Suchetaaa / Boolean-Arithmetic-SAGE

Implementation of Boolean Arithmetic in SAGE math

Implementation of Boolean Arithmetic in SAGE math

Given Boolean polynomials in several variables in ANF form the code will return their addition, products, compositions and substitutions.

Running the Script:

1. Install sagemath via: https://doc.sagemath.org/html/en/installation/
2. Go to Scripts/
3. Run the main file using: sage BooleanFunctions.sage

Functions Implemented:

The various functions implemented and the formats the user is expected to follow while inputting functions.

1. Addition
   

Input

f = [1, [ [0], [3], [4,5], [6,7], [0,1,2,4] ] ] =  1 + x0 + x3 + x4*x5 + x6*x7 + x0*x1*x2*x4
g = [1, [ [0], [3], [4,2], [6,5], [0,2,4] ] ] =  1 + x0 + x3 + x4*x2 + x6*x5 + x0*x2*x4

Output

f + g = [0, [[0, 1, 2, 4], [0, 2, 4], [2, 4], [4, 5], [5, 6], [6, 7]]] =  x0*x1*x2*x4 + x0*x2*x4 + x2*x4 + x4*x5 + x5*x6 + x6*x7

2. Product
   

Input

f = [1, [ [3], [4,5] ] ] =  1 + x3 + x4*x5  
g = [1, [ [0], [4,2] ] ] =  1 + x0 + x4*x2

Output

f * g = [1, [[0, 4, 5], [2, 3, 4], [2, 4, 5], [0, 3], [2, 4], [4, 5], [0], [3]]] =  x0*x4*x5 + x2*x3*x4 + x2*x4*x5 + x0*x3 + x2*x4 + x4*x5 + x0 + x3 + 1

3. Composition
   

Input

f = [1, [ [0], [3], [4,5] ] ] =  1 + x0 + x3 + x4*x5 
g = [0, [ [0], [3], [4,2] ] ] =  x0 + x3 + x4*x2 
h(u, v) = [ 0, [ [0], [0,1] ] ] = u + uv

Output

h(f, g) = [1, [[0, 2, 4], [0, 4, 5], [2, 3, 4], [2, 4, 5], [3, 4, 5], [2, 4], [4, 5], [0], [3]]] =  x0*x2*x4 + x0*x4*x5 + x2*x3*x4 + x2*x4*x5 + x3*x4*x5 + x2*x4 + x4*x5 + x0 + x3 + 1

4. Substitution
   

Input

f = [1, [ [0], [3], [4,5], [6,7], [0,1,2,4] ] ] =  1 + x0 + x3 + x4*x5 + x6*x7 + x0*x1*x2*x4
t = [0, 3, 5] = x0*x3*x5

Output

f/t = [1, [[1, 2, 4], [6, 7], [4]]] =  x1*x2*x4 + x6*x7 + x4 + 1  

The Output are given in ANF form and Standard Form