Theorems · Theorem · commutative algebra
Polynomial.resultant_X_sub_C_right
∀ {R : Type u_1} [inst : CommRing R] (f : Polynomial R) (m : ℕ) (r : R),
f.natDegree ≤ m → f.resultant (Polynomial.X - Polynomial.C r) m 1 = (-1) ^ m * Polynomial.eval r fRes(f, X - r) = (-1)^{deg f} * f(r)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 124 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.
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.resultantstatement · cited by 54
- Polynomial.resultant_commproof · cited by 11
- Polynomial.resultant_X_sub_C_leftproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.resultant_X_add_C_rightproof · cited by 0