Theorems · Theorem · commutative algebra
Polynomial.hilbertPoly_mul_one_sub_pow_add
∀ {F : Type u_1} [inst : Field F] [CharZero F] (p : Polynomial F) (d e : ℕ),
(p * (1 - Polynomial.X) ^ e).hilbertPoly (d + e) = p.hilbertPoly d- Cited by
- 2 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- mul_assocproof · cited by 1,667
- Polynomial.Xstatement and proof · cited by 1,639
- pow_zeroproof · cited by 1,094
- CharZerostatement and proof · cited by 932
- pow_oneproof · cited by 894
- add_assocproof · cited by 746
- pow_addproof · cited by 315
- Polynomial.hilbertPolystatement and proof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.hilbertPoly_eq_zero_of_le_rootMultiplicity_oneproof · cited by 1
- Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_ltproof · cited by 1