Theorems · Theorem · commutative algebra
MvPolynomial.eval_map
∀ {R : Type u} {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] (f : R →+* S₁)
(g : σ → S₁) (p : MvPolynomial σ R), (MvPolynomial.eval g) ((MvPolynomial.map f) p) = MvPolynomial.eval₂ f g p- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- map_mulproof · cited by 1,137
- map_addproof · cited by 964
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.evalstatement and proof · cited by 157
- MvPolynomial.mapstatement and proof · cited by 147
- MvPolynomial.eval₂statement and proof · cited by 103
- MvPolynomial.eval₂_Cproof · cited by 43
Cited by9
Results whose statement or proof uses this declaration.
- MvPolynomial.eval₂_mapproof · cited by 4
- WeierstrassCurve.Jacobian.map_equationproof · cited by 2
- MvPolynomial.eval₂_compproof · cited by 2
- WeierstrassCurve.Projective.map_equationproof · cited by 2
- WeierstrassCurve.Jacobian.map_nonsingularproof · cited by 1
- WeierstrassCurve.Projective.Equation.mapproof · cited by 1
- LinearMap.polyCharpolyAux_map_aevalproof · cited by 1
- WeierstrassCurve.Jacobian.Equation.mapproof · cited by 1
- WeierstrassCurve.Projective.map_nonsingularproof · cited by 1