A finite field is a finite set on which the four operations multiplication, addition, subtraction and division (excluding division by zero) are defined, satisfying the rules of arithmetic known as the field axioms. The simplest examples of finite fields are the fields of prime order: for each prime number p, the field GF(p) (also denoted Z/pZ, {\displaystyle \mathbb {F} _{p}} \mathbb {F} _{p}, or Fp) of order (that is, size) p may be constructed as the integers modulo p.
The elements of such a field may be represented by integers in the range 0, ..., p − 1. The sum, the difference and the product are computed by taking the remainder by p of the integer result. The multiplicative inverse of an element may be computed by using the extended Euclidean algorithm (see Extended Euclidean algorithm § Modular integers).
see: https://en.wikipedia.org/wiki/Finite_field
To get a local copy of the current code, clone it using git:
$ git clone git://github.com/jeffallen6767/finite-field.git
$ cd finite-field
If everything worked out, install all dependencies:
$ npm install
Run the tests:
C:\Users\Malachi\workspace\finite-field>npm test
> [email protected] test C:\Users\Malachi\workspace\finite-field
> node test.js
Test 1 add x + y mod p for all k in finite field order: 31 = [0, 1, ...30]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
---------------------------------------------------------------------------------------------
0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0
2| 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1
3| 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2
4| 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3
5| 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4
6| 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5
7| 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6
8| 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7
9| 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8
10| 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9
11| 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10
12| 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11
13| 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12
14| 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13
15| 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
16| 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
17| 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18| 18 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
19| 19 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
20| 20 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
21| 21 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
22| 22 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
23| 23 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
24| 24 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
25| 25 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
26| 26 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
27| 27 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
28| 28 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
29| 29 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
30| 30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
test number of rows
PASS! Time: 47 Milliseconds 31 === 31
test number of columns
PASS! Time: 47 Milliseconds 31 === 31
test values in row 2
PASS! Time: 47 Milliseconds 17,18,19,20,21,22,23,24,25,26,27,28,29,30,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 === 17,18,19,20,21,22,23,24,25,26,27,28,29,30,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
test number of entries in getRow(2)
