Theorems · Theorem · field theory
Polynomial.mul_self_modByMonic
∀ {R : Type u} [inst : CommRing R] {p q : Polynomial R}, q.Monic → p * q %ₘ q = 0See Polynomial.self_mul_modByMonic for the other multiplication order. This version, unlike
that 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
- CommRing
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.modByMonicstatement · cited by 82
- dvd_mul_leftproof · cited by 47
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
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