Theorems · Definition · linear algebra
Module.Oriented.positiveOrientation
{R : Type u_1} →
{inst : CommSemiring R} →
{inst_1 : PartialOrder R} →
{inst_2 : IsStrictOrderedRing R} →
{M : Type u_2} →
{inst_3 : AddCommMonoid M} →
{inst_4 : Module R M} → {ι : Type u_4} → [self : Module.Oriented R M ι] → Orientation R M ιFix a positive orientation.
- Defined in
- Mathlib.LinearAlgebra.Orientation
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Module.Oriented
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Orientationstatement · cited by 360
- Module.Orientedstatement and proof · cited by 190
Cited by16
Results whose statement or proof uses this declaration.
- EuclideanGeometry.oproof · cited by 48
- Orientation.eq_or_eq_neg_of_isEmptystatement · cited by 6
- Orientation.volumeForm_neg_orientationproof · cited by 6
- Orientation.volumeForm_zero_posstatement and proof · cited by 6
- Orientation.volumeForm_defstatement and proof · cited by 4
- Orientation.volumeForm_robustproof · cited by 4
- Orientation.volumeForm_robust'proof · cited by 3
- Orientation.abs_volumeForm_apply_leproof · cited by 2
- Orientation.volumeForm_mapproof · cited by 2
- Module.Basis.orientation_isEmptystatement and proof · cited by 2
- Orientation.abs_volumeForm_apply_of_pairwise_orthogonalproof · cited by 1
- Orientation.volumeForm_robust_negproof · cited by 1