Theorems · Theorem · field theory
Polynomial.as_sum_range
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R),
p = ∑ i ∈ Finset.range (p.natDegree + 1), (Polynomial.monomial i) (p.coeff i)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 99 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Finset.sumstatement · cited by 5,195
- Finset.rangestatement · cited by 1,341
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.monomialstatement · cited by 256
- lt_add_oneproof · cited by 105
- Polynomial.as_sum_range'proof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.eval₂_eq_sum_rangeproof · cited by 9
- Polynomial.eval₂_compproof · cited by 3
- Polynomial.valuation_le_one_of_valuation_X_le_oneproof · cited by 2