Theorems · Definition · field theory
AlgebraicClosure.subProdXSubC
{k : Type u} → [inst : Field k] → AlgebraicClosure.Monics k → Polynomial (MvPolynomial (AlgebraicClosure.Vars k) k)Given a monic polynomial f : k[X],
subProdXSubC f is the polynomial $f - \prod_i (X - X_{f,i})$.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- Finset.univproof · cited by 3,473
- Finset.prodproof · cited by 2,356
- MvPolynomialstatement and proof · cited by 2,140
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.mapproof · cited by 806
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicClosure.spanCoeffsproof · cited by 2
- AlgebraicClosure.spanCoeffs_ne_topproof · cited by 1
- AlgebraicClosure.toSplittingField_coeffstatement · cited by 1
- AlgebraicClosure.Monics.map_eq_prodproof · cited by 0