PASS! Time: 47 Milliseconds 31 === 31
test values of entries in getRow(2)
PASS! Time: 47 Milliseconds 17,18,19,20,21,22,23,24,25,26,27,28,29,30,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 === 17,18,19,20,21,22,23,24,25,26,27,28,29,30,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
test value of 17 + 27 % 31 using getEntry
PASS! Time: 47 Milliseconds 13 === 13
Test 2 subtract x - y mod p for all k in finite field order: 31 = [0, 1, ...30]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
---------------------------------------------------------------------------------------------
0| 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
1| 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2
2| 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3
3| 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4
4| 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5
5| 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6
6| 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7
7| 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8
8| 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
9| 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
10| 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11
11| 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12
12| 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13
13| 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14
14| 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15
15| 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
16| 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17
17| 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19 18
18| 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20 19
19| 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21 20
20| 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22 21
21| 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23 22
22| 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24 23
23| 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25 24
24| 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26 25
25| 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27 26
26| 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28 27
27| 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 28
28| 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29
29| 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30
30| 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
test number of rows
PASS! Time: 16 Milliseconds 31 === 31
test number of columns
PASS! Time: 16 Milliseconds 31 === 31
test values in row 2
PASS! Time: 16 Milliseconds 17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,30,29,28,27,26,25,24,23,22,21,20,19,18 === 17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,30,29,28,27,26,25,24,23,22,21,20,19,18
test number of entries in getRow(2)
PASS! Time: 16 Milliseconds 31 === 31
test values of entries in getRow(2)
PASS! Time: 16 Milliseconds 17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,30,29,28,27,26,25,24,23,22,21,20,19,18 === 17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,30,29,28,27,26,25,24,23,22,21,20,19,18
test value of 17 - 27 % 31 using getEntry
PASS! Time: 16 Milliseconds 21 === 21
Test 3 multiply x * y mod p for all k in finite field order: 31 = [0, 1, ...30]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
---------------------------------------------------------------------------------------------
0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
2| 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
