data.mv_polynomial.invertible
⟷
Mathlib.Data.MvPolynomial.Invertible
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
-import Data.MvPolynomial.Basic
+import Algebra.MvPolynomial.Basic
import RingTheory.AlgebraTower
#align_import data.mv_polynomial.invertible from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
-import Mathbin.Data.MvPolynomial.Basic
-import Mathbin.RingTheory.AlgebraTower
+import Data.MvPolynomial.Basic
+import RingTheory.AlgebraTower
#align_import data.mv_polynomial.invertible from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.mv_polynomial.invertible
-! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.MvPolynomial.Basic
import Mathbin.RingTheory.AlgebraTower
+#align_import data.mv_polynomial.invertible from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"
+
/-!
# Invertible polynomials
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -24,11 +24,14 @@ invertible elements in the ring of polynomials.
open MvPolynomial
+#print MvPolynomial.invertibleC /-
noncomputable instance MvPolynomial.invertibleC (σ : Type _) {R : Type _} [CommSemiring R] (r : R)
[Invertible r] : Invertible (C r : MvPolynomial σ R) :=
Invertible.map (C : R →+* MvPolynomial σ R) _
#align mv_polynomial.invertible_C MvPolynomial.invertibleC
+-/
+#print MvPolynomial.invertibleCoeNat /-
/-- A natural number that is invertible when coerced to a commutative semiring `R`
is also invertible when coerced to any polynomial ring with rational coefficients.
@@ -37,4 +40,5 @@ noncomputable instance MvPolynomial.invertibleCoeNat (σ R : Type _) (p : ℕ) [
[Invertible (p : R)] : Invertible (p : MvPolynomial σ R) :=
IsScalarTower.invertibleAlgebraCoeNat R _ _
#align mv_polynomial.invertible_coe_nat MvPolynomial.invertibleCoeNat
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -24,23 +24,11 @@ invertible elements in the ring of polynomials.
open MvPolynomial
-/- warning: mv_polynomial.invertible_C -> MvPolynomial.invertibleC is a dubious translation:
-lean 3 declaration is
- forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (r : R) [_inst_2 : Invertible.{u2} R (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) r], Invertible.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulOneClass.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroOneClass.toMulOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (MulOneClass.toHasOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroOneClass.toMulOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
-but is expected to have type
- forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (r : R) [_inst_2 : Invertible.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) r], Invertible.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toOne.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.invertible_C MvPolynomial.invertibleCₓ'. -/
noncomputable instance MvPolynomial.invertibleC (σ : Type _) {R : Type _} [CommSemiring R] (r : R)
[Invertible r] : Invertible (C r : MvPolynomial σ R) :=
Invertible.map (C : R →+* MvPolynomial σ R) _
#align mv_polynomial.invertible_C MvPolynomial.invertibleC
-/- warning: mv_polynomial.invertible_coe_nat -> MvPolynomial.invertibleCoeNat is a dubious translation:
-lean 3 declaration is
- forall (σ : Type.{u1}) (R : Type.{u2}) (p : Nat) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Invertible.{u2} R (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u2} Nat R (CoeTCₓ.coe.{1, succ u2} Nat R (Nat.castCoe.{u2} R (AddMonoidWithOne.toNatCast.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) p)], Invertible.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddMonoidWithOne.toOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) ((fun (a : Type) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{1, max (succ u1) (succ u2)} a b] => self.0) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (HasLiftT.mk.{1, max (succ u1) (succ u2)} Nat (MvPolynomial.{u1, u2} σ R _inst_1) (CoeTCₓ.coe.{1, max (succ u1) (succ u2)} Nat (MvPolynomial.{u1, u2} σ R _inst_1) (Nat.castCoe.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoidWithOne.toNatCast.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))))) p)
-but is expected to have type
- forall (σ : Type.{u1}) (R : Type.{u2}) (p : Nat) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Invertible.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) p)], Invertible.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Nat.cast.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNatCast.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) p)
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.invertible_coe_nat MvPolynomial.invertibleCoeNatₓ'. -/
/-- A natural number that is invertible when coerced to a commutative semiring `R`
is also invertible when coerced to any polynomial ring with rational coefficients.
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -28,7 +28,7 @@ open MvPolynomial
lean 3 declaration is
forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (r : R) [_inst_2 : Invertible.{u2} R (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) r], Invertible.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulOneClass.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroOneClass.toMulOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (MulOneClass.toHasOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroOneClass.toMulOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
but is expected to have type
- forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (r : R) [_inst_2 : Invertible.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) r], Invertible.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toOne.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
+ forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (r : R) [_inst_2 : Invertible.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) r], Invertible.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toOne.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
Case conversion may be inaccurate. Consider using '#align mv_polynomial.invertible_C MvPolynomial.invertibleCₓ'. -/
noncomputable instance MvPolynomial.invertibleC (σ : Type _) {R : Type _} [CommSemiring R] (r : R)
[Invertible r] : Invertible (C r : MvPolynomial σ R) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
! This file was ported from Lean 3 source module data.mv_polynomial.invertible
-! leanprover-community/mathlib commit f6c030fea3c2809bb489bc8901f307bf6b4bf0c0
+! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.AlgebraTower
/-!
