diff --git a/chapters/pcomplex.qmd b/chapters/pcomplex.qmd
index 95e2be2..60be000 100644
--- a/chapters/pcomplex.qmd
+++ b/chapters/pcomplex.qmd
@@ -21,6 +21,11 @@ z2 = PComplex1{Float32}(12, 13)
 @show z1 z2;
 ```
 
+:::{.callout-warning  collapse="true" .titlenormal}
+## 
+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).
+:::
+
 Julia stellt automatisch *default constructors* zur Verfügung:
 
 - den Konstruktor `PComplex1`, bei dem der Typ `T` von den übergebenen Argumenten abgeleitet wird und
@@ -62,7 +67,7 @@ end
 #| output: false
 
 #=
-in den ganzen quarto-runs wollen bir hier noch das default-show benutzen
+in den ganzen quarto-runs wollen wir hier noch das default-show benutzen
 =#
 zz = @which Base.show(stdout, PComplex{Float64}(2.,3.))
 if zz.module != Base
@@ -101,8 +106,6 @@ In Julia ist eine große Anzahl von Unicode-Zeichen reserviert für die Verwendu
 
 Auf Details  werden wir in einem späteren Kapitel noch eingehen. 
 
-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.  
-
 :::
 
 Das Winkel-Zeichen `∠` steht leider nicht als Operatorsymbol zur Verfügung. Wir weichen aus auf `⋖`. Das kann in Julia als  als `\lessdot<tab>` eingegeben werden.
diff --git a/chapters/types.qmd b/chapters/types.qmd
index ff7abe4..197a5b6 100644
--- a/chapters/types.qmd
+++ b/chapters/types.qmd
@@ -114,6 +114,7 @@ abstract type MySuperType end
 
 supertype(MySuperType)
 ``` 
+
 oder von einem anderen abstrakten Typ:
 
 ```{julia}
@@ -122,6 +123,8 @@ abstract type MySpecialNumber <: Integer end
 supertypes(MySpecialNumber)
 ```
 
+Mit der Definition werden die abstrakten Typen an einer Stelle des Typ-Baums "eingehängt".
+
 ## Die numerischen Typen `Bool` und `Irrational` 
 
 Da sie im Baum der numerischen Typen zu sehen sind, seien sie kurz erklärt: 
diff --git a/nb/pcomplex.ipynb b/nb/pcomplex.ipynb
index edc33ee..e96abd8 100644
--- a/nb/pcomplex.ipynb
+++ b/nb/pcomplex.ipynb
@@ -19,10 +19,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "3ee9c4ae",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "z1 = PComplex1{Float64}(-32.0, 33.0)\n",
+      "z2 = PComplex1{Float32}(12.0f0, 13.0f0)\n"
+     ]
+    }
+   ],
    "source": [
     "struct PComplex1{T <: AbstractFloat} <: Number\n",
     "    r :: T\n",
@@ -59,7 +68,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "214480f6",
    "metadata": {},
    "outputs": [],
@@ -102,10 +111,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "95c7386c",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "PComplex{Float64}(3.3, 1.0)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "z1 = PComplex{Float64}(-3.3, 7π+1)"
    ]
@@ -122,10 +142,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "e87d3a42",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "PComplex{Float64}(2.0, 0.3)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "PComplex(r::T, ϕ::T) where {T<:AbstractFloat} = PComplex{T}(r,ϕ)\n",
     "\n",
@@ -164,10 +195,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "id": "81818d42",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "PComplex{Float64}(2.0, 1.5707963267948966)"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     " ⋖(r::Real, ϕ::Real) = PComplex(r, π*ϕ/180)\n",
     "\n",
@@ -187,10 +229,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "id": "4cf73e28",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "z3 = 2.0⋖90.0°\n"
+     ]
+    }
+   ],
    "source": [
     "using Printf\n",
     "\n",
@@ -229,10 +279,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "id": "042418fd",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Main"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "f(x) = 3x^3\n",
     "@which f"
@@ -240,10 +301,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 27,
    "id": "c20d10e5",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Modul für Addition: Base, Modul für sqrt: Base\n"
+     ]
+    }
+   ],
    "source": [
     "wp = @which +\n",
     "ws = @which(sqrt)\n",
@@ -260,17 +329,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 28,
    "id": "a53f0e79",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "qwurzel (generic function with 1 method)"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "qwurzel(z::PComplex) = PComplex(sqrt(z.r), z.ϕ / 2)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 29,
    "id": "d6987594",
    "metadata": {},
    "outputs": [],
@@ -297,10 +377,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 30,
    "id": "f93f63c6",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "19"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "length(methods(sqrt))"
    ]
@@ -315,10 +406,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 32,
    "id": "b88cd74b",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "20"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "Base.sqrt(z::PComplex) = qwurzel(z)\n",
     "\n",
@@ -327,10 +429,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 33,
    "id": "e077b8bf",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1.4142135623730951⋖8.6°"
+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "sqrt(z2)"
    ]
@@ -345,10 +458,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "id": "5537f7ec",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "z1 * z2 = 6.6⋖74.5°\n"
+     ]
+    }
+   ],
    "source": [
     "Base.:*(x::PComplex, y::PComplex) = PComplex(x.r * y.r, x.ϕ + y.ϕ)\n",
     "\n",
@@ -372,10 +493,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "id": "610a38fe",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "265.53333333333336"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "1//3 + 5 + 5.2 + 0xff"
    ]
@@ -407,20 +539,40 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "id": "48cae0ae",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(12.0, 34.555, 0.7777777777777778, 255.0)"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "promote(12, 34.555, 77/99, 0xff)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "id": "768934ac",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "z = (33, 27)\n",
+      "typeof(z) = Tuple{BigInt, BigInt}\n"
+     ]
+    }
+   ],
    "source": [
     "z = promote(BigInt(33), 27)\n",
     "@show z typeof(z);"
@@ -444,10 +596,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "id": "70306adc",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "promote_type(Rational{Int64}, ComplexF64, Float32) = ComplexF64\n"
+     ]
+    }
+   ],
    "source": [
     "@show promote_type(Rational{Int64}, ComplexF64, Float32);"
    ]
@@ -465,30 +625,69 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "id": "b326a121",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3.0"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "z = convert(Float64, 3)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "id": "57606643",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "23"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "z = convert(Int64, 23.00)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "id": "a3b39504",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "ename": "LoadError",
+     "evalue": "InexactError: Int64(2.3)",
+     "output_type": "error",
+     "traceback": [
+      "InexactError: Int64(2.3)",
+      "",
+      "Stacktrace:",
+      " [1] Int64",
+      "   @ ./float.jl:912 [inlined]",
+      " [2] convert(::Type{Int64}, x::Float64)",
+      "   @ Base ./number.jl:7",
+      " [3] top-level scope",
+      "   @ In[20]:1"
+     ]
+    }
+   ],
    "source": [
     "z = convert(Int64, 2.3)"
    ]
@@ -525,10 +724,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "id": "e258330e",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "PComplex"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "## (a) r, ϕ beliebige Reals, z.B.  Integers, Rationals\n",
     "\n",
@@ -566,10 +776,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "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,
diff --git a/patch-quarto-stacktrace b/patch-quarto-stacktrace
deleted file mode 100644
index 5c62a0c..0000000
--- a/patch-quarto-stacktrace
+++ /dev/null
@@ -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(
-