examples/squares.py

   1 #!/usr/bin/env python3
   2
   3 from pypol import *
   4
   5 x, y = symbols('x y')
   6
   7 sq1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
   8 sq2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
   9
  10 sq3 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3)
  11 sq4 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 2)
  12 sq5 = Le(1, x) & Le(x, 2) & Le(1, y)
  13 u = Polyhedron([])
  14
  15 print('sq1 =', sq1) #print correct square
  16 print('sq2 =', sq2) #print correct square
  17 print('sq3 =', sq3) #print correct square
  18 print('sq4 =', sq4) #print correct square
  19 print('u =', u) #print correct square
  20 print()
  21 print('¬sq1 =', ~sq1) #test compliment
  22 print()
  23 print('sq1 + sq1 =', sq1 + sq2) #test addition
  24 print('sq1 + sq2 =', Polyhedron(sq1 + sq2))
  25 print('sq1 - sq1 =', u - u)
  26 print('sq2 - sq1 =', sq2 - sq1) #test subtraction
  27 print('sq2 - sq1 =', Polyhedron(sq2 - sq1))
  28 print('sq1 - sq1 =', Polyhedron(sq1 - sq1)) #test polyhedreon
  29 print()
  30 print('sq1 ∩ sq2 =', sq1 & sq2) #test intersection
  31 print('sq1 ∪ sq2 =', sq1 | sq2) #test union
  32 print()
  33 print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2)) #test convex union
  34 print()
  35 print('check if sq1 and sq2 disjoint:', sq1.isdisjoint(sq2)) #should return false
  36 print()
  37 print('sq1 disjoint:', sq1.disjoint()) #make disjoint
  38 print('sq2 disjoint:', sq2.disjoint()) #make disjoint
  39 print()
  40 print('is square 1 universe?:', sq1.isuniverse()) #test if square is universe
  41 print('is u universe?:', u.isuniverse()) #test if square is universe
  42 print()
  43 print('is sq1 a subset of sq2?:', sq1.issubset(sq2)) #test issubset()
  44 print('is sq4 less than sq3?:', sq4.__lt__(sq3)) # test lt(), must be a strict subset
  45 print()
  46 print('lexographic min of sq1:', sq1.lexmin()) #test lexmin()
  47 print('lexographic max of sq1:', sq1.lexmax()) #test lexmin()
  48 print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
  49 print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
  50 print()
  51 print('Polyhedral hull of sq1 is:', sq1.polyhedral_hull())
  52 print()
  53 print('is sq1 bounded?', sq1.isbounded())
  54 print('is sq5 bounded?', sq5.isbounded())