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Theorems · Definition · commutative algebra

MvPolynomial.IsSymmetric

{σ : Type u_1} → {R : Type u_3} → [inst : CommSemiring R] → MvPolynomial σ R → Prop

A MvPolynomial φ is symmetric if it is invariant under permutations of its variables by the rename operation

Defined in
Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
Cited by
18 results in Mathlib
Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPolynomial.symmetricSubalgebra · cited by 21MvPolynomial.symmetricSub…MvPolynomial.isSymmetric_esymmAlgHomMonomial · cited by 1MvPolynomial.isSymmetric_…MvPolynomial.esymm_isSymmetric · cited by 1MvPolynomial.esymm_isSymm…MvPolynomial.IsSymmetric.antitone_supDegree · cited by 1IsSymmetric.antitone_supD…MvPolynomial.IsSymmetric.rename · cited by 1IsSymmetric.renameMvPolynomial.isSymmetric_rename · cited by 0MvPolynomial.isSymmetric_…MvPolynomial.msymm_isSymmetric · cited by 0MvPolynomial.msymm_isSymm…MvPolynomial.mem_symmetricSubalgebra · cited by 0MvPolynomial.mem_symmetri…MvPolynomial.IsSymmetric.smul · cited by 0IsSymmetric.smulMvPolynomial.psum_isSymmetric · cited by 0MvPolynomial.psum_isSymme…MvPolynomial.hsymm_isSymmetric · cited by 0MvPolynomial.hsymm_isSymm…MvPolynomial.IsSymmetric.C · cited by 0IsSymmetric.CMvPolynomial.IsSymmetric.add · cited by 0IsSymmetric.addMvPolynomial.IsSymmetric.map · cited by 0IsSymmetric.mapMvPolynomial.IsSymmetric.mul · cited by 0IsSymmetric.mulDFunLike.coe · cited by 62936DFunLike.coeCommSemiring · cited by 10911CommSemiringMvPolynomial · cited by 2140MvPolynomialEquiv.Perm · cited by 1375Equiv.PermMvPolynomial.rename · cited by 168MvPolynomial.renameMvPolynomial.IsSymmetricCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by19

Results whose statement or proof uses this declaration.