Structures · Analysis
RCLike
This typeclass captures properties shared by ℝ and ℂ, with an API that closely matches that of ℂ.
- Defined in
- Mathlib.Analysis.RCLike.Basic
- Shape
- One type argument · adds re, im, I, I_re_ax, I_mul_I_ax, re_add_im_ax, ofReal_re_ax, ofReal_im_ax, mul_re_ax, mul_im_ax, conj_re_ax, conj_im_ax, conj_I_ax, norm_sq_eq_def_ax, mul_im_I_ax, toPartialOrder, le_iff_re_im, toDecidableEq
Extends4
Extended by0
Nothing extends this class yet.
Forgetful instances
Every RCLike is also a
Concrete types that are instances2
- Real
- Complex
How is a type an instance?
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Assumed by3,119
- RCLike.ofReal
- RCLike.re
- Submodule.orthogonal
- RCLike.im
- LinearMap.IsSymmetric
- RCLike.toPartialOrder
- Submodule.orthogonalProjectionOnto
- OrthonormalBasis.toBasis
- RCLike.I
- innerSL
- Submodule.starProjection
- EuclideanGeometry.orthogonalProjection
- Orthonormal
- ContinuousLinearMap.adjoint
- inner_self_eq_norm_sq_to_K
- inner_smul_right
- LinearMap.adjoint
- OrthonormalBasis.repr
- stdOrthonormalBasis
- RCLike.ofReal_re
- inner_zero_left
- Submodule.IsOrtho
- inner_smul_left
- inner_conj_symm
- OrthogonalFamily
- MeasureTheory.lpMeas
- InnerProductSpace.toDual
- MeasureTheory.integral_const_mul
- RCLike.ofReal_im
- inner_neg_right
- inner_zero_right
- LinearMap.IsPositive
- ContinuousLinearMap.IsPositive
- MeasureTheory.condExpL2
- InnerProductSpace.rankOne
- Matrix.IsHermitian.eigenvalues
- Affine.Simplex.orthogonalProjectionSpan
- inner_neg_left
- RCLike.wInner
- ContinuousLinearMap.integral_comp_comm
- curveIntegralFun
- InnerProductSpace.Core.toPreInner'
- curveIntegral
- ContinuousLinearMap.rTensor
- ClosedSubmodule.orthogonal
- Submodule.reflection
- LinearMap.IsSymmetric.eigenvalues
- ContinuousLinearMap.lTensor
- InnerProductSpace.gramSchmidt
- inner_add_left
Ancestors166
- Add
- AddAction
- AddCancelCommMonoid
- AddCancelMonoid
- AddCommGroup
- AddCommGroupWithOne
- AddCommMagma
- AddCommMonoid
- AddCommMonoidWithOne
- AddCommSemigroup
- AddGroup
- AddGroupWithOne
- AddLeftCancelMonoid
- AddLeftCancelSemigroup
- AddMonoid
- AddMonoidWithOne
- AddRightCancelMonoid
- AddRightCancelSemigroup
- AddSemigroup
- AddSemigroupAction
- AddTorsor
- AddZero
- AddZeroClass
- Algebra
- AlgebraicGeometry.QuasiSeparated
- Bornology
- Bracket
- ChartedSpace
- CommGroupWithZero
- CommMagma
- CommMonoid
- CommMonoidWithZero
- CommRing
- CommSemigroup
- CommSemiring
- CompactSpace
- CompactlyCoherentSpace
- CompleteSpace
- DenselyNormedField
- Dist
- Distrib
- Div
- DivInvMonoid
- DivInvOneMonoid
- DivisionCommMonoid
- DivisionMonoid
- DivisionRing
- DivisionSemiring
- Dvd
- EDist
- EMetricSpace
- ENorm
- EuclideanDomain
- Field
- GroupWithZero
- HAdd
- HDiv
- HMod
- HMul
- HSMul
- HSub
- HVAdd
- Ideal.FiniteHeight
- Infinite
- IntCast
- Inv
- InvOneClass
- InvolutiveInv
- InvolutiveNeg
- InvolutiveStar
- IsJacobsonRing
- IsLeftCancelAdd
- IsRightCancelAdd
- IsSemiprimaryRing
- Lean.Grind.AddCommGroup
- Lean.Grind.AddCommMonoid
- Lean.Grind.CommRing
- Lean.Grind.CommSemiring
- Lean.Grind.Field
- Lean.Grind.IntModule
- Lean.Grind.NatModule
- Lean.Grind.Ring
- Lean.Grind.Semiring
- LocallyPathConnectedSpace
- MeasurableSpace
- MetricSpace
- Mod
- Monoid
- MonoidWithZero
- Mul
- MulAction
- MulOne
- MulOneClass
- MulZeroClass
- MulZeroOneClass
- NNDist
- NNNorm
- NNRatCast
- NPow
- NSMul
- NatCast
- Neg
- NegZeroClass
- NonAssocCommRing
- NonAssocCommSemiring
- NonAssocRing
- NonAssocSemiring
- NonUnitalCommRing
- NonUnitalCommSemiring
- NonUnitalNonAssocCommRing
- NonUnitalNonAssocCommSemiring
- NonUnitalNonAssocRing
- NonUnitalNonAssocSemiring
- NonUnitalNormedCommRing
- NonUnitalNormedRing
- NonUnitalRing
- NonUnitalSeminormedCommRing
- NonUnitalSeminormedRing
- NonUnitalSemiring
- Nonempty
- Nontrivial
- NontriviallyNormedField
- Norm
- NormedAddCommGroup
- NormedAddGroup
- NormedAlgebra
- NormedCommRing
- NormedDivisionRing
- NormedField
- NormedRing
- OfNat
- OfScientific
- One
- PrespectralSpace
- PseudoEMetricSpace
- PseudoMetricSpace
- QuasiSeparatedSpace
- RatCast
- Ring
- SMul
- Semifield
- Semigroup
- SemigroupAction
- SemigroupWithZero
- SeminormedAddCommGroup
- SeminormedAddGroup
- SeminormedCommRing
- SeminormedRing
- Semiring
- SequentialSpace
- Star
- StarMul
- StarRing
- Sub
- SubNegMonoid
- SubNegZeroMonoid
- SubtractionCommMonoid
- SubtractionMonoid
- TopologicalSpace
- Topology.IsGeneratedBy
- UniformSpace
- VAdd
- VSub
- ZPow
- ZSMul
- Zero