# Invertible polynomials
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file is a stub containing some basic facts about
invertible elements in the ring of polynomials.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c
@@ -21,11 +21,23 @@ invertible elements in the ring of polynomials.
open MvPolynomial
+/- warning: mv_polynomial.invertible_C -> MvPolynomial.invertibleC is a dubious translation:
+lean 3 declaration is
+ forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (r : R) [_inst_2 : Invertible.{u2} R (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) r], Invertible.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulOneClass.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroOneClass.toMulOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (MulOneClass.toHasOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroOneClass.toMulOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
+but is expected to have type
+ forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (r : R) [_inst_2 : Invertible.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) r], Invertible.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toOne.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.invertible_C MvPolynomial.invertibleCₓ'. -/
noncomputable instance MvPolynomial.invertibleC (σ : Type _) {R : Type _} [CommSemiring R] (r : R)
[Invertible r] : Invertible (C r : MvPolynomial σ R) :=
Invertible.map (C : R →+* MvPolynomial σ R) _
#align mv_polynomial.invertible_C MvPolynomial.invertibleC
+/- warning: mv_polynomial.invertible_coe_nat -> MvPolynomial.invertibleCoeNat is a dubious translation:
+lean 3 declaration is
+ forall (σ : Type.{u1}) (R : Type.{u2}) (p : Nat) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Invertible.{u2} R (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u2} Nat R (CoeTCₓ.coe.{1, succ u2} Nat R (Nat.castCoe.{u2} R (AddMonoidWithOne.toNatCast.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) p)], Invertible.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddMonoidWithOne.toOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) ((fun (a : Type) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{1, max (succ u1) (succ u2)} a b] => self.0) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (HasLiftT.mk.{1, max (succ u1) (succ u2)} Nat (MvPolynomial.{u1, u2} σ R _inst_1) (CoeTCₓ.coe.{1, max (succ u1) (succ u2)} Nat (MvPolynomial.{u1, u2} σ R _inst_1) (Nat.castCoe.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoidWithOne.toNatCast.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))))) p)
+but is expected to have type
+ forall (σ : Type.{u1}) (R : Type.{u2}) (p : Nat) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Invertible.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) p)], Invertible.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toOne.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Nat.cast.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNatCast.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.invertible_coe_nat MvPolynomial.invertibleCoeNatₓ'. -/
/-- A natural number that is invertible when coerced to a commutative semiring `R`
is also invertible when coerced to any polynomial ring with rational coefficients.
mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd
@@ -22,8 +22,8 @@ invertible elements in the ring of polynomials.
open MvPolynomial
noncomputable instance MvPolynomial.invertibleC (σ : Type _) {R : Type _} [CommSemiring R] (r : R)
- [Invertible r] : Invertible (c r : MvPolynomial σ R) :=
- Invertible.map (c : R →+* MvPolynomial σ R) _
+ [Invertible r] : Invertible (C r : MvPolynomial σ R) :=
+ Invertible.map (C : R →+* MvPolynomial σ R) _
#align mv_polynomial.invertible_C MvPolynomial.invertibleC
/-- A natural number that is invertible when coerced to a commutative semiring `R`
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Data
(#11751)
Polynomial
and MvPolynomial
are algebraic objects, hence should be under Algebra
(or at least not under Data
)
@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
-import Mathlib.Data.MvPolynomial.Basic
+import Mathlib.Algebra.MvPolynomial.Basic
import Mathlib.RingTheory.AlgebraTower
#align_import data.mv_polynomial.invertible from "leanprover-community/mathlib"@"f6c030fea3c2809bb489bc8901f307bf6b4bf0c0"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -18,7 +18,7 @@ invertible elements in the ring of polynomials.
open MvPolynomial
-noncomputable instance MvPolynomial.invertibleC (σ : Type _) {R : Type _} [CommSemiring R] (r : R)
+noncomputable instance MvPolynomial.invertibleC (σ : Type*) {R : Type*} [CommSemiring R] (r : R)
[Invertible r] : Invertible (C r : MvPolynomial σ R) :=
Invertible.map (C : R →+* MvPolynomial σ R) _
set_option linter.uppercaseLean3 false in
@@ -28,7 +28,7 @@ set_option linter.uppercaseLean3 false in
is also invertible when coerced to any polynomial ring with rational coefficients.
Short-cut for typeclass resolution. -/
-noncomputable instance MvPolynomial.invertibleCoeNat (σ R : Type _) (p : ℕ) [CommSemiring R]
+noncomputable instance MvPolynomial.invertibleCoeNat (σ R : Type*) (p : ℕ) [CommSemiring R]
[Invertible (p : R)] : Invertible (p : MvPolynomial σ R) :=
IsScalarTower.invertibleAlgebraCoeNat R _ _
#align mv_polynomial.invertible_coe_nat MvPolynomial.invertibleCoeNat
@@ -2,15 +2,12 @@
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.mv_polynomial.invertible
-! leanprover-community/mathlib commit f6c030fea3c2809bb489bc8901f307bf6b4bf0c0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.MvPolynomial.Basic
import Mathlib.RingTheory.AlgebraTower
+#align_import data.mv_polynomial.invertible from "leanprover-community/mathlib"@"f6c030fea3c2809bb489bc8901f307bf6b4bf0c0"
+
/-!
# Invertible polynomials
The unported dependencies are