An arbitrary point in the projective line P1(K) may be given in homogeneous coordinates by a pair
of points in K which are not both zero. Two such pairs are equal if they differ by an overall (nonzero) factor λ:
The line K may be identified with the subset of P1(K) given by
This subset covers all points in P1(K) except one: the point at infinity, which may be given as
Correspondingly, arithmetic on K may be extended to P1(K) when both sides are defined:
Read more about this topic: Projective Line
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