types chapter: small changes
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@ -21,6 +21,11 @@ z2 = PComplex1{Float32}(12, 13)
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@show z1 z2;
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```
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:::{.callout-warning collapse="true" .titlenormal}
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##
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Es ist nicht möglich, in einer Julia-Session eine einmal definierte `struct` später umzudefinieren. Daher verwende ich verschiedene Namen. Eine andere Möglichkeit ist z.B. die Verwendung von [`ProtoStructs.jl`](https://juliahub.com/ui/Packages/General/ProtoStructs).
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:::
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Julia stellt automatisch *default constructors* zur Verfügung:
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- den Konstruktor `PComplex1`, bei dem der Typ `T` von den übergebenen Argumenten abgeleitet wird und
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@ -62,7 +67,7 @@ end
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#| output: false
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#=
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in den ganzen quarto-runs wollen bir hier noch das default-show benutzen
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in den ganzen quarto-runs wollen wir hier noch das default-show benutzen
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=#
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zz = @which Base.show(stdout, PComplex{Float64}(2.,3.))
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if zz.module != Base
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@ -101,8 +106,6 @@ In Julia ist eine große Anzahl von Unicode-Zeichen reserviert für die Verwendu
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Auf Details werden wir in einem späteren Kapitel noch eingehen.
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Und ja, der Julia-Parser ist in einem Lisp(genauer: Scheme)-Dialekt geschrieben. In Julia ist ein kleiner Scheme-Interpreter namens [femtolisp](https://github.com/JeffBezanson/femtolisp) integriert. Geschrieben hat ihn einer der "Väter" von Julia bevor er mit der Arbeit an Julia begann.
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:::
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Das Winkel-Zeichen `∠` steht leider nicht als Operatorsymbol zur Verfügung. Wir weichen aus auf `⋖`. Das kann in Julia als als `\lessdot<tab>` eingegeben werden.
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@ -114,6 +114,7 @@ abstract type MySuperType end
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supertype(MySuperType)
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```
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oder von einem anderen abstrakten Typ:
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```{julia}
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@ -122,6 +123,8 @@ abstract type MySpecialNumber <: Integer end
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supertypes(MySpecialNumber)
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```
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Mit der Definition werden die abstrakten Typen an einer Stelle des Typ-Baums "eingehängt".
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## Die numerischen Typen `Bool` und `Irrational`
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Da sie im Baum der numerischen Typen zu sehen sind, seien sie kurz erklärt:
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@ -19,10 +19,19 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 1,
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"id": "3ee9c4ae",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"z1 = PComplex1{Float64}(-32.0, 33.0)\n",
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"z2 = PComplex1{Float32}(12.0f0, 13.0f0)\n"
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]
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}
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],
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"source": [
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"struct PComplex1{T <: AbstractFloat} <: Number\n",
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" r :: T\n",
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@ -59,7 +68,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 2,
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"id": "214480f6",
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"metadata": {},
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"outputs": [],
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@ -102,10 +111,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 3,
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"id": "95c7386c",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"PComplex{Float64}(3.3, 1.0)"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"z1 = PComplex{Float64}(-3.3, 7π+1)"
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]
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@ -122,10 +142,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 4,
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"id": "e87d3a42",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"PComplex{Float64}(2.0, 0.3)"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"PComplex(r::T, ϕ::T) where {T<:AbstractFloat} = PComplex{T}(r,ϕ)\n",
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"\n",
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@ -164,10 +195,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 5,
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"id": "81818d42",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"PComplex{Float64}(2.0, 1.5707963267948966)"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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" ⋖(r::Real, ϕ::Real) = PComplex(r, π*ϕ/180)\n",
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"\n",
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@ -187,10 +229,18 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 6,
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"id": "4cf73e28",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"z3 = 2.0⋖90.0°\n"
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]
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}
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],
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"source": [
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"using Printf\n",
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"\n",
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@ -229,10 +279,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 7,
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"id": "042418fd",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Main"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f(x) = 3x^3\n",
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"@which f"
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@ -240,10 +301,18 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 27,
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"id": "c20d10e5",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Modul für Addition: Base, Modul für sqrt: Base\n"
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]
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}
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],
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"source": [
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"wp = @which +\n",
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"ws = @which(sqrt)\n",
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@ -260,17 +329,28 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 28,
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"id": "a53f0e79",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"qwurzel (generic function with 1 method)"
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]
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},
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"execution_count": 28,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"qwurzel(z::PComplex) = PComplex(sqrt(z.r), z.ϕ / 2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 29,
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"id": "d6987594",
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"metadata": {},
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"outputs": [],
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@ -297,10 +377,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 30,
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"id": "f93f63c6",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"19"
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]
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},