3| 0 3 6 9 12 15 18 21 24 27 30 2 5 8 11 14 17 20 23 26 29 1 4 7 10 13 16 19 22 25 28
4| 0 4 8 12 16 20 24 28 1 5 9 13 17 21 25 29 2 6 10 14 18 22 26 30 3 7 11 15 19 23 27
5| 0 5 10 15 20 25 30 4 9 14 19 24 29 3 8 13 18 23 28 2 7 12 17 22 27 1 6 11 16 21 26
6| 0 6 12 18 24 30 5 11 17 23 29 4 10 16 22 28 3 9 15 21 27 2 8 14 20 26 1 7 13 19 25
7| 0 7 14 21 28 4 11 18 25 1 8 15 22 29 5 12 19 26 2 9 16 23 30 6 13 20 27 3 10 17 24
8| 0 8 16 24 1 9 17 25 2 10 18 26 3 11 19 27 4 12 20 28 5 13 21 29 6 14 22 30 7 15 23
9| 0 9 18 27 5 14 23 1 10 19 28 6 15 24 2 11 20 29 7 16 25 3 12 21 30 8 17 26 4 13 22
10| 0 10 20 30 9 19 29 8 18 28 7 17 27 6 16 26 5 15 25 4 14 24 3 13 23 2 12 22 1 11 21
11| 0 11 22 2 13 24 4 15 26 6 17 28 8 19 30 10 21 1 12 23 3 14 25 5 16 27 7 18 29 9 20
12| 0 12 24 5 17 29 10 22 3 15 27 8 20 1 13 25 6 18 30 11 23 4 16 28 9 21 2 14 26 7 19
13| 0 13 26 8 21 3 16 29 11 24 6 19 1 14 27 9 22 4 17 30 12 25 7 20 2 15 28 10 23 5 18
14| 0 14 28 11 25 8 22 5 19 2 16 30 13 27 10 24 7 21 4 18 1 15 29 12 26 9 23 6 20 3 17
15| 0 15 30 14 29 13 28 12 27 11 26 10 25 9 24 8 23 7 22 6 21 5 20 4 19 3 18 2 17 1 16
16| 0 16 1 17 2 18 3 19 4 20 5 21 6 22 7 23 8 24 9 25 10 26 11 27 12 28 13 29 14 30 15
17| 0 17 3 20 6 23 9 26 12 29 15 1 18 4 21 7 24 10 27 13 30 16 2 19 5 22 8 25 11 28 14
18| 0 18 5 23 10 28 15 2 20 7 25 12 30 17 4 22 9 27 14 1 19 6 24 11 29 16 3 21 8 26 13
19| 0 19 7 26 14 2 21 9 28 16 4 23 11 30 18 6 25 13 1 20 8 27 15 3 22 10 29 17 5 24 12
20| 0 20 9 29 18 7 27 16 5 25 14 3 23 12 1 21 10 30 19 8 28 17 6 26 15 4 24 13 2 22 11
21| 0 21 11 1 22 12 2 23 13 3 24 14 4 25 15 5 26 16 6 27 17 7 28 18 8 29 19 9 30 20 10
22| 0 22 13 4 26 17 8 30 21 12 3 25 16 7 29 20 11 2 24 15 6 28 19 10 1 23 14 5 27 18 9
23| 0 23 15 7 30 22 14 6 29 21 13 5 28 20 12 4 27 19 11 3 26 18 10 2 25 17 9 1 24 16 8
24| 0 24 17 10 3 27 20 13 6 30 23 16 9 2 26 19 12 5 29 22 15 8 1 25 18 11 4 28 21 14 7
25| 0 25 19 13 7 1 26 20 14 8 2 27 21 15 9 3 28 22 16 10 4 29 23 17 11 5 30 24 18 12 6
26| 0 26 21 16 11 6 1 27 22 17 12 7 2 28 23 18 13 8 3 29 24 19 14 9 4 30 25 20 15 10 5
27| 0 27 23 19 15 11 7 3 30 26 22 18 14 10 6 2 29 25 21 17 13 9 5 1 28 24 20 16 12 8 4
28| 0 28 25 22 19 16 13 10 7 4 1 29 26 23 20 17 14 11 8 5 2 30 27 24 21 18 15 12 9 6 3
29| 0 29 27 25 23 21 19 17 15 13 11 9 7 5 3 1 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2
30| 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
test number of rows
PASS! Time: 31 Milliseconds 31 === 31
test number of columns
PASS! Time: 31 Milliseconds 31 === 31
test values in row 2
PASS! Time: 31 Milliseconds 0,17,3,20,6,23,9,26,12,29,15,1,18,4,21,7,24,10,27,13,30,16,2,19,5,22,8,25,11,28,14 === 0,17,3,20,6,23,9,26,12,29,15,1,18,4,21,7,24,10,27,13,30,16,2,19,5,22,8,25,11,28,14
test number of entries in getRow(2)
PASS! Time: 31 Milliseconds 31 === 31
test values of entries in getRow(2)
PASS! Time: 31 Milliseconds 0,17,3,20,6,23,9,26,12,29,15,1,18,4,21,7,24,10,27,13,30,16,2,19,5,22,8,25,11,28,14 === 0,17,3,20,6,23,9,26,12,29,15,1,18,4,21,7,24,10,27,13,30,16,2,19,5,22,8,25,11,28,14
test value of 17 * 27 % 31 using getEntry
PASS! Time: 31 Milliseconds 25 === 25
Test 4 divide x / y mod p for all k in finite field order: 31 = [0, 1, ...30]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
---------------------------------------------------------------------------------------------
0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1| 0 1 16 21 8 25 26 9 4 7 28 17 13 12 20 29 2 11 19 18 14 3 24 27 22 5 6 23 10 15 30
2| 0 2 1 11 16 19 21 18 8 14 25 3 26 24 9 27 4 22 7 5 28 6 17 23 13 10 12 15 20 30 29
3| 0 3 17 1 24 13 16 27 12 21 22 20 8 5 29 25 6 2 26 23 11 9 10 19 4 15 18 7 30 14 28
