Theorems · Theorem · field theory
Polynomial.eraseLead_add_C_mul_X_pow
∀ {R : Type u_1} [inst : Semiring R] (f : Polynomial R),
f.eraseLead + Polynomial.C f.leadingCoeff * Polynomial.X ^ f.natDegree = f- Defined in
- Mathlib.Algebra.Polynomial.EraseLead
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.leadingCoeffstatement · cited by 498
- Polynomial.eraseLeadstatement and proof · cited by 65
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
- Polynomial.eraseLead_add_monomial_natDegree_leadingCoeffproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.induction_with_natDegree_leproof · cited by 4
- Polynomial.card_support_eqproof · cited by 3
- Polynomial.IsMonicOfDegree.exists_natDegree_ltproof · cited by 1
- Polynomial.reflect_mul_inductionproof · cited by 1
- Ideal.map_C_comap_of_comap_eq_leadingCoeffproof · cited by 0