Theorems · Theorem · field theory
Polynomial.gcd_map
∀ {R : Type u} {k : Type y} [inst : Field R] {p q : Polynomial R} [inst_1 : Field k] [inst_2 : DecidableEq R]
[inst_3 : DecidableEq k] (f : R →+* k),
EuclideanDomain.gcd (Polynomial.map f p) (Polynomial.map f q) = Polynomial.map f (EuclideanDomain.gcd p q)- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement and proof · cited by 806
- EuclideanDomain.gcdstatement and proof · cited by 39
- Polynomial.map_zeroproof · cited by 33
- EuclideanDomain.gcd_zero_leftproof · cited by 7
- EuclideanDomain.gcd_valproof · cited by 5
- EuclideanDomain.GCD.inductionproof · cited by 5
- Polynomial.map_modproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Field.primitive_element_inf_auxproof · cited by 1
- Polynomial.isCoprime_mapproof · cited by 1