Ways of using(assigning) variables in Sage

I need to test an n-variable Boolean Function f = f(x0,...,xn-1). I need to fix x0, then run some tests for the g1 = f(x1,...,xn-1), then fix x1 and so on. The problem is that I don't really understand how to do it with Sage.

At first, I tried to create a vector of values, that controls "fixing" of the variables


R.<x0,x1,x2,x3> = BooleanPolynomialRing()

v = [None,1,None, 0]

if v[0] != None:
    x0=v[0]
if v[1] != None:
    x1=v[1]
if v[2] != None:
    x2=v[2]
if v[3] != None:
    x3=v[3]

f = BooleanFunction(x0+x3+x0*x1+x0*x1*x2)


print(f.algebraic_normal_form())

output:x0*x2

This works fine, but it doesn't fit my task because I want to be able to automate the fixing process. I want to replace the "if"s with a loop, but in this case, I don't know how to address variables inside the loop using indexes.

I'm new to Sage so I would appreciate any advice!

1 answer

  • answered 2020-11-21 23:42 John Palmieri

    I'm not sure what BooleanFunction is, but:

    sage: R.<x0,x1,x2,x3> = BooleanPolynomialRing()
    

    If at this point you do something like x1=1, then x1 is no longer a generator of this ring, so let's try to avoid that.

    sage: f = x0+x3+x0*x1+x0*x1*x2 # f is in R
    sage: f.substitute({x1: 1})
    x0*x2 + x3
    

    I think what you want is a good way to carry out the substitute part of this. A helpful observation: you can convert strings to variable names:

    sage: R('x0')
    x0
    

    So:

    sage: d = {}                                                                                                            
    sage: for i in range(len(v)): 
    ....:     if v[i] is not None: 
    ....:         d[R('x' + str(i))] = v[i] 
    ....:                                                                                                                   
    sage: d                                                                                                                 
    {x1: 1, x3: 0}
    sage: f.substitute(d)
    x0*x2