4| 0 4 2 22 1 7 11 5 16 28 19 6 21 17 18 23 8 13 14 10 25 12 3 15 26 20 24 30 9 29 27
5| 0 5 18 12 9 1 6 14 20 4 16 23 3 29 7 21 10 24 2 28 8 15 27 11 17 25 30 22 19 13 26
6| 0 6 3 2 17 26 1 23 24 11 13 9 16 10 27 19 12 4 21 15 22 18 20 7 8 30 5 14 29 28 25
7| 0 7 19 23 25 20 27 1 28 18 10 26 29 22 16 17 14 15 9 2 5 21 13 3 30 4 11 6 8 12 24
8| 0 8 4 13 2 14 22 10 1 25 7 12 11 3 5 15 16 26 28 20 19 24 6 30 21 9 17 29 18 27 23
9| 0 9 20 3 10 8 17 19 5 1 4 29 24 15 25 13 18 6 16 7 2 27 30 26 12 14 23 21 28 11 22
10| 0 10 5 24 18 2 12 28 9 8 1 15 6 27 14 11 20 17 4 25 16 30 23 22 3 19 29 13 7 26 21
11| 0 11 21 14 26 27 7 6 13 15 29 1 19 8 3 9 22 28 23 12 30 2 16 18 25 24 4 5 17 10 20
12| 0 12 6 4 3 21 2 15 17 22 26 18 1 20 23 7 24 8 11 30 13 5 9 14 16 29 10 28 27 25 19
13| 0 13 22 25 11 15 28 24 21 29 23 4 14 1 12 5 26 19 30 17 27 8 2 10 7 3 16 20 6 9 18
14| 0 14 7 15 19 9 23 2 25 5 20 21 27 13 1 3 28 30 18 4 10 11 26 6 29 8 22 12 16 24 17
15| 0 15 23 5 27 3 18 11 29 12 17 7 9 25 21 1 30 10 6 22 24 14 19 2 20 13 28 4 26 8 16
16| 0 16 8 26 4 28 13 20 2 19 14 24 22 6 10 30 1 21 25 9 7 17 12 29 11 18 3 27 5 23 15
17| 0 17 24 16 12 22 8 29 6 26 11 10 4 18 30 28 3 1 13 27 21 20 5 25 2 23 9 19 15 7 14
18| 0 18 9 6 20 16 3 7 10 2 8 27 17 30 19 26 5 12 1 14 4 23 29 21 24 28 15 11 25 22 13
19| 0 19 25 27 28 10 29 16 14 9 5 13 30 11 8 24 7 23 20 1 18 26 22 17 15 2 21 3 4 6 12
20| 0 20 10 17 5 4 24 25 18 16 2 30 12 23 28 22 9 3 8 19 1 29 15 13 6 7 27 26 14 21 11
21| 0 21 26 7 13 29 19 3 22 23 30 16 25 4 17 20 11 14 27 6 15 1 8 9 28 12 2 18 24 5 10
22| 0 22 11 28 21 23 14 12 26 30 27 2 7 16 6 18 13 25 15 24 29 4 1 5 19 17 8 10 3 20 9
23| 0 23 27 18 29 17 9 21 30 6 24 19 20 28 26 16 15 5 3 11 12 7 25 1 10 22 14 2 13 4 8
24| 0 24 12 8 6 11 4 30 3 13 21 5 2 9 15 14 17 16 22 29 26 10 18 28 1 27 20 25 23 19 7
25| 0 25 28 29 14 5 30 8 7 20 18 22 15 21 4 12 19 27 10 16 9 13 11 24 23 1 26 17 2 3 6
26| 0 26 13 19 22 30 25 17 11 27 15 8 28 2 24 10 21 7 29 3 23 16 4 20 14 6 1 9 12 18 5
27| 0 27 29 9 30 24 20 26 15 3 12 25 10 14 13 8 23 18 17 21 6 19 28 16 5 11 7 1 22 2 4
28| 0 28 14 30 7 18 15 4 19 10 9 11 23 26 2 6 25 29 5 8 20 22 21 12 27 16 13 24 1 17 3
29| 0 29 30 20 15 12 10 13 23 17 6 28 5 7 22 4 27 9 24 26 3 25 14 8 18 21 19 16 11 1 2
30| 0 30 15 10 23 6 5 22 27 24 3 14 18 19 11 2 29 20 12 13 17 28 7 4 9 26 25 8 21 16 1
test number of rows
PASS! Time: 47 Milliseconds 31 === 31
test number of columns
PASS! Time: 47 Milliseconds 31 === 31
test values in row 2
PASS! Time: 47 Milliseconds 0,17,24,16,12,22,8,29,6,26,11,10,4,18,30,28,3,1,13,27,21,20,5,25,2,23,9,19,15,7,14 === 0,17,24,16,12,22,8,29,6,26,11,10,4,18,30,28,3,1,13,27,21,20,5,25,2,23,9,19,15,7,14
test number of entries in getRow(2)
PASS! Time: 47 Milliseconds 31 === 31
test values of entries in getRow(2)
PASS! Time: 47 Milliseconds 0,17,24,16,12,22,8,29,6,26,11,10,4,18,30,28,3,1,13,27,21,20,5,25,2,23,9,19,15,7,14 === 0,17,24,16,12,22,8,29,6,26,11,10,4,18,30,28,3,1,13,27,21,20,5,25,2,23,9,19,15,7,14
test value of 17 / 27 % 31 using getEntry
PASS! Time: 47 Milliseconds 19 === 19
Test 5 pow x ^ y mod p for all k in finite field order: 31 = [0, 1, ...30]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
---------------------------------------------------------------------------------------------
0| 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2| 1 2 4 8 16 1 2 4 8 16 1 2 4 8 16 1 2 4 8 16 1 2 4 8 16 1 2 4 8 16 1
3| 1 3 9 27 19 26 16 17 20 29 25 13 8 24 10 30 28 22 4 12 5 15 14 11 2 6 18 23 7 21 1
4| 1 4 16 2 8 1 4 16 2 8 1 4 16 2 8 1 4 16 2 8 1 4 16 2 8 1 4 16 2 8 1
