Theorems · Theorem · commutative algebra
Polynomial.discr_of_degree_eq_two
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R},
f.degree = 2 → f.discr = f.coeff 1 ^ 2 - 4 * f.coeff 0 * f.coeff 2Standard formula for the discriminant of a quadratic polynomial.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Equivproof · cited by 8,337
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
- Set.Iccproof · cited by 1,702
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.discr_of_card_eq_twoproof · cited by 1