Documentation Verification Report

IsAdjoinRoot

πŸ“ Source: Mathlib/RingTheory/IsAdjoinRoot.lean

Statistics

MetricCount
DefinitionsisAdjoinRoot, isAdjoinRootMonic, IsAdjoinRoot, adjoinRootAlgEquiv, algEquiv, liftHom, map, mkOfAdjoinEqTop, mkOfPrimitiveElement, ofAdjoinRootEquiv, ofAlgEquiv, repr, root, IsAdjoinRootMonic, basis, coeff, liftPolyβ‚—, mkOfAdjoinEqTop, mkOfPrimitiveElement, modByMonicHom, powerBasis, toIsAdjoinRoot
22
TheoremsisAdjoinRootMonic_toAdjoinRoot, isAdjoinRoot_map_eq_mkₐ, isAdjoinRoot_root_eq_root, powerBasis'_minpoly_gen, adjoinRootAlgEquiv_apply_eq_map, adjoinRootAlgEquiv_apply_mk, adjoinRootAlgEquiv_apply_root, adjoinRootAlgEquiv_symm_apply_eq_mk, adjoinRootAlgEquiv_symm_apply_root, adjoin_root_eq_top, aeval_root_eq_map, aeval_root_self, algEquiv_algEquiv, algEquiv_apply_map, algEquiv_def, algEquiv_map, algEquiv_ofAlgEquiv, algEquiv_root, algEquiv_self, algEquiv_symm, algEquiv_trans, algebraMap_apply, apply_eq_lift, coe_liftHom, eq_lift, eq_liftHom, evalβ‚‚_repr_eq_evalβ‚‚_of_map_eq, ext, ext_iff, ext_map, isAlgebraic_root, ker_map, liftHom_algEquiv, liftHom_map, liftHom_root, lift_algEquiv, lift_algebraMap, lift_algebraMap_apply, lift_map, lift_root, lift_self, lift_self_apply, map_X, map_eq_zero_iff, map_repr, map_self, map_surjective, mem_ker_map, mkOfAdjoinEqTop_root, ofAlgEquiv_algEquiv, ofAlgEquiv_map_apply, ofAlgEquiv_root, primitive_element_root, repr_add_sub_repr_add_repr_mem_span, repr_zero_mem_span, subsingleton, basis_apply, basis_one, basis_repr, coeff_algebraMap, coeff_apply, coeff_apply_coe, coeff_apply_le, coeff_apply_lt, coeff_injective, coeff_one, coeff_root, coeff_root_pow, deg_ne_zero, deg_pos, ext_elem, ext_elem_iff, finite, finrank, isIntegral_root, liftPolyβ‚—_apply, map_modByMonic, map_modByMonicHom, minpoly_eq, modByMonicHom_map, modByMonicHom_root, modByMonicHom_root_pow, modByMonic_repr_map, monic, powerBasis_basis, powerBasis_dim, powerBasis_gen, finrank_quotient_span_eq_natDegree'
88
Total110

AdjoinRoot

Definitions

NameCategoryTheorems
isAdjoinRoot πŸ“–CompOp
3 mathmath: isAdjoinRoot_root_eq_root, isAdjoinRoot_map_eq_mkₐ, isAdjoinRootMonic_toAdjoinRoot
isAdjoinRootMonic πŸ“–CompOp
1 mathmath: isAdjoinRootMonic_toAdjoinRoot

Theorems

NameKindAssumesProvesValidatesDepends On
isAdjoinRootMonic_toAdjoinRoot πŸ“–mathematicalPolynomial.Monic
CommSemiring.toSemiring
CommRing.toCommSemiring
IsAdjoinRootMonic.toIsAdjoinRoot
AdjoinRoot
instCommRing
instAlgebra
Algebra.id
isAdjoinRootMonic
isAdjoinRoot
β€”β€”
isAdjoinRoot_map_eq_mkₐ πŸ“–mathematicalβ€”IsAdjoinRoot.map
AdjoinRoot
CommRing.toCommSemiring
CommSemiring.toSemiring
instCommRing
instAlgebra
Algebra.id
isAdjoinRoot
mkₐ
β€”β€”
isAdjoinRoot_root_eq_root πŸ“–mathematicalβ€”IsAdjoinRoot.root
AdjoinRoot
CommRing.toRing
instCommRing
instAlgebra
CommRing.toCommSemiring
Algebra.id
isAdjoinRoot
root
β€”β€”

Algebra.adjoin

Theorems

NameKindAssumesProvesValidatesDepends On
powerBasis'_minpoly_gen πŸ“–mathematicalIsIntegral
CommRing.toRing
minpoly
Subalgebra
CommRing.toCommSemiring
CommSemiring.toSemiring
SetLike.instMembership
Subalgebra.instSetLike
Algebra.adjoin
Set
Set.instSingletonSet
Subalgebra.toRing
Subalgebra.algebra
PowerBasis.gen
powerBasis'
β€”AdjoinRoot.isDomain_of_prime
minpoly.prime_of_isIntegrallyClosed
AdjoinRoot.noZeroSMulDivisors_of_prime_of_degree_ne_zero
LT.lt.ne'
minpoly.degree_pos
IsDomain.toNontrivial
PowerBasis.minpolyGen_eq
powerBasis'.eq_1
PowerBasis.minpolyGen_map
AdjoinRoot.powerBasis'_gen
AdjoinRoot.isAdjoinRoot_root_eq_root
minpoly.monic
AdjoinRoot.isAdjoinRootMonic_toAdjoinRoot
IsAdjoinRootMonic.minpoly_eq
minpoly.irreducible

IsAdjoinRoot

Definitions

NameCategoryTheorems
adjoinRootAlgEquiv πŸ“–CompOp
6 mathmath: adjoinRootAlgEquiv_symm_apply_eq_mk, adjoinRootAlgEquiv_apply_root, algEquiv_def, adjoinRootAlgEquiv_apply_eq_map, adjoinRootAlgEquiv_apply_mk, adjoinRootAlgEquiv_symm_apply_root
algEquiv πŸ“–CompOp
12 mathmath: algEquiv_symm, algEquiv_algEquiv, algEquiv_self, algEquiv_def, algEquiv_trans, lift_algEquiv, algEquiv_ofAlgEquiv, ofAlgEquiv_algEquiv, algEquiv_root, algEquiv_map, liftHom_algEquiv, algEquiv_apply_map
liftHom πŸ“–CompOp
6 mathmath: liftHom_root, eq_liftHom, liftHom_map, coe_liftHom, liftHom_algEquiv, lift_algebraMap_apply
map πŸ“–CompOp
21 mathmath: mem_ker_map, IsAdjoinRootMonic.map_modByMonic, map_repr, map_X, IsAdjoinRootMonic.modByMonicHom_map, AdjoinRoot.isAdjoinRoot_map_eq_mkₐ, adjoinRootAlgEquiv_apply_eq_map, lift_map, adjoinRootAlgEquiv_apply_mk, IsAdjoinRootMonic.map_modByMonicHom, liftHom_map, algebraMap_apply, map_self, ofAlgEquiv_map_apply, map_eq_zero_iff, algEquiv_map, aeval_root_eq_map, map_surjective, algEquiv_apply_map, ker_map, IsAdjoinRootMonic.modByMonic_repr_map
mkOfAdjoinEqTop πŸ“–CompOp
1 mathmath: mkOfAdjoinEqTop_root
mkOfPrimitiveElement πŸ“–CompOpβ€”
ofAdjoinRootEquiv πŸ“–CompOpβ€”
ofAlgEquiv πŸ“–CompOp
4 mathmath: algEquiv_ofAlgEquiv, ofAlgEquiv_map_apply, ofAlgEquiv_algEquiv, ofAlgEquiv_root
repr πŸ“–CompOp
6 mathmath: repr_add_sub_repr_add_repr_mem_span, adjoinRootAlgEquiv_symm_apply_eq_mk, map_repr, repr_zero_mem_span, evalβ‚‚_repr_eq_evalβ‚‚_of_map_eq, IsAdjoinRootMonic.modByMonic_repr_map
root πŸ“–CompOp
26 mathmath: AdjoinRoot.isAdjoinRoot_root_eq_root, lift_self, liftHom_root, isAlgebraic_root, map_X, adjoinRootAlgEquiv_apply_root, lift_root, IsAdjoinRootMonic.powerBasis_gen, ext_iff, IsAdjoinRootMonic.isIntegral_root, lift_self_apply, adjoinRootAlgEquiv_symm_apply_root, IsAdjoinRootMonic.modByMonicHom_root_pow, mkOfAdjoinEqTop_root, IsAdjoinRootMonic.modByMonicHom_root, aeval_root_self, algEquiv_root, aeval_root_eq_map, IsAdjoinRootMonic.coeff_root, primitive_element_root, ofAlgEquiv_root, IsAdjoinRootMonic.minpoly_eq, adjoin_root_eq_top, IsAdjoinRootMonic.coeff_root_pow, IsAdjoinRootMonic.basis_one, IsAdjoinRootMonic.basis_apply

Theorems

NameKindAssumesProvesValidatesDepends On
adjoinRootAlgEquiv_apply_eq_map πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
AdjoinRoot
CommRing.toCommSemiring
CommSemiring.toSemiring
AdjoinRoot.instCommRing
Ring.toSemiring
AdjoinRoot.instAlgebra
Algebra.id
AlgEquiv.instFunLike
adjoinRootAlgEquiv
AlgHom
Polynomial
Polynomial.semiring
Polynomial.algebraOfAlgebra
AlgHom.funLike
map
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
AdjoinRoot.mk_surjective
β€”AdjoinRoot.mk_surjective
adjoinRootAlgEquiv_apply_mk πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
AdjoinRoot
CommRing.toCommSemiring
CommSemiring.toSemiring
AdjoinRoot.instCommRing
Ring.toSemiring
AdjoinRoot.instAlgebra
Algebra.id
AlgEquiv.instFunLike
adjoinRootAlgEquiv
RingHom
Polynomial
Semiring.toNonAssocSemiring
Polynomial.semiring
RingHom.instFunLike
AlgHom
Polynomial.algebraOfAlgebra
AlgHom.funLike
map
β€”β€”
adjoinRootAlgEquiv_apply_root πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
AdjoinRoot
CommRing.toCommSemiring
CommSemiring.toSemiring
AdjoinRoot.instCommRing
Ring.toSemiring
AdjoinRoot.instAlgebra
Algebra.id
AlgEquiv.instFunLike
adjoinRootAlgEquiv
AdjoinRoot.root
root
β€”β€”
adjoinRootAlgEquiv_symm_apply_eq_mk πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
AdjoinRoot
CommRing.toCommSemiring
Ring.toSemiring
CommSemiring.toSemiring
AdjoinRoot.instCommRing
AdjoinRoot.instAlgebra
Algebra.id
AlgEquiv.instFunLike
AlgEquiv.symm
adjoinRootAlgEquiv
RingHom
Polynomial
Semiring.toNonAssocSemiring
Polynomial.semiring
RingHom.instFunLike
repr
β€”AlgEquiv.symm_apply_eq
map_repr
adjoinRootAlgEquiv_symm_apply_root πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
AdjoinRoot
CommRing.toCommSemiring
Ring.toSemiring
CommSemiring.toSemiring
AdjoinRoot.instCommRing
AdjoinRoot.instAlgebra
Algebra.id
AlgEquiv.instFunLike
AlgEquiv.symm
adjoinRootAlgEquiv
root
AdjoinRoot.root
β€”AlgEquiv.symm_apply_eq
adjoin_root_eq_top πŸ“–mathematicalβ€”Algebra.adjoin
CommRing.toCommSemiring
Ring.toSemiring
Set
Set.instSingletonSet
root
Top.top
Subalgebra
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Algebra.instCompleteLatticeSubalgebra
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”Algebra.adjoin_singleton_eq_range_aeval
AlgHom.range_eq_top
aeval_root_eq_map
map_surjective
aeval_root_eq_map πŸ“–mathematicalβ€”Polynomial.aeval
CommRing.toCommSemiring
Ring.toSemiring
root
map
β€”Polynomial.algHom_ext
Polynomial.aeval_X
aeval_root_self πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
Polynomial.aeval
root
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
β€”aeval_root_eq_map
map_self
algEquiv_algEquiv πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
CommRing.toCommSemiring
Ring.toSemiring
AlgEquiv.instFunLike
algEquiv
β€”AlgEquiv.symm_apply_apply
algEquiv_apply_map πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
CommRing.toCommSemiring
Ring.toSemiring
AlgEquiv.instFunLike
algEquiv
AlgHom
Polynomial
CommSemiring.toSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
β€”AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
algEquiv_map
algEquiv_def πŸ“–mathematicalβ€”algEquiv
AlgEquiv.trans
AdjoinRoot
CommRing.toCommSemiring
Ring.toSemiring
CommSemiring.toSemiring
AdjoinRoot.instCommRing
AdjoinRoot.instAlgebra
Algebra.id
AlgEquiv.symm
adjoinRootAlgEquiv
β€”β€”
algEquiv_map πŸ“–mathematicalβ€”AlgHom.comp
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHomClass.toAlgHom
AlgEquiv
AlgEquiv.instFunLike
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
algEquiv
map
β€”Polynomial.algHom_ext
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
algEquiv_root
algEquiv_ofAlgEquiv πŸ“–mathematicalβ€”algEquiv
ofAlgEquiv
AlgEquiv.trans
CommRing.toCommSemiring
Ring.toSemiring
β€”AlgEquiv.ext
AdjoinRoot.mk_surjective
adjoinRootAlgEquiv_apply_eq_map
algEquiv_root πŸ“–mathematicalβ€”DFunLike.coe
AlgEquiv
CommRing.toCommSemiring
Ring.toSemiring
AlgEquiv.instFunLike
algEquiv
root
β€”adjoinRootAlgEquiv_symm_apply_root
algEquiv_self πŸ“–mathematicalβ€”algEquiv
AlgEquiv.refl
CommRing.toCommSemiring
Ring.toSemiring
β€”AlgEquiv.ext
AlgEquiv.symm_trans_self
algEquiv_symm πŸ“–mathematicalβ€”AlgEquiv.symm
CommRing.toCommSemiring
Ring.toSemiring
algEquiv
β€”β€”
algEquiv_trans πŸ“–mathematicalβ€”AlgEquiv.trans
CommRing.toCommSemiring
Ring.toSemiring
algEquiv
β€”AlgEquiv.ext
algEquiv_algEquiv
algebraMap_apply πŸ“–mathematicalβ€”DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
AlgHom
Polynomial
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
Polynomial.C
β€”AlgHom.algebraMap_eq_apply
apply_eq_lift πŸ“–mathematicalPolynomial.evalβ‚‚
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
root
liftβ€”map_repr
Polynomial.as_sum_range_C_mul_X_pow
map_sum
DistribMulActionSemiHomClass.toAddMonoidHomClass
NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgHom.algHomClass
Finset.sum_congr
map_mul
NonUnitalAlgSemiHomClass.toMulHomClass
algebraMap_apply
map_pow
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
AlgHomClass.toRingHomClass
RingHomClass.toAddMonoidHomClass
RingHom.instRingHomClass
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
lift_algebraMap
lift_root
coe_liftHom πŸ“–mathematicalDFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
Polynomial.aeval
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
RingHomClass.toRingHom
Ring.toSemiring
Semiring.toNonAssocSemiring
AlgHomClass.toRingHomClass
AlgHom.algHomClass
liftHom
lift
algebraMap
β€”AlgHomClass.toRingHomClass
AlgHom.algHomClass
eq_lift πŸ“–mathematicalPolynomial.evalβ‚‚
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
root
liftβ€”RingHom.ext
apply_eq_lift
eq_liftHom πŸ“–mathematicalDFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
Polynomial.aeval
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Ring.toSemiring
root
liftHomβ€”AlgHom.ext
apply_eq_lift
AlgHomClass.toRingHomClass
AlgHom.algHomClass
AlgHom.commutes
evalβ‚‚_repr_eq_evalβ‚‚_of_map_eq πŸ“–mathematicalPolynomial.evalβ‚‚
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
AlgHom
Polynomial
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
reprβ€”map_eq_zero_iff
map_sub
DistribMulActionSemiHomClass.toAddMonoidHomClass
NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgHom.algHomClass
map_repr
sub_eq_zero
Polynomial.evalβ‚‚_sub
Polynomial.evalβ‚‚_mul
MulZeroClass.zero_mul
ext πŸ“–β€”rootβ€”β€”ext_map
aeval_root_eq_map
ext_iff πŸ“–mathematicalβ€”rootβ€”ext
ext_map πŸ“–β€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
β€”β€”AlgHomClass.toRingHomClass
AlgHom.algHomClass
AlgHom.ext
isAlgebraic_root πŸ“–mathematicalβ€”IsAlgebraic
root
β€”aeval_root_eq_map
map_self
ker_map πŸ“–mathematicalβ€”RingHom.ker
Polynomial
CommSemiring.toSemiring
AlgHom
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
map
Ideal.span
Set
Set.instSingletonSet
β€”β€”
liftHom_algEquiv πŸ“–mathematicalDFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
Polynomial.aeval
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Ring.toSemiring
CommRing.toRing
liftHom
AlgEquiv
AlgEquiv.instFunLike
algEquiv
β€”lift_algEquiv
liftHom_map πŸ“–mathematicalDFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
Polynomial.aeval
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Ring.toSemiring
liftHom
map
β€”lift_algebraMap_apply
lift_map
Polynomial.aeval_def
liftHom_root πŸ“–mathematicalDFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
Polynomial.aeval
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Ring.toSemiring
liftHom
root
β€”lift_algebraMap_apply
lift_root
lift_algEquiv πŸ“–mathematicalPolynomial.evalβ‚‚
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
CommRing.toRing
RingHom.instFunLike
lift
AlgEquiv
AlgEquiv.instFunLike
algEquiv
β€”map_repr
algEquiv_apply_map
lift_map
lift_algebraMap πŸ“–mathematicalPolynomial.evalβ‚‚
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
lift
algebraMap
β€”algebraMap_apply
lift_map
Polynomial.evalβ‚‚_C
lift_algebraMap_apply πŸ“–mathematicalDFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
Polynomial.aeval
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
lift
algebraMap
liftHom
β€”β€”
lift_map πŸ“–mathematicalPolynomial.evalβ‚‚
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
lift
AlgHom
Polynomial
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
β€”evalβ‚‚_repr_eq_evalβ‚‚_of_map_eq
lift_root πŸ“–mathematicalPolynomial.evalβ‚‚
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
lift
root
β€”map_X
lift_map
Polynomial.evalβ‚‚_X
lift_self πŸ“–mathematicalβ€”lift
CommRing.toRing
algebraMap
CommRing.toCommSemiring
CommSemiring.toSemiring
root
aeval_root_self
RingHom.id
Semiring.toNonAssocSemiring
β€”RingHom.ext
aeval_root_self
lift_self_apply
lift_self_apply πŸ“–mathematicalβ€”DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
CommRing.toRing
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
lift
algebraMap
root
aeval_root_self
β€”aeval_root_self
map_repr
lift_map
Polynomial.aeval_def
aeval_root_eq_map
map_X πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
Polynomial.X
root
β€”β€”
map_eq_zero_iff πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
CommRing.toNonUnitalCommRing
Polynomial.commRing
β€”AlgHomClass.toRingHomClass
AlgHom.algHomClass
mem_ker_map
map_repr πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
repr
β€”map_surjective
map_self πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
β€”β€”
map_surjective πŸ“–mathematicalβ€”Polynomial
CommSemiring.toSemiring
DFunLike.coe
AlgHom
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
β€”β€”
mem_ker_map πŸ“–mathematicalβ€”Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal
Polynomial.semiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.ker
AlgHom
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
map
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
CommRing.toNonUnitalCommRing
Polynomial.commRing
β€”AlgHomClass.toRingHomClass
AlgHom.algHomClass
ker_map
Ideal.mem_span_singleton
mkOfAdjoinEqTop_root πŸ“–mathematicalIsIntegral
CommRing.toRing
Algebra.adjoin
CommRing.toCommSemiring
CommSemiring.toSemiring
Set
Set.instSingletonSet
Top.top
Subalgebra
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Algebra.instCompleteLatticeSubalgebra
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
root
minpoly
mkOfAdjoinEqTop
β€”Polynomial.aeval_X
ofAlgEquiv_algEquiv πŸ“–mathematicalβ€”algEquiv
ofAlgEquiv
AlgEquiv.trans
CommRing.toCommSemiring
Ring.toSemiring
AlgEquiv.symm
β€”AlgEquiv.ext
EquivLike.toEmbeddingLike
AdjoinRoot.mk_surjective
adjoinRootAlgEquiv_apply_eq_map
AlgEquiv.apply_symm_apply
ofAlgEquiv_map_apply πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
map
ofAlgEquiv
AlgEquiv
AlgEquiv.instFunLike
β€”β€”
ofAlgEquiv_root πŸ“–mathematicalβ€”root
ofAlgEquiv
DFunLike.coe
AlgEquiv
CommRing.toCommSemiring
Ring.toSemiring
AlgEquiv.instFunLike
β€”β€”
primitive_element_root πŸ“–mathematicalβ€”IntermediateField.adjoin
Set
Set.instSingletonSet
root
EuclideanDomain.toCommRing
Field.toEuclideanDomain
DivisionRing.toRing
Field.toDivisionRing
Top.top
IntermediateField
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
IntermediateField.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”IntermediateField.adjoin_eq_top_of_algebra
adjoin_root_eq_top
repr_add_sub_repr_add_repr_mem_span πŸ“–mathematicalβ€”Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal
Polynomial.semiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.span
Set
Set.instSingletonSet
Polynomial.instSub
CommRing.toRing
repr
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Polynomial.instAdd
β€”AlgHomClass.toRingHomClass
AlgHom.algHomClass
ker_map
map_sub
DistribMulActionSemiHomClass.toAddMonoidHomClass
NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
map_repr
map_add
SemilinearMapClass.toAddHomClass
NonUnitalAlgHomClass.instLinearMapClass
sub_self
repr_zero_mem_span πŸ“–mathematicalβ€”Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal
Polynomial.semiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.span
Set
Set.instSingletonSet
repr
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
β€”AlgHomClass.toRingHomClass
AlgHom.algHomClass
ker_map
map_repr
subsingleton πŸ“–β€”β€”β€”β€”Algebra.subsingleton

IsAdjoinRootMonic

Definitions

NameCategoryTheorems
basis πŸ“–CompOp
7 mathmath: coeff_apply, basis_repr, powerBasis_basis, coeff_apply_lt, coeff_apply_coe, basis_one, basis_apply
coeff πŸ“–CompOp
10 mathmath: coeff_apply, ext_elem_iff, coeff_apply_lt, coeff_injective, coeff_algebraMap, coeff_one, coeff_apply_coe, coeff_apply_le, coeff_root, coeff_root_pow
liftPolyβ‚— πŸ“–CompOp
1 mathmath: liftPolyβ‚—_apply
mkOfAdjoinEqTop πŸ“–CompOpβ€”
mkOfPrimitiveElement πŸ“–CompOpβ€”
modByMonicHom πŸ“–CompOp
6 mathmath: basis_repr, modByMonicHom_map, map_modByMonicHom, modByMonicHom_root_pow, modByMonicHom_root, liftPolyβ‚—_apply
powerBasis πŸ“–CompOp
3 mathmath: powerBasis_dim, powerBasis_gen, powerBasis_basis
toIsAdjoinRoot πŸ“–CompOp
14 mathmath: map_modByMonic, modByMonicHom_map, powerBasis_gen, AdjoinRoot.isAdjoinRootMonic_toAdjoinRoot, isIntegral_root, map_modByMonicHom, modByMonicHom_root_pow, modByMonicHom_root, coeff_root, minpoly_eq, coeff_root_pow, basis_one, modByMonic_repr_map, basis_apply

Theorems

NameKindAssumesProvesValidatesDepends On
basis_apply πŸ“–mathematicalβ€”DFunLike.coe
Module.Basis
Polynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Algebra.toModule
Ring.toSemiring
Module.Basis.instFunLike
basis
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
IsAdjoinRoot.root
toIsAdjoinRoot
β€”RingHomInvPair.ids
Module.Basis.apply_eq_iff
modByMonicHom_root_pow
Polynomial.toFinsupp_X_pow
Finsupp.comapDomain.congr_simp
Finsupp.comapDomain_single
basis_one πŸ“–mathematicalPolynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
Module.Basis
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Algebra.toModule
Ring.toSemiring
Module.Basis.instFunLike
basis
IsAdjoinRoot.root
toIsAdjoinRoot
β€”basis_apply
pow_one
basis_repr πŸ“–mathematicalβ€”DFunLike.coe
Finsupp
Polynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Finsupp.instFunLike
LinearEquiv
RingHom.id
RingHomInvPair.ids
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Finsupp.instAddCommMonoid
Algebra.toModule
Ring.toSemiring
Finsupp.module
Semiring.toModule
EquivLike.toFunLike
DFinsupp.instEquivLikeLinearEquiv
Module.Basis.repr
basis
Polynomial.coeff
LinearMap
Polynomial
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Polynomial.commRing
Polynomial.module
LinearMap.instFunLike
modByMonicHom
β€”RingHomInvPair.ids
Polynomial.toFinsupp_apply
coeff_algebraMap πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
RingHom.instFunLike
algebraMap
Pi.single
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”Algebra.algebraMap_eq_smul_one
map_smul
SemilinearMapClass.toMulActionSemiHomClass
LinearMap.semilinearMapClass
coeff_one
Pi.smul_apply
smul_eq_mul
Pi.apply_single
MulZeroClass.mul_zero
Pi.single.congr_simp
mul_one
coeff_apply πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
Polynomial.natDegree
Finsupp
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Finsupp.instFunLike
LinearEquiv
RingHomInvPair.ids
Finsupp.instAddCommMonoid
Finsupp.module
EquivLike.toFunLike
DFinsupp.instEquivLikeLinearEquiv
Module.Basis.repr
basis
β€”RingHomInvPair.ids
coeff_apply_lt
coeff_apply_le
le_of_not_gt
coeff_apply_coe πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
Polynomial.natDegree
Finsupp
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Finsupp.instFunLike
LinearEquiv
RingHomInvPair.ids
Finsupp.instAddCommMonoid
Finsupp.module
EquivLike.toFunLike
DFinsupp.instEquivLikeLinearEquiv
Module.Basis.repr
basis
β€”coeff_apply_lt
Fin.prop
coeff_apply_le πŸ“–mathematicalPolynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
Polynomial.coeff_eq_zero_of_degree_lt
LT.lt.trans_le
Polynomial.degree_modByMonic_lt
monic
Polynomial.degree_le_of_natDegree_le
coeff_apply_lt πŸ“–mathematicalPolynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
Finsupp
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Finsupp.instFunLike
LinearEquiv
RingHomInvPair.ids
Finsupp.instAddCommMonoid
Finsupp.module
EquivLike.toFunLike
DFinsupp.instEquivLikeLinearEquiv
Module.Basis.repr
basis
β€”RingHomInvPair.ids
basis_repr
coeff_injective πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
β€”ext_elem
coeff_one πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Pi.single
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
CommRing.toRing
β€”coeff_root_pow
deg_pos
pow_zero
coeff_root πŸ“–mathematicalPolynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
IsAdjoinRoot.root
toIsAdjoinRoot
Pi.single
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
β€”coeff_root_pow
pow_one
coeff_root_pow πŸ“–mathematicalPolynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
IsAdjoinRoot.root
toIsAdjoinRoot
Pi.single
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
β€”RingHomInvPair.ids
coeff_apply
basis_apply
Module.Basis.repr_self
Finsupp.single_eq_pi_single
Finsupp.single_apply_left
Fin.val_injective
Pi.single_eq_of_ne
deg_ne_zero πŸ“–β€”β€”β€”β€”LT.lt.ne'
deg_pos
deg_pos πŸ“–mathematicalβ€”Polynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”Module.Basis.index_nonempty
ext_elem πŸ“–β€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
β€”β€”EquivLike.injective
RingHomInvPair.ids
Finite.of_fintype
Module.Basis.equivFun_apply
coeff_apply_coe
Fin.prop
ext_elem_iff πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Pi.addCommMonoid
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Algebra.toModule
Ring.toSemiring
Pi.Function.module
Semiring.toModule
LinearMap.instFunLike
coeff
β€”ext_elem
finite πŸ“–mathematicalβ€”Module.Finite
CommSemiring.toSemiring
CommRing.toCommSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Algebra.toModule
Ring.toSemiring
β€”PowerBasis.finite
finrank πŸ“–mathematicalβ€”Module.finrank
CommSemiring.toSemiring
CommRing.toCommSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Algebra.toModule
Ring.toSemiring
Polynomial.natDegree
β€”PowerBasis.finrank
isIntegral_root πŸ“–mathematicalβ€”IsIntegral
