Theorems · Theorem · commutative algebra
Polynomial.X_sub_C_scaleRoots
∀ {R : Type u_1} [inst : Ring R] (r s : R),
(Polynomial.X - Polynomial.C r).scaleRoots s = Polynomial.X - Polynomial.C (r * s)- Defined in
- Mathlib.RingTheory.Polynomial.ScaleRoots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- mul_oneproof · cited by 3,885
- Nontrivialproof · cited by 2,416
- 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
- map_mulproof · cited by 1,137
- pow_zeroproof · cited by 1,094
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.rootMultiplicity_scaleRootsproof · cited by 1