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"execution_count": 30,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"length(methods(sqrt))"
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]
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@ -315,10 +406,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 32,
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"id": "b88cd74b",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"20"
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]
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},
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"execution_count": 32,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"Base.sqrt(z::PComplex) = qwurzel(z)\n",
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"\n",
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@ -327,10 +429,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 33,
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"id": "e077b8bf",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1.4142135623730951⋖8.6°"
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]
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},
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"execution_count": 33,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sqrt(z2)"
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]
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@ -345,10 +458,18 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 13,
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"id": "5537f7ec",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"z1 * z2 = 6.6⋖74.5°\n"
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]
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}
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],
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"source": [
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"Base.:*(x::PComplex, y::PComplex) = PComplex(x.r * y.r, x.ϕ + y.ϕ)\n",
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"\n",
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@ -372,10 +493,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 14,
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"id": "610a38fe",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"265.53333333333336"
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]
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},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"1//3 + 5 + 5.2 + 0xff"
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]
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@ -407,20 +539,40 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 15,
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"id": "48cae0ae",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(12.0, 34.555, 0.7777777777777778, 255.0)"
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"promote(12, 34.555, 77/99, 0xff)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 16,
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"id": "768934ac",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"z = (33, 27)\n",
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"typeof(z) = Tuple{BigInt, BigInt}\n"
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]
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}
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],
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"source": [
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"z = promote(BigInt(33), 27)\n",
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"@show z typeof(z);"
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@ -444,10 +596,18 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 17,
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"id": "70306adc",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"promote_type(Rational{Int64}, ComplexF64, Float32) = ComplexF64\n"
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]
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}
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],
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"source": [
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"@show promote_type(Rational{Int64}, ComplexF64, Float32);"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 18,
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"id": "b326a121",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"3.0"
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]
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},
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"z = convert(Float64, 3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 19,
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"id": "57606643",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"23"
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]
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},
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"execution_count": 19,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"z = convert(Int64, 23.00)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 20,
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"id": "a3b39504",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"ename": "LoadError",
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"evalue": "InexactError: Int64(2.3)",
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"output_type": "error",
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"traceback": [
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"InexactError: Int64(2.3)",
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"",
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"Stacktrace:",
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" [1] Int64",
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" @ ./float.jl:912 [inlined]",
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" [2] convert(::Type{Int64}, x::Float64)",
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" @ Base ./number.jl:7",
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" [3] top-level scope",
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" @ In[20]:1"
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]
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}
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],
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"source": [
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"z = convert(Int64, 2.3)"
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]
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@ -525,10 +724,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 21,
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"id": "e258330e",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"PComplex"
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"## (a) r, ϕ beliebige Reals, z.B. Integers, Rationals\n",
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"\n",
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@ -566,10 +776,21 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 22,
|
||||
"id": "ec747779",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(0.6⋖45.0°, 1.4142135623730951⋖45.0°, 13.0⋖180.0°)"
|
||||
]
|
||||
},
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"3//5 ⋖ 45, PComplex(Complex(1,1)), PComplex(-13) "
|
||||
]
|
||||
@ -586,7 +807,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 24,
|
||||
"id": "806fff6a",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
@ -616,20 +837,42 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 25,
|
||||
"id": "cc47939d",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(2.0⋖90.0°, 6.0⋖90.0°)"
|
||||
]
|
||||
},
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"z3, 3z3"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 26,
|
||||
"id": "63c20bc7",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(43.26661530556787⋖64.0°, 16.970562748477143⋖8.6°)"
|
||||
]
|
||||
},
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"(3.0+2im) * (12⋖30.3), 12sqrt(z2) "
|
||||
]
|
||||
@ -733,6 +976,12 @@
|
||||
"display_name": "Julia 1.10.2",
|
||||
"language": "julia",
|
||||
"name": "julia-1.10"
|
||||
},
|
||||
"language_info": {
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.10.2"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
@ -1,14 +0,0 @@
|
||||
diff --git a/src/core/jupyter/jupyter.ts b/src/core/jupyter/jupyter.ts
|
||||
index 4a1d04963..2fbda1d12 100644
|
||||
--- a/src/core/jupyter/jupyter.ts
|
||||
+++ b/src/core/jupyter/jupyter.ts
|
||||
@@ -1575,7 +1575,7 @@ function mdOutputStream(output: JupyterOutputStream) {
|
||||
}
|
||||
|
||||
function mdOutputError(output: JupyterOutputError) {
|
||||
- return mdCodeOutput([output.ename + ": " + output.evalue]);
|
||||
+ return mdCodeOutput([output.ename + ": " + output.traceback.join('\n')]);
|
||||
}
|
||||
|
||||
async function mdOutputDisplayData(
|
||||
|
||||
Loading…
Reference in New Issue
Block a user