Theorems · Theorem · algebraic geometry
Polynomial.homogenize_monomial
∀ {R : Type u_1} [inst : CommSemiring R] {m n : ℕ},
m ≤ n → ∀ (r : R), ((Polynomial.monomial m) r).homogenize n = (MvPolynomial.monomial fun₀ | 0 => m | 1 => n - m) r- Defined in
- Mathlib.Algebra.Polynomial.Homogenize
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 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.
Cites19
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
- Polynomialstatement · cited by 5,681
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.singlestatement and proof · cited by 943
- Polynomial.monomialstatement and proof · cited by 256
- MvPolynomial.monomialstatement and proof · cited by 253
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- Finset.sum_eq_singleproof · cited by 98
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.homogenize_X_powproof · cited by 3
- Polynomial.coeff_homogenizeproof · cited by 2
- Polynomial.homogenize_Cproof · cited by 1