Theorems · Theorem · commutative algebra
MvPolynomial.coeff_C_mul
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (m : σ →₀ ℕ) (a : R) (p : MvPolynomial σ R),
MvPolynomial.coeff m (MvPolynomial.C a * p) = a * MvPolynomial.coeff m p- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 85 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.
Cites23
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialstatement and proof · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Finsupp.sumproof · cited by 481
- MvPolynomial.Cstatement · cited by 400
- AddMonoidAlgebra.coeffproof · cited by 365
Cited by9
Results whose statement or proof uses this declaration.
- map_wittStructureIntproof · cited by 13
- MvPolynomial.finSuccEquiv_coeff_coeffproof · cited by 5
- MvPolynomial.C_dvd_iff_dvd_coeffproof · cited by 3
- MvPolynomial.vars_C_mulproof · cited by 2
- MvPolynomial.irreducible_of_disjoint_supportproof · cited by 1
- MvPolynomial.irreducible_of_totalDegree_eq_oneproof · cited by 1
- MvPowerSeries.trunc'_C_mulproof · cited by 0
- MvPolynomial.degreeOf_C_mulproof · cited by 0
- MvPowerSeries.trunc_C_mulproof · cited by 0