Theorems · Theorem · field theory
Polynomial.self_mul_modByMonic
∀ {R : Type u} [inst : Ring R] {p q : Polynomial R}, q.Monic → q * p %ₘ q = 0See Polynomial.mul_self_modByMonic for the other multiplication order. That version, unlike
this one, requires commutativity.
- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Monicstatement and proof · cited by 461
- dvd_mul_rightproof · cited by 89
- Polynomial.modByMonicstatement · cited by 82
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
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