby nie przekazywać referencji
|
|
||||||
this.normalize();
|
|
||||||
}
|
|
||||||
normalize() {
|
|
||||||
while (this.coefficients && this.coefficients[this.coefficients.length - 1] == 0) {
|
|
||||||
this.coefficients.pop();
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
exports.Class = Polynomial;
|
|
||||||
|
|
||||||
function get_mod(p1, p2) {
|
|
||||||
let n;
|
|
||||||
if (p1.mod !== p2.mod) {
|
|
||||||
throw "different modulo"
|
|
||||||
} else {
|
|
||||||
return p1.mod;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
function prepare(p1, p2) {
|
|
||||||
let n = get_mod(p1, p2);
|
|
||||||
let len_p1 = p1.coefficients.length;
|
|
||||||
let len_p2 = p2.coefficients.length;
|
|
||||||
result = new Array(Math.max(len_p1, len_p2)).fill(0);
|
|
||||||
if (len_p1 > len_p2) {
|
|
||||||
for (let x = 0; x < len_p1 - len_p2; x++) p2.coefficients.push(0);
|
|
||||||
} else {
|
|
||||||
for (let x = 0; x < len_p2 - len_p1; x++) p1.coefficients.push(0);
|
|
||||||
}
|
|
||||||
return {
|
|
||||||
result,
|
|
||||||
n
|
|
||||||
};
|
|
||||||
|
|
||||||
}
|
|
||||||
|
|
||||||
function add(p1, p2) {
|
|
||||||
|
|
||||||
let {
|
|
||||||
result,
|
|
||||||
n
|
|
||||||
} = prepare(p1, p2);
|
|
||||||
for (let i = 0; i < result.length; i++) {
|
|
||||||
result[i] = (p1.coefficients[i] + p2.coefficients[i]) % n;
|
|
||||||
}
|
|
||||||
return new Polynomial(n, result);
|
|
||||||
}
|
|
||||||
exports.add = add;
|
|
||||||
|
|
||||||
function sub(p1, p2) {
|
|
||||||
let {
|
|
||||||
result,
|
|
||||||
n
|
|
||||||
} = prepare(p1, p2);
|
|
||||||
for (let i = 0; i < result.length; i++) {
|
|
||||||
result[i] = (p1.coefficients[i] - p2.coefficients[i]) % n;
|
|
||||||
}
|
|
||||||
return new Polynomial(n, result);
|
|
||||||
}
|
|
||||||
exports.sub = sub;
|
|
||||||
|
|
||||||
function sub(p1, p2) {
|
|
||||||
let n = get_mod(p1, p2);
|
|
||||||
let len_p1 = p1.coefficients.length;
|
|
||||||
let len_p2 = p2.coefficients.length;
|
|
||||||
result = new Array(Math.max(len_p1, len_p2)).fill(0);
|
|
||||||
if (len_p1 > len_p2) {
|
|
||||||
for (let x = 0; x < len_p1 - len_p2; x++) p2.coefficients.push(0);
|
|
||||||
} else {
|
|
||||||
for (let x = 0; x < len_p2 - len_p1; x++) p1.coefficients.push(0);
|
|
||||||
}
|
|
||||||
for (let i = 0; i < result.length; i++) {
|
|
||||||
result[i] = (p1.coefficients[i] - p2.coefficients[i]) % n;
|
|
||||||
}
|
|
||||||
return new Polynomial(n, result);
|
|
||||||
}
|
|
||||||
exports.add = add;
|
|
||||||
|
|
||||||
function multiply(p1, p2) {
|
|
||||||
let n = get_mod(p1, p2);
|
|
||||||
let f = p1.coefficients;
|
|
||||||
let g = p2.coefficients;
|
|
||||||
result = new Array(f.length + g.length - 1).fill(0);
|
|
||||||
|
|
||||||
let tmp = [];
|
|
||||||
for (let i = 0; i < f.length; i++) {
|
|
||||||
for (let j = 0; j < g.length; j++) {
|
|
||||||
result[i + j] += f[i] * g[j];
|
|
||||||
}
|
|
||||||
}
|
|
||||||
return new Polynomial(n, result.map(x => (x % n) + (x < 0 ? n : 0)));
|
|
||||||
}
|
|
||||||
exports.multiply = multiply;
|
|
||||||
|
|
||||||
function power(p1, pow) {
|
|
||||||
let result = p1;
|
|
||||||
for (let i = 1; i < pow; i++) {
|
|
||||||
result = multiply(result, p1);
|
|
||||||
}
|
|
||||||
return result;
|
|
||||||
}
|
|
||||||
exports.power = power;
|
|
||||||
|
|
||||||
function divide(p1, p2) {
|
|
||||||
let n;
|
|
||||||
if (p1.mod !== p2.mod) {
|
|
||||||
throw "different modulo"
|
|
||||||
} else {
|
|
||||||
n = p1.mod;
|
|
||||||
}
|
|
||||||
let inverse = (x) => {
|
|
||||||
for (let i = 1; i < 2; i++) {
|
|
||||||
let r = (i * x) % 2;
|
|
||||||
if (r == 1)
|
|
||||||
return i
|
|
||||||
else
|
|
||||||
throw "divisionError"
|
|
||||||
|
|
||||||
}
|
|
||||||
}
|
|
||||||
if (p1.degree < p2.degree)
|
|
||||||
return p1;
|
|
||||||
let f = p1.coefficients;
|
|
||||||
let g = p2.coefficients;
|
|
||||||
let g_lead_coef = g[g.length - 1];
|
|
||||||
let g_deg = p2.degree;
|
|
||||||
|
|
||||||
while (f.length >= g.length) {
|
|
||||||
|
|
||||||
let f_lead_coef = f[f.length - 1];
|
|
||||||
let tmp_coef = f_lead_coef * inverse(g_lead_coef);
|
|
||||||
let tmp_exp = f.length - 1 - g_deg;
|
|
||||||
let tmp = [];
|
|
||||||
for (let i = 0; i < tmp_exp; i++) {
|
|
||||||
tmp.push(0);
|
|
||||||
}
|
|
||||||
tmp.push(tmp_coef);
|
|
||||||
tmp_poly = new Polynomial(n, tmp);
|
|
||||||
let sub = multiply(p2, tmp_poly, n);
|
|
||||||
let tmp_f = [];
|
|
||||||
for (let i = 0; i < f.length; i++) {
|
|
||||||
for (let j = 0; j < sub.coefficients.length; j++) {
|
|
||||||
if (i == j)
|
|
||||||
tmp_f.push(f[i] - sub.coefficients[j]);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
f = tmp_f.map(x => (x % n) + (x < 0 ? n : 0));
|
|
||||||
while (f && f[f.length - 1] === 0)
|
|
||||||
f.pop();
|
|
||||||
|
|
||||||
}
|
|
||||||
return new Polynomial(n, f);
|
|
||||||
}
|
|
||||||
|
|
||||||
exports.divide = divide;
|
|
||||||
|
|
||||||
function gcd(p1, p2) {
|
|
||||||
if (p2.coefficients.length === 0) {
|
|
||||||
return p1;
|
|
||||||
}
|
|
||||||
return gcd(p2, divide(p1, p2));
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
exports.gcd = gcd;
|
|
||||||
|
|
||||||
function Mono(n, c, mod) {
|
|
||||||
let coef = new Array(n).fill(0);
|
|
||||||
coef.push(c);
|
|
||||||
return new Polynomial(mod, coef);
|
|
||||||
}
|
|
||||||
exports.Mono = Mono;
|
|
||||||
Loading…
Reference in New Issue
Block a user