Section Ratio.
Variable R : realFieldType.
Variable n : nat.
Implicit Types (v : (@Vector R n)).
Definition ratio v1 v2 :=
if [pick k : 'I_(n.+1) | v2 0 k != 0] is Some k
then v1 0 k / v2 0 k else 0.

Lemma ratioNr v1 v2 : ratio (- v1) v2 = - ratio v1 v2.