multi_polynomial_libsingular.pyx: global_height

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -5486,6 +5486,44 @@ cdef class MPolynomial_libsingular(MPolynomial):
             p = pNext(p)
         return coeffs
 
+    def global_height(self, prec=None):
+        """
+        Return the absolute logarithmic height of the polynomial.
+
+        INPUT:
+        - ``prec`` -- desired floating point precision (default:
+          default RealField precision).
+
+        OUTPUT:
+
+        - a real number.
+
+        EXAMPLES::
+        sage: R.<x,y> = PolynomialRing(QQbar)
+        sage: f = 3 * x^3 + 2 * x * y^2
+        sage: exp(f.global_height())
+        3
+        """
+        from sage.schemes.projective.projective_space import ProjectiveSpace
+        #from sage.schemes.projective.projective_morphism import _number_field_from_algebraics
+        from sage.rings.number_field.order import is_NumberFieldOrder
+        from sage.categories.number_fields import NumberFields
+        from sage.rings.qqbar import QQbar
+        if prec is None:
+            prec = 53
+
+        K = self.base_ring()
+        if K in NumberFields() or is_NumberFieldOrder(K):
+            f = self
+        #elif K is QQbar:
+        #    f = self._number_field_from_algebraics()
+        else:
+            raise TypeError("Must be over a Numberfield or a Numberfield Order or QQbar.")
+
+        P = ProjectiveSpace(K, f.number_of_terms()-1)
+        proj_point = P.point(f.coefficients())
+        return proj_point.global_height()
+
     def gradient(self):
         """
         Return a list of partial derivatives of this polynomial,