This was raised at Ask Sage question 55698.

Number fields have an iterator to yield all elements of bounded global height. This is used in an incorrect way to enumerate points of bounded height on projective space: in schemes.projective.projective_space the iterator points_of_bounded_height appears to iterate over all points whose projective coordinates all have height less than the given bound -- this is not just wrong, it is not well-defined. Similarly, in schemes.projective.projective_point the global height of a point is incorrectly implemented as the max of the heights of its coordinates -- again, not well defined.

CC: @slel @EnderWannabe

Component: number theory

Keywords: projective height

Author: Jieao Song, Frédéric Chapoton

Branch: 71e63df

Reviewer: Alexander Galarraga

Issue created by migration from https://trac.sagemath.org/ticket/31400