Theorems · Definition · field theory
Polynomial.factor
{K : Type v} → [inst : Field K] → Polynomial K → Polynomial KNon-computably choose an irreducible factor from a polynomial.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 98 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.
Cites4
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
- Polynomial.Xproof · cited by 1,639
- Irreducibleproof · cited by 496
Cited by15
Results whose statement or proof uses this declaration.
- Polynomial.removeFactorstatement and proof · cited by 7
- Polynomial.fact_irreducible_factorstatement · cited by 5
- Polynomial.natDegree_removeFactor'statement · cited by 2
- Polynomial.X_sub_C_mul_removeFactorstatement and proof · cited by 2
- Polynomial.SplittingFieldAux.algebraMap_succstatement · cited by 2
- Polynomial.factor_dvd_of_not_isUnitstatement and proof · cited by 2
- Polynomial.natDegree_removeFactorstatement and proof · cited by 1
- Polynomial.factor_dvd_of_degree_ne_zerostatement · cited by 1
- Polynomial.factor_dvd_of_natDegree_ne_zerostatement · cited by 1
- Polynomial.irreducible_factorstatement · cited by 1
- Polynomial.SplittingFieldAux.adjoin_rootSetproof · cited by 0
- Polynomial.isCoprime_iff_aeval_ne_zeroproof · cited by 0