exposed root isolation algorithm in the API

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

src/api/python/z3num.py

@@ -505,6 +505,34 @@ def eval_sign_at(p, vs):
     for i in range(num):
         _vs[i] = vs[i].ast
     return Z3_algebraic_eval(p.ctx_ref(), p.as_ast(), num, _vs)
+
+def isolate_roots(p, vs=[]):
+    """
+    Given a multivariate polynomial p(x_0, ..., x_{n-1}, x_n), returns the 
+    roots of the univariate polynomial p(vs[0], ..., vs[len(vs)-1], x_n).
+       
+    Remarks:
+    * p is a Z3 expression that contains only arithmetic terms and free variables.
+    * forall i in [0, n) vs is a numeral.
+    
+    The result is a list of numerals
+
+    >>> x0 = RealVar(0)
+    >>> isolate_roots(x0**5 - x0 - 1)
+    [1.1673039782?]
+    >>> x1 = RealVar(1)
+    >>> isolate_roots(x0**2 - x1**4 - 1, [ Numeral(Sqrt(3)) ])
+    [-1.1892071150?, 1.1892071150?]
+    >>> x2 = RealVar(2)
+    >>> isolate_roots(x2**2 + x0 - x1, [ Numeral(Sqrt(3)), Numeral(Sqrt(2)) ])
+    []
+    """
+    num = len(vs)
+    _vs = (Ast * num)()
+    for i in range(num):
+        _vs[i] = vs[i].ast
+    _roots = AstVector(Z3_algebraic_roots(p.ctx_ref(), p.as_ast(), num, _vs), p.ctx)
+    return [ Numeral(r) for r in _roots ]
         
 if __name__ == "__main__":
     import doctest