Theorems · Theorem · commutative algebra
MvPolynomial.X_pow_eq_monomial
∀ {R : Type u} {σ : Type u_1} {e : ℕ} {n : σ} [inst : CommSemiring R],
MvPolynomial.X n ^ e = (MvPolynomial.monomial fun₀ | n => e) 1- 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.
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 · cited by 5,255
- mul_oneproof · cited by 3,885
- MvPolynomialstatement · cited by 2,140
- Finsupp.singlestatement and proof · cited by 943
- MvPolynomial.Xstatement · cited by 552
- one_powproof · cited by 521
- MvPolynomial.monomialstatement and proof · cited by 253
- Finsupp.smul_singleproof · cited by 48
Cited by9
Results whose statement or proof uses this declaration.
- MvPolynomial.monomial_eqproof · cited by 20
- MvPolynomial.monomial_add_singleproof · cited by 5
- MvPolynomial.monomial_single_addproof · cited by 3
- Polynomial.homogenize_X_powproof · cited by 3
- MvPolynomial.totalDegree_X_powproof · cited by 0
- MvPolynomial.degreeOf_mul_X_self_pow_eq_add_of_ne_zeroproof · cited by 0
- MvPolynomial.eval₂_X_powproof · cited by 0
- MvPolynomial.support_X_powproof · cited by 0
- MvPolynomial.degreeOf_X_self_powproof · cited by 0