Remove license and add to doc examples

[linpy.git] / examples / squares.py

diff --git a/examples/squares.py b/examples/squares.py
index 7f1aa30..98e2ca8 100755 (executable)
--- a/examples/squares.py
+++ b/examples/squares.py
@@ -1,21 +1,87 @@
 #!/usr/bin/env python3
 
-from pypol import *
+from linpy import *
+import matplotlib.pyplot as plt
+from matplotlib import pylab
 
-x, y = symbols('x y')
+a, x, y, z = symbols('a x y z')
 
 sq1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
 sq2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
+sq3 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3)
+sq4 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 2)
+sq5 = Le(1, x) & Le(x, 2) & Le(1, y)
+sq6 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 3)
+sq7 = Le(0, x) & Le(x, 2) & Le(0, y) & Eq(z, 2) & Le(a, 3)
+p = Le(2*x+1, y) & Le(-2*x-1, y) & Le(y, 1)
 
-print('sq1 =', sq1)
-print('sq2 =', sq2)
+universe = Polyhedron([])
+q = sq1 - sq2
+e = Empty
+
+print('sq1 =', sq1) #print correct square
+print('sq2 =', sq2) #print correct square
+print('sq3 =', sq3) #print correct square
+print('sq4 =', sq4) #print correct square
+print('universe =', universe) #print correct square
+print()
+print('¬sq1 =', ~sq1) #test complement
+print()
+print('sq1 + sq1 =', sq1 + sq2) #test addition
+print('sq1 + sq2 =', Polyhedron(sq1 + sq2)) #test addition
+print()
+print('universe + universe =', universe + universe)#test addition
+print('universe - universe =', universe - universe) #test subtraction
+print()
+print('sq2 - sq1 =', sq2 - sq1) #test subtraction
+print('sq2 - sq1 =', Polyhedron(sq2 - sq1)) #test subtraction
+print('sq1 - sq1 =', Polyhedron(sq1 - sq1)) #test subtraction
+print()
+print('sq1 ∩ sq2 =', sq1 & sq2) #test intersection
+print('sq1 ∪ sq2 =', sq1 | sq2) #test union
+print()
+print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2)) # test convex union
+print()
+print('check if sq1 and sq2 disjoint:', sq1.isdisjoint(sq2)) #should return false
+print()
+print('sq1 disjoint:', sq1.disjoint()) #make disjoint
+print('sq2 disjoint:', sq2.disjoint()) #make disjoint
+print()
+print('is square 1 universe?:', sq1.isuniverse()) #test if square is universe
+print('is u universe?:', universe.isuniverse()) #test if square is universe
 print()
-print('¬sq1 =', ~sq1)
+print('is sq1 a subset of sq2?:', sq1.issubset(sq2)) #test issubset()
+print('is sq4 less than sq3?:', sq4.__lt__(sq3)) # test lt(), must be a strict subset
 print()
-print('sq1 - sq2 =', sq1 - sq2)
-print('sq1 - sq2 =', Polyhedron(sq1 - sq2))
+print('lexographic min of sq1:', sq1.lexmin()) #test lexmin()
+print('lexographic max of sq1:', sq1.lexmax()) #test lexmin()
 print()
-print('sq1 ∩ sq2 =', sq1 & sq2)
-print('sq1 ∪ sq2 =', sq1 | sq2)
+print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
+print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
 print()
-print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2))
+print('Polyhedral hull of sq1 + sq2 is:', q.aspolyhedron()) #test polyhedral hull
+print()
+print('is sq1 bounded?', sq1.isbounded()) #bounded should return True
+print('is sq5 bounded?', sq5.isbounded()) #unbounded should return False
+print()
+print('sq6:', sq6)
+print('sample Polyhedron from sq6:', sq6.sample())
+print()
+print('sq7 with out constraints involving y and a', sq7.project([a, z, x, y])) 
+print()
+print('the verticies for s are:', p.vertices())
+
+
+# plotting the intersection of two squares
+square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
+square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
+
+fig = plt.figure()
+plot = fig.add_subplot(1, 1, 1, aspect='equal')
+square1.plot(plot, facecolor='red', alpha=0.3)
+square2.plot(plot, facecolor='blue', alpha=0.3)
+
+squares = Polyhedron(square1 + square2)
+squares.plot(plot, facecolor='blue', alpha=0.3)
+
+pylab.show()