Linear Programming

edit

I wonder if there is not a little display bug inside the SageMath linear program since the display of the result here is given before the display of the program (for some other programs it is given inside).

# Nombre de contraintes et de variables.
nmd, mmd = 10, 6
# Coefficients pour chaque contrainte.
coeffs = [(250, 770, 360, 190, 230, -1),
          (0, 0, 0, 0, 0, 1),
          (31, 44, 14, 27, 3, 0),
          (480, 1770, 800, 580, 160, 0),
          (1, 0, 0, 0, 0, 0),
          (0, 1, 0, 0, 0, 0),
          (0, 0, 1, 0, 0, 0),
          (0, 0, 0, 1, 0, 0),
          (0, 0, 0, 0, 1, 0),
          (0, 0, 0, 0, 0, 1)]
# Matrice des contraintes.
Amd = matrix(nmd, mmd, coeffs)
# Bornes inférieures pour les contraintes.
bmdmin = [0, 600, 30, 0, 0, 0, 0, 0, 0]
# Bornes supérieures pour les  contraintes (oo = infini).
bmdmax = [0, 900, 1000, oo, oo, oo, oo, oo, oo, oo]
# Visualisons.
show(LatexExpr("A="), Amd)
show(LatexExpr("bmin="), bmdmin)
show(LatexExpr("bmax="), bmdmax)
# On crée le programme de maximisation.
md = MixedIntegerLinearProgram(maximization=False, solver="GLPK")
# Nouvelles variables: x_0 ... x_2; 'integer' dit si variables à valeurs entières
x = md.new_variable(integer=False, nonnegative=True, indices=[0 .. mmd - 1])
# Fonction linéaire pour les contraintes.
Bmd = Amd * x
# On fixe l'objectif.
md.set_objective(1.2*x[0] + 4.5*x[1] + 3.7*x[2] + 6.3*x[3] + 3.2*x[4])
# On construit les contraintes avec leurs bornes.
for i in range(0,4):
    md.add_constraint(Bmd[i], min=bmdmin[i], max=bmdmax[i])
md.show()
md.solve()
md.get_values(x)
xmd = md.get_values(x)
# Le résultat.
show(xmd)

Output:

𝐴=(...)
𝑏𝑚𝑖𝑛=[0,600,30,0,0,0,0,0,0]
𝑏𝑚𝑎𝑥=[0,900,1000,+∞,+∞,+∞,+∞,+∞,+∞,+∞]

Minimization:
  1.2 x_0 + 4.5 x_1 + 3.7 x_2 + 6.3 x_3 + 3.2 x_4 

Constraints:
  0.0 <= 250.0 x_0 + 770.0 x_1 + 360.0 x_2 + 190.0 x_3 + 230.0 x_4 - x_5 <= 0.0
  600.0 <= x_5 <= 900.0
  30.0 <= 31.0 x_0 + 44.0 x_1 + 14.0 x_2 + 27.0 x_3 + 3.0 x_4 <= 1000.0
  0.0 <= 480.0 x_0 + 1770.0 x_1 + 800.0 x_2 + 580.0 x_3 + 160.0 x_4 <= inf
Variables:
  x_0 is a continuous variable (min=0.0, max=+oo)
  x_1 is a continuous variable (min=0.0, max=+oo)
  x_2 is a continuous variable (min=0.0, max=+oo)
  x_3 is a continuous variable (min=0.0, max=+oo)
  x_4 is a continuous variable (min=0.0, max=+oo)
  x_5 is a continuous variable (min=0.0, max=+oo)

{0:2.4000000000000004,1:0.0,2:0.0,3:0.0,4:0.0,5:600.0000000000001}

Of course I am aware that without the show() command there is no problem. But, for uniformity of presentation I need this command. As I could call it in an other cell the problem an be circumvented. But for economic reasons I would prefer to have the code and the result in the same cell. Nevertheless, this is just a remark.

Edit to address a comment by slelievre.

Inside a notebook this works perfectly. But inside a "Sage Cell" here is the result:

𝐴=(...)
𝑏𝑚𝑖𝑛=[0,600,30,0,0,0,0,0,0]
𝑏𝑚𝑎𝑥=[0,900,1000,+∞,+∞,+∞,+∞,+∞,+∞,+∞]

{0:2.4000000000000004,1:0.0,2:0.0,3:0.0,4:0.0,5:600.0000000000001}

Minimization:
  1.2 x_0 + 4.5 x_1 + 3.7 x_2 + 6.3 x_3 + 3.2 x_4 

Constraints:
  0.0 <= 250.0 x_0 + 770.0 x_1 + 360.0 x_2 + 190.0 x_3 + 230.0 x_4 - x_5 <= 0.0
  600.0 <= x_5 <= 900.0
  30.0 <= 31.0 x_0 + 44.0 x_1 + 14.0 x_2 + 27.0 x_3 + 3.0 x_4 <= 1000.0
  0.0 <= 480.0 x_0 + 1770.0 x_1 + 800.0 x_2 + 580.0 x_3 + 160.0 x_4 <= inf
Variables:
  x_0 is a continuous variable (min=0.0, max=+oo)
  x_1 is a continuous variable (min=0.0, max=+oo)
  x_2 is a continuous variable (min=0.0, max=+oo)
  x_3 is a continuous variable (min=0.0, max=+oo)
  x_4 is a continuous variable (min=0.0, max=+oo)
  x_5 is a continuous variable (min=0.0, max=+oo)

That is, the result, {0:2.40...,1:0.0,2:0.0,3:0.0,4:0.0,5:600.00...}, is printed before the program's output, and sometimes inside it.