Theorems · Theorem · algebraic geometry
Polynomial.coeff_homogenize
∀ {R : Type u_1} [inst : CommSemiring R] (p : Polynomial R) (n : ℕ) (m : Fin 2 →₀ ℕ),
MvPolynomial.coeff m (p.homogenize n) = if m 0 + m 1 = n then p.coeff (m 0) else 0- Defined in
- Mathlib.Algebra.Polynomial.Homogenize
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 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.
Cites32
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
- Polynomialstatement and proof · cited by 5,681
- Finsuppstatement and proof · cited by 5,255
- add_zeroproof · cited by 2,707
- MvPolynomialproof · cited by 2,140
- Polynomial.coeffstatement and proof · cited by 1,045
- Finsupp.singleproof · cited by 943
- Finsupp.extproof · cited by 399
- MvPolynomial.coeffstatement and proof · cited by 315
- le_or_gtproof · cited by 269
- Polynomial.monomialproof · cited by 256
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.eq_zero_of_homogenize_eq_zeroproof · cited by 1
- Polynomial.finsuppSum_homogenize_eqproof · cited by 0