Theorems · Theorem · commutative algebra
MvPolynomial.expand_X
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] (p : ℕ) (i : σ),
(MvPolynomial.expand p) (MvPolynomial.X i) = MvPolynomial.X i ^ p- Defined in
- Mathlib.Algebra.MvPolynomial.Expand
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Xstatement and proof · cited by 552
- MvPolynomial.expandstatement · cited by 44
- MvPolynomial.eval₂Hom_X'proof · cited by 17
Cited by8
Results whose statement or proof uses this declaration.
- MvPolynomial.expand_oneproof · cited by 2
- MvPolynomial.expand_zeroproof · cited by 2
- MvPolynomial.rename_comp_expandproof · cited by 1
- MvPolynomial.frobenius_zmodproof · cited by 1
- wittPolynomial_zmod_selfproof · cited by 1
- MvPolynomial.expand_mul_eq_compproof · cited by 1
- MvPolynomial.eval₂Hom_comp_expandproof · cited by 1
- MvPolynomial.aeval_comp_expandproof · cited by 0