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!
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
The code can now be made more compact in two ways.
Call x
the list of generators and use x[i]
rather than R('x' + str(i)')
:
sage: R.<x0, x1, x2, x3> = BooleanPolynomialRing()
sage: x = R.gens()
sage: x[0]*x[3] + x[1]*x[2]*x[3]
x0*x3 + x1*x2*x3
Use comprehension syntax rather than empty dictionary and for loop:
sage: f = x0 + x3 + x0*x1 + x0*x1*x2
sage: v = [None, 1, None, 0]
sage: f.subs({x[i]: vi for i, vi in enumerate(v) if vi is not None})
x0*x2