5| 1 5 25 1 5 25 1 5 25 1 5 25 1 5 25 1 5 25 1 5 25 1 5 25 1 5 25 1 5 25 1
6| 1 6 5 30 25 26 1 6 5 30 25 26 1 6 5 30 25 26 1 6 5 30 25 26 1 6 5 30 25 26 1
7| 1 7 18 2 14 5 4 28 10 8 25 20 16 19 9 1 7 18 2 14 5 4 28 10 8 25 20 16 19 9 1
8| 1 8 2 16 4 1 8 2 16 4 1 8 2 16 4 1 8 2 16 4 1 8 2 16 4 1 8 2 16 4 1
9| 1 9 19 16 20 25 8 10 28 4 5 14 2 18 7 1 9 19 16 20 25 8 10 28 4 5 14 2 18 7 1
10| 1 10 7 8 18 25 2 20 14 16 5 19 4 9 28 1 10 7 8 18 25 2 20 14 16 5 19 4 9 28 1
11| 1 11 28 29 9 6 4 13 19 23 5 24 16 21 14 30 20 3 2 22 25 27 18 12 8 26 7 15 10 17 1
12| 1 12 20 23 28 26 2 24 9 15 25 21 4 17 18 30 19 11 8 3 5 29 7 22 16 6 10 27 14 13 1
13| 1 13 14 27 10 6 16 22 7 29 5 3 8 11 19 30 18 17 4 21 25 15 9 24 2 26 28 23 20 12 1
14| 1 14 10 16 7 5 8 19 18 4 25 9 2 28 20 1 14 10 16 7 5 8 19 18 4 25 9 2 28 20 1
15| 1 15 8 27 2 30 16 23 4 29 1 15 8 27 2 30 16 23 4 29 1 15 8 27 2 30 16 23 4 29 1
16| 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1
17| 1 17 10 15 7 26 8 12 18 27 25 22 2 3 20 30 14 21 16 24 5 23 19 13 4 6 9 29 28 11 1
18| 1 18 14 4 10 25 16 9 7 2 5 28 8 20 19 1 18 14 4 10 25 16 9 7 2 5 28 8 20 19 1
19| 1 19 20 8 28 5 2 7 9 16 25 10 4 14 18 1 19 20 8 28 5 2 7 9 16 25 10 4 14 18 1
20| 1 20 28 2 9 25 4 18 19 8 5 7 16 10 14 1 20 28 2 9 25 4 18 19 8 5 7 16 10 14 1
21| 1 21 7 23 18 6 2 11 14 15 5 12 4 22 28 30 10 24 8 13 25 29 20 17 16 26 19 27 9 3 1
22| 1 22 19 15 20 6 8 21 28 27 5 17 2 13 7 30 9 12 16 11 25 23 10 3 4 26 14 29 18 24 1
23| 1 23 2 15 4 30 8 29 16 27 1 23 2 15 4 30 8 29 16 27 1 23 2 15 4 30 8 29 16 27 1
24| 1 24 18 29 14 26 4 3 10 23 25 11 16 12 9 30 7 13 2 17 5 27 28 21 8 6 20 15 19 22 1
25| 1 25 5 1 25 5 1 25 5 1 25 5 1 25 5 1 25 5 1 25 5 1 25 5 1 25 5 1 25 5 1
26| 1 26 25 30 5 6 1 26 25 30 5 6 1 26 25 30 5 6 1 26 25 30 5 6 1 26 25 30 5 6 1
27| 1 27 16 29 8 30 4 15 2 23 1 27 16 29 8 30 4 15 2 23 1 27 16 29 8 30 4 15 2 23 1
28| 1 28 9 4 19 5 16 14 20 2 25 18 8 7 10 1 28 9 4 19 5 16 14 20 2 25 18 8 7 10 1
29| 1 29 4 23 16 30 2 27 8 15 1 29 4 23 16 30 2 27 8 15 1 29 4 23 16 30 2 27 8 15 1
30| 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1
test number of rows
PASS! Time: 78 Milliseconds 31 === 31
test number of columns
PASS! Time: 78 Milliseconds 31 === 31
test values in row 2
PASS! Time: 78 Milliseconds 1,17,10,15,7,26,8,12,18,27,25,22,2,3,20,30,14,21,16,24,5,23,19,13,4,6,9,29,28,11,1 === 1,17,10,15,7,26,8,12,18,27,25,22,2,3,20,30,14,21,16,24,5,23,19,13,4,6,9,29,28,11,1
test number of entries in getRow(2)
PASS! Time: 78 Milliseconds 31 === 31
test values of entries in getRow(2)
PASS! Time: 78 Milliseconds 1,17,10,15,7,26,8,12,18,27,25,22,2,3,20,30,14,21,16,24,5,23,19,13,4,6,9,29,28,11,1 === 1,17,10,15,7,26,8,12,18,27,25,22,2,3,20,30,14,21,16,24,5,23,19,13,4,6,9,29,28,11,1
test value of 17 ^ 27 % 31 using getEntry
PASS! Time: 78 Milliseconds 29 === 29
Test 6 compute 24 * 19 % 31 in finite field order: 31 = [0, 1, ...30]
test value of 24 * 19 % 31 using getEntry
PASS! Time: 0 Milliseconds 22 === 22
Test 7 compute 17 ^ 3 % 31 in finite field order: 31 = [0, 1, ...30]
test value of 17 ^ 3 % 31 using getEntry
PASS! Time: 0 Milliseconds 15 === 15
Test 8 compute 5 ^ 5 * 18 % 31 in finite field order: 31 = [0, 1, ...30]
test value of 5 ^ 5 * 18 % 31 using getEntry
PASS! Time: 0 Milliseconds 16 === 16
Test 9 k^30 % 31 for all k ( except zero ) in in finite field order: 31 = [0, 1, ...30]
test values in row 30
PASS! Time: 0 Milliseconds 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 === 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
results:
34 tests
34 pass
0 fail
Time: 329 Milliseconds
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