Theorems · Definition · linear algebra

LinearMap.toMvPolynomial

{R : Type u_1} →
  {M₁ : Type u_2} →
    {M₂ : Type u_3} →
      {ι₁ : Type u_4} →
        {ι₂ : Type u_5} →
          [inst : CommRing R] →
            [inst_1 : AddCommGroup M₁] →
              [inst_2 : AddCommGroup M₂] →
                [inst_3 : Module R M₁] →
                  [inst_4 : Module R M₂] →
                    [Fintype ι₁] →
                      [Finite ι₂] →
                        [DecidableEq ι₁] →
                          Module.Basis ι₁ R M₁ → Module.Basis ι₂ R M₂ → (M₁ →ₗ[R] M₂) → ι₂ → MvPolynomial ι₁ R

Let f : M₁ →ₗ[R] M₂ be an R-linear map between modules M₁ and M₂ with bases b₁ and b₂ respectively. Then LinearMap.toMvPolynomial b₁ b₂ f is the family of multivariate polynomials over R that evaluates on an element x of M₁ (represented on the basis b₁) to the element f x of M₂ (represented on the basis b₂).

Defined in

Mathlib.Algebra.Module.LinearMap.Polynomial

Cited by

17 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleFintypeFiniteDecidableEq