Check if it's a totally real number field

diofant/core/numbers.py

@@ -1854,6 +1854,9 @@ def __new__(cls, expr, coeffs=(1, 0), alias=None, **kwargs):
 
         return obj
 
+    def _eval_is_real(self):
+        return self.root.is_real
+
     @property
     def free_symbols(self):
         return set()

diofant/domains/algebraicfield.py

@@ -127,6 +127,10 @@ def is_nonnegative(self, a):
         """Returns True if ``a`` is non-negative. """
         return self.domain.is_nonnegative(a.LC())
 
+    @property
+    def is_real(self):
+        return self.ext.is_real
+
 
 class AlgebraicElement(DomainElement, CantSympify):
     """Dense Algebraic Number Polynomials over a field. """

diofant/domains/tests/test_domains.py

@@ -676,6 +676,11 @@ def test_Domain__algebraic_field():
 
     assert alg.characteristic() == 0
 
+    assert alg.is_real is True
+
+    alg = QQ.algebraic_field(I)
+    assert alg.is_real is False
+
 
 def test_PolynomialRing_from_FractionField():
     F,  x, y = field("x,y", ZZ)