mathlib documentation

data.finsupp.pointwise

The pointwise product on finsupp. #

TODO per issue #1864: We intend to remove the convolution product on finsupp, and define it only on a type synonym add_monoid_algebra. After we've done this, it would be good to make this the default product on finsupp.

Declarations about the pointwise product on finsupps #

@[instance]
def finsupp.has_mul {α : Type u₁} {β : Type u₂} [mul_zero_class β] :
has_mul →₀ β)

The product of f g : α →₀ β is the finitely supported function whose value at a is f a * g a.

Equations
@[simp]
theorem finsupp.mul_apply {α : Type u₁} {β : Type u₂} [mul_zero_class β] {g₁ g₂ : α →₀ β} {a : α} :
(g₁ * g₂) a = (g₁ a) * g₂ a
theorem finsupp.support_mul {α : Type u₁} {β : Type u₂} [mul_zero_class β] {g₁ g₂ : α →₀ β} :
(g₁ * g₂).support g₁.support g₂.support
@[instance]
def finsupp.mul_zero_class {α : Type u₁} {β : Type u₂} [mul_zero_class β] :
Equations
@[instance]
def finsupp.semigroup {α : Type u₁} {β : Type u₂} [semiring β] :
Equations
@[instance]
def finsupp.distrib {α : Type u₁} {β : Type u₂} [semiring β] :
distrib →₀ β)
Equations