PoincarΓ© disc #
In this file we define Complex.UnitDisc
to be the unit disc in the complex plane. We also
introduce some basic operations on this disc.
The complex unit disc, denoted as π»
withinin the Complex namespace
Equations
- Complex.UnitDisc = β(Metric.ball 0 1)
The complex unit disc, denoted as π»
withinin the Complex namespace
Equations
- UnitDisc.termπ» = Lean.ParserDescr.node `UnitDisc.termπ» 1024 (Lean.ParserDescr.symbol "π»")
Coercion to β
.
Equations
Equations
@[deprecated Complex.UnitDisc.norm_lt_one (since := "2025-02-16")]
Alias of Complex.UnitDisc.norm_lt_one
.
@[deprecated Complex.UnitDisc.norm_ne_one (since := "2025-02-16")]
Alias of Complex.UnitDisc.norm_ne_one
.
Equations
- Complex.UnitDisc.instInhabited = { default := 0 }
instance
Complex.UnitDisc.isScalarTower_closedBall_closedBall :
IsScalarTower (β(Metric.closedBall 0 1)) (β(Metric.closedBall 0 1)) UnitDisc
instance
Complex.UnitDisc.isScalarTower_closedBall :
IsScalarTower (β(Metric.closedBall 0 1)) UnitDisc UnitDisc
instance
Complex.UnitDisc.instSMulCommClass_closedBall :
SMulCommClass (β(Metric.closedBall 0 1)) UnitDisc UnitDisc
instance
Complex.UnitDisc.instSMulCommClass_closedBall' :
SMulCommClass UnitDisc (β(Metric.closedBall 0 1)) UnitDisc
@[simp]
Conjugate point of the unit disc.
Equations
- z.conj = Complex.UnitDisc.mk ((starRingEnd β) βz) β―