Skip to content

[Merged by Bors] - chore(Charpoly/Disc): use nontriviality to drop a Nontrivial assumption #35117

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Closed
urkud wants to merge 4 commits into from
+8 −8
Closed

[Merged by Bors] - chore(Charpoly/Disc): use nontriviality to drop a Nontrivial assumption #35117

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
4 commits
Select commit Hold shift + click to select a range
de18b50
chore(Charpoly/Disc): use `nontriviality` to drop a `Nontrivial` assu…
urkud Feb 11, 2026
603eb09
Update Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup/FinTwo.lean
urkud Feb 12, 2026
abb53c1
Update Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup/FinTwo.lean
urkud Feb 12, 2026
35cd860
Merge branch 'master' into nontriviality
urkud Feb 12, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
3 changes: 2 additions & 1 deletion Mathlib/LinearAlgebra/Matrix/Charpoly/Disc.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -19,14 +19,15 @@ open Polynomial

namespace Matrix

variable {R n : Type*} [CommRing R] [Nontrivial R] [Fintype n] [DecidableEq n]
variable {R n : Type*} [CommRing R] [Fintype n] [DecidableEq n]

/-- The discriminant of a matrix is defined to be the discriminant of its characteristic
polynomial. -/
noncomputable def discr (A : Matrix n n R) : R := A.charpoly.discr

lemma discr_of_card_eq_two (A : Matrix n n R) (hn : Fintype.card n = 2) :
A.discr = A.trace ^ 2 - 4 * A.det := by
nontriviality R
rw [discr, Polynomial.discr_of_degree_eq_two (by simp; norm_cast)]
simp [A.charpoly_of_card_eq_two hn]

Expand Down
13 changes: 6 additions & 7 deletions Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup/FinTwo.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@ namespace Matrix

section CommRing

variable {R : Type*} [CommRing R] [Nontrivial R] (m : Matrix (Fin 2) (Fin 2) R) (g : GL (Fin 2) R)
variable {R : Type*} [CommRing R] (m : Matrix (Fin 2) (Fin 2) R) (g : GL (Fin 2) R)

/-- A `2 × 2` matrix is *parabolic* if it is non-scalar and its discriminant is 0. -/
def IsParabolic : Prop := m ∉ Set.range (scalar _) ∧ m.discr = 0
Expand Down Expand Up @@ -115,10 +115,9 @@ lemma isParabolic_iff_exists [NeZero (2 : K)] :

end Field

section LinearOrderedRing
section Preorder

variable {R : Type*} [CommRing R] [Nontrivial R] [Preorder R]
(m : Matrix (Fin 2) (Fin 2) R) (g : GL (Fin 2) R)
variable {R : Type*} [CommRing R] [Preorder R] (m : Matrix (Fin 2) (Fin 2) R) (g : GL (Fin 2) R)

/-- A `2 × 2` matrix is *hyperbolic* if its discriminant is strictly positive. -/
def IsHyperbolic : Prop := 0 < m.discr
Expand All @@ -140,7 +139,7 @@ lemma isElliptic_conj_iff : (g.val * m * g.val⁻¹).IsElliptic ↔ m.IsElliptic
lemma isElliptic_conj'_iff : (g.val⁻¹ * m * g.val).IsElliptic ↔ m.IsElliptic := by
simpa using isElliptic_conj_iff g⁻¹

end LinearOrderedRing
end Preorder

namespace GeneralLinearGroup

Expand All @@ -166,11 +165,11 @@ variable {R K : Type*} [CommRing R] [Field K]
/-- Synonym of `Matrix.IsParabolic`, for dot-notation. -/
abbrev IsParabolic (g : GL (Fin 2) R) : Prop := g.val.IsParabolic

@[simp] lemma isParabolic_conj_iff [Nontrivial R] (g h : GL (Fin 2) R) :
@[simp] lemma isParabolic_conj_iff (g h : GL (Fin 2) R) :
IsParabolic (g * h * g⁻¹) ↔ IsParabolic h := by
simp [IsParabolic]

@[simp] lemma isParabolic_conj_iff' [Nontrivial R] (g h : GL (Fin 2) R) :
@[simp] lemma isParabolic_conj_iff' (g h : GL (Fin 2) R) :
IsParabolic (g⁻¹ * h * g) ↔ IsParabolic h := by
simp [IsParabolic]

Expand Down