Theorems · Definition · ring theory
AddMonoidAlgebra.update
{R : Type u_1} → {M : Type u_4} → [inst : Semiring R] → M → R → AddMonoidAlgebra R M → AddMonoidAlgebra R MReplace the m-th coefficient of an element x of the monoid algebra by a given value r : R.
If r = 0, this is equal to x.erase m.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffproof · cited by 365
- Finsupp.updateproof · cited by 52
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.updateproof · cited by 10
- AddMonoidAlgebra.coeff_updatestatement · cited by 0
- AddMonoidAlgebra.ofCoeff_updatestatement · cited by 0