Theorems · Definition · ring theory
Finsupp.sum
{α : Type u_1} → {M : Type u_8} → {N : Type u_10} → [inst : Zero M] → [AddCommMonoid N] → (α →₀ M) → (α → M → N) → Nsum f g is the sum of g a (f a) over the support of f.
- Cited by
- 481 results in Mathlib
- Foundations
- Depth 59 from the axioms, rests on 846 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Finsupp.supportproof · cited by 828
Cited by521
Results whose statement or proof uses this declaration.
- Finsupp.mapDomainproof · cited by 168
- Finsupp.sum_single_indexstatement · cited by 130
- MvPolynomial.eval₂proof · cited by 103
- MvPolynomial.totalDegreeproof · cited by 76
- Matrix.PosSemidefproof · cited by 76
- Matrix.PosDefproof · cited by 68
- Algebra.Generators.compproof · cited by 52
- SkewMonoidAlgebra.sumproof · cited by 46
- Finsupp.toMultisetproof · cited by 44
- map_finsuppSumstatement · cited by 43
- Finsupp.lsumproof · cited by 40
- Finsupp.linearCombination_applystatement · cited by 38
Showing the 200 most cited of 521.