2

I will provide some context on the problem if necessary. I've thought about this problem, but cannot seem to see why SageMath wont solve it. I am asking this question here as I think it has more a place here than the mathematics StackExchange.

When I run this code, it just returns/shows the equations I have put in. I know there is a solution to these equations, but I have no idea why it wont solve them.

Even running this simple code gives the same output:

var('a b c d e f g h i')
equations=solve([a*b+a*c+b*c==0,c*d+a*e+b*f==1,c*g+a*h+b*i==0,b*d+c*e+a*f==0,d*e+d*f+e*f==0,f*g+d*h+e*i==1,b*g+c*h+a*i==1,e*g+f*h+d*i==0,g*h+g*i+h*i==0],a,b,c,d,e,f,g,h,i)
show(equations)

Output:

[a*b + a*c + b*c == 0, b*d + c*e + a*f == 0, c*d + a*e + b*f == 1, d*e + d*f + e*f == 0, b*g + c*h + a*i == 1, c*g + a*h + b*i == 0, e*g + f*h + d*i == 0, f*g + d*h + e*i == 1, g*h + g*i + h*i == 0]
Patrick Lewis
  • 83
  • 1
  • 1
  • 10
  • Wow, that is a pretty non-linear set of equations. Sage is just giving you the originals back because it doesn't have a closed form for them. Are you looking for a symbolic solution, integer solutions, ... ? I'm kind of skeptical there is a nice closed form, so maybe you want something more specific in terms of the domain of solution. – kcrisman Apr 24 '18 at 01:46
  • I'm looking for a matrix solution to the equation of the form, PXP(dagger) = X. So I know the only solution to this is the identity, a,e,i=1, the rest zero. The exact problem I'm setting up is that I have some general matrix, P, and the Pauli-X matrix. I then equate it to X^2 and X^3 and so on, and looking for solutions which are permutation matrices. I hope this helps, if not, please ask. – Patrick Lewis Apr 25 '18 at 21:01
  • I do admit, I haven't taken any particular advanced classes in SageMath - if there is a way to specify that the solution domain is {0,1} that may make this solvable. However, I'm unsure how to do this. – Patrick Lewis Apr 25 '18 at 22:16
  • Wait, are these matrices over the field with two elements? Then there are totally different methods to solve them (I don't recall exact commands). Or do you just mean they are only 0,1 but not 1+1=0? Maybe a MILP might help you http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/mip.html – kcrisman Apr 28 '18 at 04:07

0 Answers0