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Theorems · Definition · field theory

Polynomial.Bivariate.equivMvPolynomial

(R : Type u_1) → [inst : CommSemiring R] → Polynomial (Polynomial R) ≃ₐ[R] MvPolynomial (Fin 2) R

The equiv between R[X][Y] and R[X, Y].

Defined in
Mathlib.Algebra.Polynomial.Bivariate
Cited by
13 results in Mathlib
Foundations
Depth 116 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.

StandardEtalePresentation.toPresentation · cited by 5StandardEtalePresentation…Polynomial.Bivariate.equivMvPolynomial_X · cited by 3Bivariate.equivMvPolynomi…Polynomial.Bivariate.equivMvPolynomial_C_X · cited by 3Bivariate.equivMvPolynomi…StandardEtalePair.equivMvPolynomialQuotient · cited by 3StandardEtalePair.equivMv…Polynomial.Bivariate.equivMvPolynomial_C_C · cited by 2Bivariate.equivMvPolynomi…StandardEtalePresentation.aeval_val_equivMvPolynomial · cited by 1StandardEtalePresentation…StandardEtalePresentation.toPresentation_relation · cited by 1StandardEtalePresentation…StandardEtalePresentation.toPresentation_val · cited by 1StandardEtalePresentation…Polynomial.Bivariate.equivMvPolynomial_symm_X_0 · cited by 1Bivariate.equivMvPolynomi…Polynomial.Bivariate.pderiv_one_equivMvPolynomial · cited by 1Bivariate.pderiv_one_equi…Polynomial.Bivariate.pderiv_zero_equivMvPolynomial · cited by 1Bivariate.pderiv_zero_equ…StandardEtalePair.equivMvPolynomialQuotient_symm_apply · cited by 1StandardEtalePair.equivMv…Polynomial.Bivariate.equivMvPolynomial_symm_X_1 · cited by 0Bivariate.equivMvPolynomi…Polynomial.Bivariate.equivMvPolynomial_symm_C · cited by 0Bivariate.equivMvPolynomi…StandardEtalePresentation.toSubmersivePresentation_jacobian · cited by 0StandardEtalePresentation…DFunLike.coe · cited by 62936DFunLike.coeCommSemiring · cited by 10911CommSemiringPolynomial · cited by 5681PolynomialFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialAlgEquiv · cited by 1681AlgEquivPolynomial.X · cited by 1639Polynomial.XPolynomial.C · cited by 1598Polynomial.CMatrix.vecCons · cited by 852Matrix.vecConsMatrix.vecEmpty · cited by 832Matrix.vecEmptyMvPolynomial.X · cited by 552MvPolynomial.XMvPolynomial.aeval · cited by 298MvPolynomial.aevalAlgEquiv.ofAlgHom · cited by 13AlgEquiv.ofAlgHomPolynomial.aevalAeval · cited by 13Polynomial.aevalAevalBivariate.equivMvPolynomialCITED BYCITES

Cites14

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Cited by15

Results whose statement or proof uses this declaration.