Theorems · Theorem · field theory
Cubic.of_a_eq_zero
∀ {R : Type u_1} {P : Cubic R} [inst : Semiring R],
P.a = 0 → P.toPoly = Polynomial.C P.b * Polynomial.X ^ 2 + Polynomial.C P.c * Polynomial.X + Polynomial.C P.d- Defined in
- Mathlib.Algebra.CubicDiscriminant
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 103 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.
Cites15
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- zero_addproof · cited by 2,366
- Polynomial.Xstatement and proof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cstatement and proof · cited by 1,598
- Cubic.toPolystatement · cited by 88
- Cubicstatement and proof · cited by 71
- Cubic.astatement and proof · cited by 46
- Polynomial.C_0proof · cited by 40
Cited by7
Results whose statement or proof uses this declaration.
- Cubic.of_b_eq_zeroproof · cited by 7
- Cubic.leadingCoeff_of_b_ne_zeroproof · cited by 2
- Cubic.natDegree_of_b_ne_zeroproof · cited by 1
- Cubic.natDegree_of_a_eq_zeroproof · cited by 1
- Cubic.degree_of_a_eq_zeroproof · cited by 1
- Cubic.degree_of_b_ne_zeroproof · cited by 1
- Cubic.of_a_eq_zero'proof · cited by 0