Add new example

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

examples/python/complex/complex.py

@@ -0,0 +1,110 @@
+############################################
+# Copyright (c) 2012 Microsoft Corporation
+# 
+# Complex numbers in Z3
+# See http://research.microsoft.com/en-us/um/people/leonardo/blog/2013/01/26/complex.html 
+#
+# Author: Leonardo de Moura (leonardo)
+############################################
+from z3 import *
+
+def _to_complex(a):
+    if isinstance(a, ComplexExpr):
+        return a
+    else:
+        return ComplexExpr(a, RealVal(0))
+
+def _is_zero(a):
+    return (isinstance(a, int) and a == 0) or (is_rational_value(a) and a.numerator_as_long() == 0)
+
+class ComplexExpr:
+    def __init__(self, r, i):
+        self.r = r
+        self.i = i
+
+    def __add__(self, other):
+        other = _to_complex(other)
+        return ComplexExpr(self.r + other.r, self.i + other.i)
+
+    def __radd__(self, other):
+        other = _to_complex(other)
+        return ComplexExpr(other.r + self.r, other.i + self.i)
+
+    def __sub__(self, other):
+        other = _to_complex(other)
+        return ComplexExpr(self.r - other.r, self.i - other.i)
+
+    def __rsub__(self, other):
+        other = _to_complex(other)
+        return ComplexExpr(other.r - self.r, other.i - self.i)
+
+    def __mul__(self, other):
+        other = _to_complex(other)
+        return ComplexExpr(self.r*other.r - self.i*other.i, self.r*other.i + self.i*other.r)
+
+    def __mul__(self, other):
+        other = _to_complex(other)
+        return ComplexExpr(other.r*self.r - other.i*self.i, other.i*self.r + other.r*self.i)
+
+    def inv(self):
+        den = self.r*self.r + self.i*self.i
+        return ComplexExpr(self.r/den, -self.i/den)
+
+    def __div__(self, other):
+        inv_other = _to_complex(other).inv()
+        return self.__mul__(inv_other)
+
+    def __rdiv__(self, other):
+        other = _to_complex(other)
+        return self.inv().__mul__(other)
+
+    def __eq__(self, other):
+        other = _to_complex(other)
+        return And(self.r == other.r, self.i == other.i)
+
+    def __neq__(self, other):
+        return Not(self.__eq__(other))
+
+    def __pow__(self, k):
+        
+
+    def simplify(self):
+        return ComplexExpr(simplify(self.r), simplify(self.i))
+
+    def repr_i(self):
+        if is_rational_value(self.i):
+            return "%s*I" % self.i
+        else:
+            return "(%s)*I" % str(self.i)
+
+    def __repr__(self):
+        if _is_zero(self.i):
+            return str(self.r)
+        elif _is_zero(self.r):
+            return self.repr_i()
+        else:
+            return "%s + %s" % (self.r, self.repr_i())
+
+def Complex(a):
+    return ComplexExpr(Real('%s.r' % a), Real('%s.i' % a))
+I = ComplexExpr(RealVal(0), RealVal(1))
+
+def evaluate_cexpr(m, e):
+    return ComplexExpr(m[e.r], m[e.i])
+
+x = Complex("x")
+s = Tactic('qfnra-nlsat').solver()
+s.add(x*x == -2)
+print(s)
+print(s.check())
+m = s.model()
+print('x = %s' % evaluate_cexpr(m, x))
+print((evaluate_cexpr(m,x)*evaluate_cexpr(m,x)).simplify())
+s.add(x.i != -1)
+print(s)
+print(s.check())
+print(s.model())
+s.add(x.i != 1)
+print(s.check())
+# print(s.model())
+print (3 + I)^2/(5 - I)