Theorems · Theorem · field theory
Polynomial.eq_C_of_derivative_eq_zero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} [IsAddTorsionFree R],
Polynomial.derivative p = 0 → p = Polynomial.C (p.coeff 0)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIsAddTorsionFree
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 and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.derivativestatement and proof · cited by 331
- IsAddTorsionFreestatement and proof · cited by 155
- Polynomial.eq_C_of_natDegree_eq_zeroproof · cited by 22
- Polynomial.derivative_eq_zeroproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.card_roots_toFinset_le_card_roots_derivative_sdiff_roots_succproof · cited by 3
- Polynomial.isRoot_of_isRoot_of_dvd_derivative_mulproof · cited by 1
- Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mulproof · cited by 0