Theorems · Theorem · commutative algebra
MonomialOrder.leadingCoeff_monomial
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {d : σ →₀ ℕ} (c : R),
m.leadingCoeff ((MvPolynomial.monomial d) c) = c- Cited by
- 10 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.monomialstatement and proof · cited by 253
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.leadingCoeffstatement · cited by 72
- MvPolynomial.coeff_monomialproof · cited by 32
- MvPolynomial.monomial_zeroproof · cited by 19
Cited by10
Results whose statement or proof uses this declaration.
- MonomialOrder.sPolynomial_monomial_mulproof · cited by 3
- MonomialOrder.monic_monomial_oneproof · cited by 3
- MonomialOrder.degree_reduce_ltproof · cited by 1
- MonomialOrder.leadingCoeff_oneproof · cited by 0
- MonomialOrder.leadingTerm_leadingTermproof · cited by 0
- MonomialOrder.leadingTerm_monomialproof · cited by 0
- MonomialOrder.leadingCoeff_Xproof · cited by 0
- MonomialOrder.leadingCoeff_leadingTermproof · cited by 0
- MonomialOrder.monic_leadingTermproof · cited by 0
- MonomialOrder.monic_monomialproof · cited by 0