Theorems · Definition · ring theory
SkewPolynomial.update
{R : Type u_1} → [inst : Semiring R] → SkewPolynomial R → ℕ → R → SkewPolynomial RReplace the coefficient of a p : SkewPolynomial R at a given degree n : ℕ
by a given value a : R. If a = 0, this is equal to p.erase n
If p.natDegree < n and a ≠ 0, this increases the degree to n.
- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 64 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.
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
- Semiringstatement and proof · cited by 13,802
- Multiplicative.ofAddproof · cited by 237
- SkewPolynomialstatement and proof · cited by 124
- SkewMonoidAlgebra.updateproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- SkewPolynomial.coeff_update_applystatement · cited by 2
- SkewPolynomial.support_updatestatement · cited by 1
- SkewPolynomial.update_zero_eq_erasestatement · cited by 1
- SkewPolynomial.coeff_updatestatement · cited by 1
- SkewPolynomial.support_update_ne_zerostatement · cited by 0
- SkewPolynomial.support_update_zerostatement · cited by 0
- SkewPolynomial.update_defstatement · cited by 0
- SkewPolynomial.coeff_update_nestatement · cited by 0
- SkewPolynomial.coeff_update_samestatement · cited by 0