update work flow

quarto/derivatives/newtons_method.qmd

@@ -1,33 +1,7 @@
 # Newton's method
 
 
-```{julia}
-#| echo: false
-
-import Logging
-Logging.disable_logging(Logging.Info) # or e.g. Logging.Info
-Logging.disable_logging(Logging.Warn)
-
-import SymPy
-function Base.show(io::IO, ::MIME"text/html", x::T) where {T <: SymPy.SymbolicObject}
-    println(io, "<span class=\"math-left-align\" style=\"padding-left: 4px; width:0; float:left;\"> ")
-    println(io, "\\[")
-    println(io, sympy.latex(x))
-    println(io, "\\]")
-    println(io, "</span>")
-end
-
-# hack to work around issue
-import Markdown
-import CalculusWithJulia
-function CalculusWithJulia.WeaveSupport.ImageFile(d::Symbol, f::AbstractString, caption; kwargs...)
-    nm = joinpath("..", string(d), f)
-    u = "![$caption]($nm)"
-    Markdown.parse(u)
-end
-
-nothing
-```
+{{< include ../_common_code.qmd >}}
 
 This section uses these add-on packages:
 
@@ -311,6 +285,97 @@ gif(anim, imgfile, fps = 1)
 ImageFile(imgfile, caption)
 ```
 
+---
+
+
+This interactive graphic (built using [JSXGraph](https://jsxgraph.uni-bayreuth.de/wp/index.html)) allows the adjustment of the point `x0`, initially at $0.85$. Five iterations of Newton's method are illustrated. Different positions of `x0` clearly converge, others will not.
+
+
+```{=html}
+<div id="jsxgraph" style="width: 500px; height: 500px;"></div>
+```
+
+```{ojs}
+//| echo: false
+//| output: false
+
+JXG = require("jsxgraph");
+
+// newton's method
+
+b = JXG.JSXGraph.initBoard('jsxgraph', {
+    boundingbox: [-3,5,3,-5], axis:true
+});
+
+
+f = function(x) {return x*x*x*x*x - x - 1};
+fp = function(x) { return 4*x*x*x*x - 1};
+x0 = 0.85;
+
+nm = function(x) { return x - f(x)/fp(x);};
+
+l = b.create('point', [-1.5,0], {name:'', size:0});
+r = b.create('point', [1.5,0], {name:'', size:0});
+xaxis = b.create('line', [l,r])
+
+
+P0 = b.create('glider', [x0,0,xaxis], {name:'x0'});
+P0a = b.create('point', [function() {return P0.X();},
+			     function() {return f(P0.X());}], {name:''});
+
+P1 = b.create('point', [function() {return nm(P0.X());},
+			    0], {name:''});
+P1a = b.create('point', [function() {return P1.X();},
+			     function() {return f(P1.X());}], {name:''});
+
+P2 = b.create('point', [function() {return nm(P1.X());},
+			    0], {name:''});
+P2a = b.create('point', [function() {return P2.X();},
+			     function() {return f(P2.X());}], {name:''});
+
+P3 = b.create('point', [function() {return nm(P2.X());},
+			    0], {name:''});
+P3a = b.create('point', [function() {return P3.X();},
+			     function() {return f(P3.X());}], {name:''});
+
+P4 = b.create('point', [function() {return nm(P3.X());},
+			    0], {name:''});
+P4a = b.create('point', [function() {return P4.X();},
+			     function() {return f(P4.X());}], {name:''});
+P5 = b.create('point', [function() {return nm(P4.X());},
+			    0], {name:'x5', strokeColor:'black'});
+
+
+
+
+
+P0a.setAttribute({fixed:true});
+P1.setAttribute({fixed:true});
+P1a.setAttribute({fixed:true});
+P2.setAttribute({fixed:true});
+P2a.setAttribute({fixed:true});
+P3.setAttribute({fixed:true});
+P3a.setAttribute({fixed:true});
+P4.setAttribute({fixed:true});
+P4a.setAttribute({fixed:true});
+P5.setAttribute({fixed:true});
+
+sc = '#000000';
+b.create('segment', [P0,P0a], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P0a, P1], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P1,P1a], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P1a, P2], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P2,P2a], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P2a, P3], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P3,P3a], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P3a, P4], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P4,P4a], {strokeColor:sc, strokeWidth:1});
+b.create('segment', [P4a, P5], {strokeColor:sc, strokeWidth:1});
+
+b.create('functiongraph', [f, -1.5, 1.5])
+
+```
+
 ##### Example: numeric not algebraic