New example: Menger sponge, to be plotted

[linpy.git] / examples / squares.py

diff --git a/examples/squares.py b/examples/squares.py
index 898f765..e00821e 100755 (executable)
--- a/examples/squares.py
+++ b/examples/squares.py
@@ -2,53 +2,77 @@
 
 from pypol import *
 
-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(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
-
+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) 
-u = Polyhedron([])
+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)
+
+
+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('u =', u) #print correct square
+print('universe =', universe) #print correct square
 print()
-print('¬sq1 =', ~sq1) #test compliment
+print('¬sq1 =', ~sq1) #test complement
 print()
 print('sq1 + sq1 =', sq1 + sq2) #test addition
-print('sq1 + sq2 =', Polyhedron(sq1 + sq2))
-print('sq1 - sq1 =', u - u)
+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))
-print('sq1 - sq1 =', Polyhedron(sq1 - sq1)) #test polyhedreon 
+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('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('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?:', u.isuniverse()) #test if square is universe
+print('is u universe?:', universe.isuniverse()) #test if square is universe
 print()
 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('lexographic min of sq1:', sq1.lexmin()) #test lexmin()
 print('lexographic max of sq1:', sq1.lexmax()) #test lexmin()
+print()
 print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
 print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
 print()
-print('Polyhedral hull of sq1 is:', sq1.polyhedral_hull())
+print('Polyhedral hull of sq1 + sq2 is:', q.aspolyhedron()) #test polyhedral hull
+print()
+print('is sq1 bounded?', sq1.isbounded()) #unbounded should return True
+print('is sq5 bounded?', sq5.isbounded()) #unbounded should return False
+print()
+print('sq6:', sq6)
+print('sq6 simplified:', sq6.sample())
+print()
+print(universe.project([x]))
+print('sq7 with out constraints involving y and a', sq7.project([a, z, x, y])) #drops dims that are passed
+print()
+print('sq1 has {} parameters'.format(sq1.num_parameters()))
+print()
+print('does sq1 constraints involve x?', sq1.involves_dims([x]))
+print()
+print('the verticies for s are:', p.vertices())
 print()
-print('is sq1 bounded?', sq1.isbounded())
-print('is sq5 bounded?', sq5.isbounded())
+print(p.plot())