Theorems · Definition · field theory
Polynomial.divModByMonicAux
{R : Type u} → [inst : Ring R] → Polynomial R → {q : Polynomial R} → q.Monic → Polynomial R × Polynomial RSee divByMonic.
- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 113 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.
Cites3
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
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.modByMonicproof · cited by 82
- Polynomial.divByMonicproof · cited by 77
- Polynomial.divByMonic_eq_zero_iffproof · cited by 7
- Polynomial.divModByMonicAux.eq_defstatement · cited by 6
- Polynomial.modByMonic_eq_self_iffproof · cited by 3
- Polynomial.coeff_divModByMonicAux_mem_span_pow_mul_spanstatement · cited by 2
- Polynomial.mod_eq_self_iffproof · cited by 1
- Polynomial.coeff_divByMonic_mem_pow_natDegree_mulproof · cited by 0
- Polynomial.divModByMonicAux.congr_simpstatement and proof · cited by 0
- Polynomial.coeff_modByMonic_mem_pow_natDegree_mulproof · cited by 0