Theorems · Theorem · commutative algebra
Polynomial.degree_wronskian_lt_add
∀ {R : Type u_1} [inst : CommRing R] {a b : Polynomial R}, a ≠ 0 → b ≠ 0 → (a.wronskian b).degree < a.degree + b.degreeDegree of W(a,b) is strictly less than the sum of degrees of a and b (both nonzero).
- Defined in
- Mathlib.RingTheory.Polynomial.Wronskian
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- lt_of_le_of_ltproof · cited by 432
- Polynomial.derivativeproof · cited by 331
- max_lt_iffproof · cited by 22
- Polynomial.wronskianstatement · cited by 16
- Polynomial.degree_ne_botproof · cited by 11
- Polynomial.degree_mul_leproof · cited by 10
- Polynomial.degree_sub_leproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_wronskian_lt_addproof · cited by 0