# Linear programming with a strange result

I have encoutered a strange behavior in solving a linear program.

def sol_zero_sum_game(M=matrix([[1,-1], [-1,1]]),code=1) :
dim = M.nrows()
U=ones_matrix(dim,dim)
zsg=MixedIntegerLinearProgram(maximization=False, solver="GLPK")
x=zsg.new_variable(real=True,nonnegative=True, indices=[0..dim-1])
minM=min(min(M))
Id= identity_matrix(dim)
M1=(abs(minM)+1)*U+M
Bzsgl=M1*x
zsg.set_objective(sum(x[i] for i in range(dim)))
zsg.solve()
xx=zsg.get_values(x)
#show(xx)
for i in range(0,dim) :
if code==1 :
return zsg.show()
if code==2 :
return xx


The above code can display the program for the following G matrix :

G=matrix([[1,-1], [-1,1]])
sol_zero_sum_game(G,1)


The solution is given by :

G=matrix([[1,-1], [-1,1]])
sol_zero_sum_game(G,2)


which gives {0: 0.0, 1: 0.0} as a solution. But this is obviously false since after substitution of $(0,0)$ in the constrains it doesn't work. As this is the formalisation of a game I know that the solution is $(0.25, 0.25)$ as confirmed by an other software LIPS (see the screen capture below). I have certainly made a mistake but I can't see where. Thanks for help.

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After a long time looking at my code I have found that the constraints were defined after calling solve

def sol_zero_sum_game(M=matrix([[1,-1], [-1,1]]),code=1) :
dim = M.nrows()
U=ones_matrix(dim,dim)
zsg=MixedIntegerLinearProgram(maximization=False, solver="GLPK")
x=zsg.new_variable(real=True,nonnegative=True, indices=[0..dim-1])
minM=min(min(M))
Id= identity_matrix(dim)
M1=(abs(minM)+1)*U+M
Bzsgl=M1*x
zsg.set_objective(sum(x[i] for i in range(dim)))
#show(xx)
for i in range(0,dim) :
zsg.solve()
xx=zsg.get_values(x)
if code==1 :
return zsg.show()
if code==2 :
return xx

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