CoCalc -- GFq Addition and Multiplication Table.sagews

Project: Build GF(q) Addition and Multiplication Tables

Path: GFq Addition and Multiplication Table.sagews

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#----------------------------------------------------------------
# File name: GFq Addition and Multiplication Table.sage
# by Chong Zan Kai
# Email [email protected]
#
# To build the addition and multiplication tables for GF(2^q).
#
# Last modified on 01-May-2015.
# Share at https://cloud.sagemath.com/projects/6b6b76fb-7e82-4b88-9f2f-7377a502aa28/files/GFq%20Addition%20and%20Multiplication%20Table.sagews
#----------------------------------------------------------------

#
# User
#
q = 2**2  # select the q. GF(q).


#
#
#
GFq = GF(q, 'x')
GFq_list = sorted(GFq)

#
# Build addition table for GF(2^q)
#
addition_list_list = []

for a in GFq_list:
    addition_list = [ a + b for b in GFq_list]
    addition_list_list.append(addition_list)

__header_row = GFq_list
__header_col = ['+'] + GFq_list
print ('Addition Table for GF(%d)' % q)
print table(header_row = __header_row, header_column= __header_col, rows=addition_list_list, frame = True, align = 'center')
print


#
# Build multiplication table for GF(2^q)
#
multiplication_list_list = []

for a in GFq_list:
    multiplication_list = [ a* b for b in GFq_list]
    multiplication_list_list.append(multiplication_list)

__header_row = GFq_list
__header_col = ['*'] + GFq_list
print ('Multiplication Table for GF(%d)' % q)
print table(header_row = __header_row, header_column= __header_col, rows=multiplication_list_list, frame = True, align = 'center')
# print table(header_row = __header_row, header_column= __header_col, rows=multiplication_list_list, align = 'center')

Addition Table for GF(4)
+-------++-------+-------+-------+-------+
|   +   ||   0   |   1   |   x   | x + 1 |
+=======++=======+=======+=======+=======+
|   0   ||   0   |   1   |   x   | x + 1 |
+-------++-------+-------+-------+-------+
|   1   ||   1   |   0   | x + 1 |   x   |
+-------++-------+-------+-------+-------+
|   x   ||   x   | x + 1 |   0   |   1   |
+-------++-------+-------+-------+-------+
| x + 1 || x + 1 |   x   |   1   |   0   |
+-------++-------+-------+-------+-------+

Multiplication Table for GF(4)
+-------++---+-------+-------+-------+
|   *   || 0 |   1   |   x   | x + 1 |
+=======++===+=======+=======+=======+
|   0   || 0 |   0   |   0   |   0   |
+-------++---+-------+-------+-------+
|   1   || 0 |   1   |   x   | x + 1 |
+-------++---+-------+-------+-------+
|   x   || 0 |   x   | x + 1 |   1   |
+-------++---+-------+-------+-------+
| x + 1 || 0 | x + 1 |   1   |   x   |
+-------++---+-------+-------+-------+