Theorems · Definition · field theory
Polynomial.divByMonic
{R : Type u} → [inst : Ring R] → Polynomial R → Polynomial R → Polynomial RdivByMonic, denoted as p /ₘ q, gives the quotient of p by a monic polynomial q.
- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 77 results in Mathlib
- Foundations
- Depth 114 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.
Cites4
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.Monicproof · cited by 461
- Polynomial.divModByMonicAuxproof · cited by 8
Cited by80
Results whose statement or proof uses this declaration.
- Polynomial.modByMonic_add_divstatement · cited by 25
- minpolyDivproof · cited by 20
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
- Polynomial.dvd_iff_isRootproof · cited by 15
- Polynomial.modByMonic_eq_sub_mul_divstatement · cited by 13
- Polynomial.div_modByMonic_uniquestatement and proof · cited by 12
- minpoly.isIntegrallyClosed_dvdproof · cited by 9
- Polynomial.modByMonic_X_sub_C_eq_C_evalproof · cited by 7
- Polynomial.removeFactorproof · cited by 7
- Polynomial.divByMonic_eq_zero_iffstatement and proof · cited by 7
- minpolyDiv_specproof · cited by 7
- Polynomial.aeval_modByMonic_eq_self_of_rootproof · cited by 6