Theorems · Definition · linear algebra

CliffordAlgebra.foldr

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : AddCommGroup M] →
          [inst_2 : AddCommGroup N] →
            [inst_3 : Module R M] →
              [inst_4 : Module R N] →
                (Q : QuadraticForm R M) →
                  (f : M →ₗ[R] N →ₗ[R] N) →
                    (∀ (m : M) (x : N), (f m) ((f m) x) = Q m • x) → N →ₗ[R] CliffordAlgebra Q →ₗ[R] N

Fold a bilinear map along the generators of a term of the clifford algebra, with the rule given by foldr Q f hf n (ι Q m * x) = f m (foldr Q f hf n x). For example, foldr f hf n (r • ι R u + ι R v * ι R w) = r • f u n + f v (f w n).

Defined in

Mathlib.LinearAlgebra.CliffordAlgebra.Fold

Cited by

18 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModule