Theorems · Theorem · commutative algebra
MvPolynomial.coeff_sub
∀ {R : Type u} (σ : Type u_1) [inst : CommRing R] (m : σ →₀ ℕ) (p q : MvPolynomial σ R),
MvPolynomial.coeff m (p - q) = MvPolynomial.coeff m p - MvPolynomial.coeff m q- Defined in
- Mathlib.Algebra.MvPolynomial.CommRing
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 84 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffstatement · cited by 315
- Equiv.toFunproof · cited by 279
- AddMonoidAlgebra.coeffEquivproof · cited by 22
- Finsupp.sub_applyproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- MvPolynomial.isUnit_iffproof · cited by 2
- MvPolynomial.degrees_sub_leproof · cited by 2
- MvPolynomial.notMem_support_sub_monomial_sub_monomialproof · cited by 1
- MvPolynomial.irreducible_of_disjoint_supportproof · cited by 1
- MonomialOrder.degree_reduce_ltproof · cited by 1
- MonomialOrder.degree_sub_LTerm_ltproof · cited by 1
- MonomialOrder.degree_sub_leadingTerm_lt_degreeproof · cited by 1
- MonomialOrder.coeff_sPolynomial_sup_eq_zeroproof · cited by 1
- MvPowerSeries.truncTotal_mul_sub_mul_truncTotal_mem_pow_idealOfVarsproof · cited by 0
- MvPowerSeries.toAdicCompletion_coeproof · cited by 0
- MvPowerSeries.truncTotal_sub_truncTotal_mem_pow_idealOfVarsproof · cited by 0
- chevalley_mvPolynomial_mvPolynomialproof · cited by 0