F2Matrices

Description

Matrices) and polynomials over field Z/2Z).
Documentation for files will be found here.

Examples:

Example 1

 a = F2Polynomial([1, 1, 1, 0])
 b = F2Polynomial([0, 1, 0, 0])
 c = F2Polynomial([1, 1, 1, 1])
 d = F2Polynomial([1, 0, 1, 1])
 f = F2Matrix([[a, b],
               [c, d]])
 g = F2Matrix([[d, c],
               [b, a]])
 h = f + g
 print(str(f), " + \n")
 print(str(g), " = \n")
 print(str(h), "\n")

will print out:

 |      1 + D + D^2,                 D|
 |1 + D + D^2 + D^3,     1 + D^2 + D^3|  +
 |    1 + D^2 + D^3, 1 + D + D^2 + D^3|
 |                D,       1 + D + D^2|  =
 |      D + D^3, 1 + D^2 + D^3|
 |1 + D^2 + D^3,       D + D^3|

Example 2

 a = F2Polynomial([1, 0, 0, 0])
 b = F2Polynomial([1, 1, 0, 0])
 c = F2Polynomial([1, 1, 1, 0])
 d = F2Polynomial([1, 1, 1, 1])
 f = F2Matrix([[a, b],
               [c, d]])
 g = F2Matrix([[d, c],
               [b, a]])
 h = f * g
 print(str(f), " * \n")
 print(str(g), " = \n")
 print(str(h), "\n")

will print out:

 |                1,             1 + D|
 |      1 + D + D^2, 1 + D + D^2 + D^3|  *
 |1 + D + D^2 + D^3,       1 + D + D^2|
 |            1 + D,                 1|  =
 |              D + D^3,                   D^2|
 |D^2 + D^3 + D^4 + D^5,         D + D^3 + D^4|

Example 3

 a = F2Polynomial([1, 0, 0, 0])
 b = F2Polynomial([1, 1, 0, 0])
 c = F2Polynomial([1, 1, 1, 0])
 d = F2Polynomial([1, 1, 1, 1])
 f = F2Matrix([[a, b],
               [c, d]])
 h = f ** 2
 print(str(f), " ** 2 = \n")
 print(str(h), "\n")

will print out:

 |                1,             1 + D|
 |      1 + D + D^2, 1 + D + D^2 + D^3|  ** 2 =
 |                  D^3,               D + D^4|
 |        D + D^3 + D^5, D^2 + D^3 + D^4 + D^6|

State

[x] F2Polynomial
- __init__
- __str__
- degree
- __add__
- __iadd__
- __mul__
- __imul__
- __pow__
- evaluate
[x] dotProduct
[x] F2Matrix
- __init__
- __str__
- __add__
- __iadd__
- transpose
- __mul__
- __imul__
- __pow__
- changeColumns
- changeRows
- addColumns
[x] findPivot
smithNormalForm