Theorems · Theorem · number theory

QuadraticMap.apply_linearCombination

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : AddCommGroup N] [inst_3 : Module R M] [inst_4 : Module R N] [inst_5 : DecidableEq ι]
  (Q : QuadraticMap R M N) {g : ι → M} (l : ι →₀ R),
  Q ((Finsupp.linearCombination R g) l) =
    (Finsupp.linearCombination R (⇑Q ∘ g)) (l * l) +
      ∑ p ∈ l.support.sym2 with ¬p.IsDiag, (Sym2.map (⇑l) p).mul • QuadraticMap.polarSym2 (⇑Q) (Sym2.map g p)

The quadratic version of Finsupp.apply_linearCombination.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Basis

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleDecidableEq