Documentation Verification Report

Smeval

πŸ“ Source: Mathlib/Algebra/Polynomial/Smeval.lean

Statistics

MetricCount
Definitionssmeval, linearMap, smul_pow
3
Theoremsaeval_coe_eq_smeval, aeval_eq_smeval, eval_eq_smeval, evalβ‚‚_smulOneHom_eq_smeval, leval_coe_eq_smeval, linearMap, linearMap_apply, smeval_C, smeval_C_mul, smeval_X, smeval_X_mul, smeval_X_pow, smeval_X_pow_assoc, smeval_X_pow_mul, smeval_add, smeval_assoc_X_pow, smeval_at_natCast, smeval_at_zero, smeval_commute, smeval_commute_left, smeval_comp, smeval_def, smeval_eq_sum, smeval_monomial, smeval_monomial_mul, smeval_mul, smeval_mul_X, smeval_mul_X_pow, smeval_natCast, smeval_neg, smeval_neg_nat, smeval_one, smeval_pow, smeval_smul, smeval_sub, smeval_zero
36
Total39

Polynomial

Definitions

NameCategoryTheorems
smeval πŸ“–CompOp
54 mathmath: ascPochhammer_smeval_neg_eq_descPochhammer, smeval_monomial_mul, smeval_commute, smeval_mul_X, Ring.choose_eq_smul, smeval_X_pow, smeval_assoc_X_pow, smeval.linearMap_apply, smeval_neg_nat, smeval_smul, smeval_sub, LaurentSeries.derivative_iterate_coeff, smeval_natCast, descPochhammer_smeval_eq_descFactorial, smeval_C, smeval_mul, Ring.factorial_nsmul_multichoose_eq_ascPochhammer, smeval_X_pow_mul, smeval_X, Ring.descPochhammer_smeval_add, aeval_eq_smeval, smeval_at_natCast, smeval_C_mul, Ring.ascPochhammer_succ_succ, BinomialRing.factorial_nsmul_multichoose, smeval_X_mul, Ring.smeval_ascPochhammer_int_ofNat, aeval_coe_eq_smeval, smeval_one, Ring.smeval_ascPochhammer_nat_cast, ascPochhammer_smeval_cast, smeval_at_zero, smeval_def, smeval_pow, Ring.smeval_ascPochhammer_neg_add, smeval_comp, smeval_monomial, smeval_X_pow_assoc, Ring.smeval_ascPochhammer_succ_neg, smeval_eq_sum, ascPochhammer_smeval_eq_eval, leval_coe_eq_smeval, eval_eq_smeval, smeval_add, Ring.smeval_ascPochhammer_neg_of_lt, Ring.descPochhammer_eq_factorial_smul_choose, Ring.descPochhammer_succ_succ_smeval, descPochhammer_smeval_eq_ascPochhammer, smeval_neg, Ring.smeval_ascPochhammer_self_neg, smeval_commute_left, smeval_zero, smeval_mul_X_pow, evalβ‚‚_smulOneHom_eq_smeval
smul_pow πŸ“–CompOp
2 mathmath: smeval_def, smeval_eq_sum

Theorems

NameKindAssumesProvesValidatesDepends On
aeval_coe_eq_smeval πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
semiring
algebraOfAlgebra
Algebra.id
AlgHom.funLike
aeval
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toMulActionWithZero
Algebra.toModule
β€”aeval_eq_smeval
aeval_eq_smeval πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
semiring
algebraOfAlgebra
Algebra.id
AlgHom.funLike
aeval
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toMulActionWithZero
Algebra.toModule
β€”aeval_def
evalβ‚‚_def
Algebra.algebraMap_eq_smul_one'
smeval_def
Algebra.smul_mul_assoc
one_mul
eval_eq_smeval πŸ“–mathematicalβ€”eval
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MonoidWithZero.toMulActionWithZero
β€”eval_eq_sum
smeval_eq_sum
evalβ‚‚_smulOneHom_eq_smeval πŸ“–mathematicalβ€”evalβ‚‚
RingHom.smulOneHom
Semiring.toNonAssocSemiring
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toMulActionWithZero
β€”smeval_eq_sum
evalβ‚‚_eq_sum
smul_one_mul
leval_coe_eq_smeval πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
Polynomial
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
semiring
module
Semiring.toModule
LinearMap.instFunLike
leval
smeval
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MonoidWithZero.toMulActionWithZero
β€”eval_eq_smeval
smeval_C πŸ“–mathematicalβ€”smeval
DFunLike.coe
RingHom
Polynomial
Semiring.toNonAssocSemiring
semiring
RingHom.instFunLike
C
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SMulWithZero.toSMulZeroClass
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Semiring.toMonoidWithZero
MulActionWithZero.toSMulWithZero
β€”smeval_eq_sum
sum_C_index
zero_smul
smeval_C_mul πŸ“–mathematicalβ€”smeval
Polynomial
instMul
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
semiring
RingHom.instFunLike
C
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”induction_on'
mul_add
Distrib.leftDistribClass
smeval_add
smul_add
C_mul_monomial
smeval_monomial
SemigroupAction.mul_smul
smeval_X πŸ“–mathematicalβ€”smeval
X
β€”smeval_eq_sum
sum_X_index
zero_smul
one_smul
smeval_X_mul πŸ“–mathematicalβ€”smeval
Polynomial
instMul
X
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”induction_on'
mul_add
Distrib.leftDistribClass
smeval_add
monomial_one_one_eq_X
monomial_mul_monomial
smeval_monomial
one_mul
npow_add
npow_one
mul_smul_comm
smeval_X_pow πŸ“–mathematicalβ€”smeval
Polynomial
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
semiring
X
β€”X_pow_eq_monomial
smeval_eq_sum
sum_monomial_index
zero_smul
one_smul
smeval_X_pow_assoc πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
Module.toMulActionWithZero
β€”induction_on'
smeval_add
mul_add
Distrib.leftDistribClass
smeval_monomial
mul_smul_comm
npow_mul_assoc
smeval_X_pow_mul πŸ“–mathematicalβ€”smeval
Polynomial
instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
semiring
X
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”pow_zero
one_mul
npow_zero
add_comm
npow_add
Monoid.PowAssoc
mul_assoc
npow_one
smeval_X_mul
smeval_X_pow_assoc
smeval_add πŸ“–mathematicalβ€”smeval
Polynomial
instAdd
Module.toMulActionWithZero
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”smeval_eq_sum
sum_add_index
smul_pow.eq_1
zero_smul
add_smul
smeval_assoc_X_pow πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
Module.toMulActionWithZero
β€”induction_on'
smeval_add
add_mul
Distrib.rightDistribClass
smeval_monomial
smul_mul_assoc
npow_mul_assoc
smeval_at_natCast πŸ“–mathematicalβ€”smeval
Nat.instSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
AddCommMonoid.toNatModule
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAddCommMonoid
Monoid.toNatPow
Nat.instMonoid
MonoidWithZero.toMulActionWithZero
Semiring.toMonoidWithZero
β€”induction_on'
smeval_add
Nat.cast_add
smeval_monomial
nsmul_eq_mul
smul_eq_mul
Nat.cast_mul
Nat.cast_npow
smeval_at_zero πŸ“–mathematicalβ€”smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
coeff
AddMonoidWithOne.toOne
β€”induction_on'
smeval_add
coeff_add
add_smul
smeval_C
npow_zero
coeff_C_zero
coeff_monomial_succ
smeval_monomial
npow_add
npow_one
MulZeroClass.mul_zero
zero_smul
smul_zero
smeval_commute πŸ“–mathematicalCommute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toMulActionWithZero
β€”induction_on'
Commute.add_left
smeval_add
smeval_monomial
Commute.smul_left
npow_zero
Monoid.PowAssoc
commute_iff_eq
Commute.symm
smeval_commute_left
pow_succ
mul_assoc
smeval_commute_left πŸ“–mathematicalCommute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
smeval
NonUnitalNonAssocSemiring.toAddCommMonoid
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toMulActionWithZero
β€”induction_on'
Commute.add_left
smeval_add
smeval_monomial
Commute.smul_left
npow_zero
Monoid.PowAssoc
commute_iff_eq
pow_succ
mul_assoc
Commute.right_comm
smeval_comp πŸ“–mathematicalβ€”smeval
comp
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
β€”induction_on'
add_comp
smeval_add
monomial_comp
smeval_C_mul
smeval_pow
smeval_monomial
smeval_def πŸ“–mathematicalβ€”smeval
sum
smul_pow
β€”β€”
smeval_eq_sum πŸ“–mathematicalβ€”smeval
sum
smul_pow
β€”smeval_def
smeval_monomial πŸ“–mathematicalβ€”smeval
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
Polynomial
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
semiring
Semiring.toModule
module
LinearMap.instFunLike
monomial
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SMulWithZero.toSMulZeroClass
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Semiring.toMonoidWithZero
MulActionWithZero.toSMulWithZero
β€”smeval_eq_sum
sum_monomial_index
zero_smul
smeval_monomial_mul πŸ“–mathematicalβ€”smeval
Polynomial
instMul
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
semiring
Semiring.toModule
module
LinearMap.instFunLike
monomial
Module.toMulActionWithZero
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”induction_on'
smeval_add
C_mul_X_pow_eq_monomial
mul_assoc
smeval_C_mul
smeval_X_pow_mul
smeval_monomial
monomial_mul_monomial
npow_add
SemigroupAction.mul_smul
mul_smul_comm
smeval_mul πŸ“–mathematicalβ€”smeval
Polynomial
instMul
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”induction_on'
add_mul
Distrib.rightDistribClass
smeval_add
smeval_monomial_mul
smeval_monomial
smul_mul_assoc
smeval_mul_X πŸ“–mathematicalβ€”smeval
Polynomial
instMul
X
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”induction_on'
add_mul
Distrib.rightDistribClass
smeval_add
monomial_mul_monomial
mul_one
smeval_monomial
npow_add
npow_one
smul_mul_assoc
smeval_mul_X_pow πŸ“–mathematicalβ€”smeval
Polynomial
instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
semiring
X
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”npow_zero
Monoid.PowAssoc
mul_one
npow_add
mul_assoc
npow_one
smeval_mul_X
smeval_assoc_X_pow
smeval_natCast πŸ“–mathematicalβ€”smeval
Polynomial
instNatCast
Module.toMulActionWithZero
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
β€”Nat.cast_zero
smeval_zero
zero_smul
Nat.cast_succ
smeval_add
smeval_one
add_nsmul
smeval_neg πŸ“–mathematicalβ€”smeval
Ring.toSemiring
Polynomial
instNeg
AddCommGroup.toAddCommMonoid
Module.toMulActionWithZero
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”add_eq_zero_iff_eq_neg
smeval_add
neg_add_cancel
smeval_zero
smeval_neg_nat πŸ“–mathematicalβ€”smeval
Nat.instSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Module.toMulActionWithZero
AddCommMonoid.toNatModule
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
AddGroupWithOne.toIntCast
Int.instAddCommMonoid
Monoid.toNatPow
Int.instMonoid
β€”smeval_eq_sum
Finset.sum_congr
nsmul_eq_mul
Int.cast_sum
Int.cast_mul
Int.cast_natCast
Int.cast_npow
Int.cast_neg
smeval_one πŸ“–mathematicalβ€”smeval
Polynomial
instOne
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
β€”C_1
smeval_C
one_smul
smeval_pow πŸ“–mathematicalβ€”smeval
Polynomial
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
semiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
β€”npow_zero
Monoid.PowAssoc
smeval_one
one_smul
npow_add
smeval_mul
pow_one
npow_one
smeval_smul πŸ“–mathematicalβ€”smeval
Polynomial
SMulZeroClass.toSMul
instZero
smulZeroClass
DistribSMul.toSMulZeroClass
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instDistribSMul
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toMulActionWithZero
AddZero.toZero
AddZeroClass.toAddZero
AddCommMonoid.toAddMonoid
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”induction_on'
smul_add
smeval_add
smul_monomial
smeval_monomial
smul_assoc
IsScalarTower.left
smeval_sub πŸ“–mathematicalβ€”smeval
Ring.toSemiring
Polynomial
instSub
AddCommGroup.toAddCommMonoid
Module.toMulActionWithZero
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_eq_add_neg
smeval_add
smeval_neg
smeval_zero πŸ“–mathematicalβ€”smeval
Polynomial
instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”smeval_eq_sum
sum_zero_index

Polynomial.leval_eq_smeval

Theorems

NameKindAssumesProvesValidatesDepends On
linearMap πŸ“–mathematicalβ€”Polynomial.leval
Polynomial.smeval.linearMap
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Semiring.toModule
β€”LinearMap.ext
Polynomial.leval_apply
Polynomial.smeval.linearMap_apply
Polynomial.eval_eq_smeval

Polynomial.smeval

Definitions

NameCategoryTheorems
linearMap πŸ“–CompOp
2 mathmath: linearMap_apply, Polynomial.leval_eq_smeval.linearMap

Theorems

NameKindAssumesProvesValidatesDepends On
linearMap_apply πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
Polynomial
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Polynomial.semiring
Polynomial.module
Semiring.toModule
LinearMap.instFunLike
linearMap
Polynomial.smeval
Module.toMulActionWithZero
β€”β€”

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