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Theorems · Theorem · commutative algebra

Polynomial.resultant_zero_left_deg

∀ {R : Type u_1} [inst : CommRing R] (f g : Polynomial R) (m : ℕ), f.resultant g 0 m = f.coeff 0 ^ m
Defined in
Mathlib.RingTheory.Polynomial.Resultant.Basic
Cited by
13 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.resultant_zero_right_deg · cited by 8Polynomial.resultant_zero…Polynomial.resultant_zero_right · cited by 3Polynomial.resultant_zero…Polynomial.resultant_eq_prod_eval · cited by 3Polynomial.resultant_eq_p…Polynomial.isUnit_resultant_iff_isCoprime · cited by 2Polynomial.isUnit_resulta…Polynomial.resultant_prod_left · cited by 2Polynomial.resultant_prod…Polynomial.resultant_C_left · cited by 1Polynomial.resultant_C_le…Polynomial.resultant_scaleRoots · cited by 1Polynomial.resultant_scal…Polynomial.resultant_dvd_leadingCoeff_pow · cited by 1Polynomial.resultant_dvd_…Polynomial.resultant_integralNormalization · cited by 0Polynomial.resultant_inte…Polynomial.resultant_ne_zero · cited by 0Polynomial.resultant_ne_z…Polynomial.resultant_C_zero_left · cited by 0Polynomial.resultant_C_ze…Polynomial.resultant_taylor · cited by 0Polynomial.resultant_tayl…Polynomial.resultant_eq_zero_iff · cited by 0Polynomial.resultant_eq_z…CommRing · cited by 17173CommRingPolynomial · cited by 5681Polynomialzero_add · cited by 2366zero_addPolynomial.coeff · cited by 1045Polynomial.coeffMatrix.diagonal · cited by 314Matrix.diagonalFintype.card_fin · cited by 270Fintype.card_finFinset.prod_const · cited by 154Finset.prod_constMatrix.det.congr_simp · cited by 91det.congr_simpFintype.card_congr' · cited by 60Fintype.card_congr'Polynomial.resultant · cited by 54Polynomial.resultantMatrix.det_diagonal · cited by 27Matrix.det_diagonalPolynomial.sylvester · cited by 18Polynomial.sylvesterPolynomial.sylvester_zero_left_deg · cited by 1Polynomial.sylvester_zero…Polynomial.resultant_zero_lef…CITED BYCITES

Cites13

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Cited by13

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