Merge branch 'zero_height' into height_bound

src/sage/rings/polynomial/multi_polynomial_element.py

@@ -69,7 +69,7 @@
 from sage.rings.fraction_field import FractionField
 from sage.rings.number_field.order import is_NumberFieldOrder
 from sage.categories.number_fields import NumberFields
-
+from sage.rings.real_mpfr import RealField
 
 def is_MPolynomial(x):
     return isinstance(x, MPolynomial)
@@ -1023,14 +1023,14 @@ def global_height(self, prec=None):
             sage: R.<x,y> = PolynomialRing(QQ, implementation='generic')
             sage: f = 0*x*y
             sage: f.global_height()
-            0
+            0.000000000000000
         """
-        if self.is_zero():
-            return 0
-
         if prec is None:
             prec = 53
 
+        if self.is_zero():
+            return RealField(prec).zero()
+
         from sage.rings.qqbar import QQbar, number_field_elements_from_algebraics
 
         K = self.base_ring()

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -247,6 +247,7 @@ from sage.structure.factorization import Factorization
 from sage.structure.sequence import Sequence
 
 from sage.rings.fraction_field import FractionField
+from sage.rings.all import RealField
 
 from sage.interfaces.singular import singular as singular_default, is_SingularElement, SingularElement
 from sage.interfaces.macaulay2 import macaulay2 as macaulay2_default, is_Macaulay2Element
@@ -5553,14 +5554,14 @@ cdef class MPolynomial_libsingular(MPolynomial):
             sage: R.<x,y> = QQ[]
             sage: f = 0*x*y
             sage: f.global_height()
-            0
+            0.000000000000000
         """
-        if self.is_zero():
-            return 0
-
         if prec is None:
             prec = 53
 
+        if self.is_zero():
+            return RealField(prec).zero()
+
         K = self.base_ring()
         if K in NumberFields() or is_NumberFieldOrder(K):
             f = self

src/sage/rings/polynomial/polynomial_element.pyx

@@ -5807,14 +5807,14 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: R.<x> = QQ[]
             sage: f = 0*x
             sage: f.global_height()
-            0
+            0.000000000000000
         """
-        if self.is_zero():
-            return 0
-
         if prec is None:
             prec = 53
 
+        if self.is_zero():
+            return RealField(prec).zero()
+
         from sage.rings.qqbar import QQbar, number_field_elements_from_algebraics
 
         K = self.base_ring()