Theorems · Theorem · number theory
QuadraticMap.pi_apply
∀ {ι : Type u_1} {R : Type u_2} {P : Type u_7} {Mᵢ : ι → Type u_8} [inst : CommSemiring R]
[inst_1 : (i : ι) → AddCommMonoid (Mᵢ i)] [inst_2 : AddCommMonoid P] [inst_3 : (i : ι) → Module R (Mᵢ i)]
[inst_4 : Module R P] [inst_5 : Fintype ι] (Q : (i : ι) → QuadraticMap R (Mᵢ i) P) (x : (i : ι) → Mᵢ i),
(QuadraticMap.pi Q) x = ∑ i, (Q i) (x i)- Defined in
- Mathlib.LinearAlgebra.QuadraticForm.Prod
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- QuadraticMapstatement and proof · cited by 262
- sum_applyproof · cited by 83
- LinearMap.projproof · cited by 71
- QuadraticMap.compproof · cited by 20
- QuadraticMap.pistatement · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- QuadraticMap.Ring.polar_piproof · cited by 1
- QuadraticMap.anisotropic_of_piproof · cited by 1
- QuadraticMap.pi_apply_singleproof · cited by 0
- QuadraticMap.posDef_pi_iffproof · cited by 0