Theorems · Theorem · field theory
Polynomial.leadingCoeff_neg
∀ {R : Type u} [inst : Ring R] (p : Polynomial R), (-p).leadingCoeff = -p.leadingCoeff- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 81 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.
Cites7
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.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.natDegree_negproof · cited by 26
- Polynomial.coeff_negproof · cited by 15
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.degree_comp_neg_Xproof · cited by 7
- Polynomial.comp_neg_X_leadingCoeff_eqproof · cited by 4
- Polynomial.isIntegral_of_mahlerMeasure_eq_oneproof · cited by 2
- Polynomial.tendsto_atBot_iff_leadingCoeff_nonposproof · cited by 1
- Polynomial.eval_lt_zero_of_roots_lt_of_leadingCoeff_nonposproof · cited by 1
- Polynomial.leadingCoeff_sub_of_degree_eqproof · cited by 0
- Polynomial.negOnePow_mul_eval_le_zero_of_le_roots_of_leadingCoeff_nonposproof · cited by 0
- Polynomial.leadingCoeff_sub_of_degree_lt'proof · cited by 0
- Polynomial.negOnePow_mul_eval_lt_zero_of_lt_roots_of_leadingCoeff_nonposproof · cited by 0
- Polynomial.eval_le_zero_of_roots_le_of_leadingCoeff_nonposproof · cited by 0