IsAdjoinRoot.root
toIsAdjoinRoot
CommRing.toCommSemiring
Ring.toSemiring
β€”monic
IsAdjoinRoot.aeval_root_self
liftPolyβ‚—_apply πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddCommGroup.toAddCommMonoid
Algebra.toModule
Ring.toSemiring
LinearMap.instFunLike
liftPolyβ‚—
Polynomial
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Polynomial.commRing
Polynomial.module
Semiring.toModule
modByMonicHom
β€”β€”
map_modByMonic πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
IsAdjoinRoot.map
toIsAdjoinRoot
Polynomial.modByMonic
CommRing.toRing
β€”AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.sub_mem_ker_iff
IsAdjoinRoot.mem_ker_map
Polynomial.modByMonic_eq_sub_mul_div
monic
sub_right_comm
sub_self
zero_sub
dvd_neg
map_modByMonicHom πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial.semiring
Ring.toSemiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
IsAdjoinRoot.map
toIsAdjoinRoot
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Polynomial.commRing
Algebra.toModule
Polynomial.module
Semiring.toModule
LinearMap.instFunLike
modByMonicHom
β€”map_modByMonic
IsAdjoinRoot.map_repr
minpoly_eq πŸ“–mathematicalIrreducible
Polynomial
CommSemiring.toSemiring
CommRing.toCommSemiring
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Polynomial.semiring
minpoly
CommRing.toRing
IsAdjoinRoot.root
toIsAdjoinRoot
β€”minpoly.isIntegrallyClosed_dvd
isIntegral_root
IsAdjoinRoot.aeval_root_self
symm
IsEquiv.toSymm
eq_isEquiv
Polynomial.eq_of_monic_of_associated
monic
minpoly.monic
mul_one
Associated.mul_left
associated_one_iff_isUnit
Irreducible.isUnit_or_isUnit
minpoly.not_isUnit
IsDomain.toNontrivial
modByMonicHom_map πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.id
Semiring.toNonAssocSemiring
Polynomial
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Polynomial.commRing
Algebra.toModule
Ring.toSemiring
Polynomial.module
Semiring.toModule
LinearMap.instFunLike
modByMonicHom
AlgHom
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
IsAdjoinRoot.map
toIsAdjoinRoot
Polynomial.modByMonic
CommRing.toRing
β€”modByMonic_repr_map
modByMonicHom_root πŸ“–mathematicalPolynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
Polynomial
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Polynomial.commRing
Algebra.toModule
Ring.toSemiring
Polynomial.module
Semiring.toModule
LinearMap.instFunLike
modByMonicHom
IsAdjoinRoot.root
toIsAdjoinRoot
Polynomial.X
β€”pow_one
modByMonicHom_root_pow
modByMonicHom_root_pow πŸ“–mathematicalPolynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
Polynomial
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Polynomial.commRing
Algebra.toModule
Ring.toSemiring
Polynomial.module
Semiring.toModule
LinearMap.instFunLike
modByMonicHom
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
IsAdjoinRoot.root
toIsAdjoinRoot
Polynomial.semiring
Polynomial.X
β€”Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
Unique.instSubsingleton
IsAdjoinRoot.map_X
map_pow
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
AlgHomClass.toRingHomClass
AlgHom.algHomClass
modByMonicHom_map
Polynomial.modByMonic_eq_self_iff
monic
Polynomial.degree_X_pow
Mathlib.Tactic.Contrapose.contrapose₁
modByMonic_repr_map πŸ“–mathematicalβ€”Polynomial.modByMonic
CommRing.toRing
IsAdjoinRoot.repr
toIsAdjoinRoot
CommRing.toCommSemiring
Ring.toSemiring
DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
Polynomial.semiring
Polynomial.algebraOfAlgebra
Algebra.id
AlgHom.funLike
IsAdjoinRoot.map
β€”Polynomial.modByMonic_eq_of_dvd_sub
monic
AlgHomClass.toRingHomClass
AlgHom.algHomClass
IsAdjoinRoot.mem_ker_map
RingHom.sub_mem_ker_iff
IsAdjoinRoot.map_repr
monic πŸ“–mathematicalβ€”Polynomial.Monic
CommSemiring.toSemiring
β€”β€”
powerBasis_basis πŸ“–mathematicalβ€”PowerBasis.basis
powerBasis
basis
β€”β€”
powerBasis_dim πŸ“–mathematicalβ€”PowerBasis.dim
powerBasis
Polynomial.natDegree
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”β€”
powerBasis_gen πŸ“–mathematicalβ€”PowerBasis.gen
powerBasis
IsAdjoinRoot.root
toIsAdjoinRoot
CommRing.toCommSemiring
Ring.toSemiring
β€”β€”

(root)

Definitions

NameCategoryTheorems
IsAdjoinRoot πŸ“–CompDataβ€”
IsAdjoinRootMonic πŸ“–CompDataβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_quotient_span_eq_natDegree' πŸ“–mathematicalPolynomial.Monic
CommSemiring.toSemiring
CommRing.toCommSemiring
Module.finrank
HasQuotient.Quotient
Polynomial
Ideal
Polynomial.semiring
Ideal.instHasQuotient_1
Polynomial.commRing
Ideal.span
Set
Set.instSingletonSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Ideal.Quotient.commRing
Submodule.Quotient.module'
Polynomial.ring
CommRing.toRing
Ring.toAddCommGroup
Semiring.toModule
Algebra.toSMul
Polynomial.algebraOfAlgebra
Algebra.id
Polynomial.module
IsScalarTower.right
Polynomial.natDegree
β€”IsAdjoinRootMonic.finrank

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