The set of interactive pages with the following structure:
Example of Computations
Click the
@interact
def _(t=slider(.05,.95,.05,.05)):
def f(x): return -ln(x)
def g(x): return -ln(x)*x
var('x'); x_max=solve((-ln(x)*x).diff(),x)[0].rhs()
p=plot(f,(0,1),color='#3636ff',legend_label='y=-ln(x)')+\
plot(g,(0,1),color='#ff36ff',legend_label='y*x=-ln(x)*x')
pp=point((x_max,f(x_max)),color='#ff3636')+\
point((x_max,g(x_max)),color='#ff3636')
a=plot(f(x_max),(0,x_max),fill='axis',color='#ff3636',fillcolor='#ff3636')
an=text('-ln(x)*x='+str(g(x_max)),(x_max/2,f(x_max)+.2),color='#ff3636')
pt=point((t,f(t)),color='#3636ff')+point((t,g(t)),color='#ff36ff')
at=plot(f(t),(0,t),fill='axis',color='#3636ff',fillcolor='#3636ff')
ant=text('-ln(x)*x='+str(g(t).n()),(t+.1,f(t)+.2))
(p+pp+a+an+pt+at+ant).show(figsize=(7,4))
Type your own SageMath code lines below and click the
xxxxxxxxxxpretty_print(html('<p>Random Color Walk</p>'))n=100; p=[0,0,0]; rw=[copy(p)]c=[colormaps.hsv((1/n).n()*i)[:3] for i in [0..n]]for i in [1..n]: for j in [0..2]: p[j]+=random()-.5; rw.append(copy(p))l=sum([line3d([rw[i],rw[i+1]],color=c[i],radius=.1) for i in [0..n-1]])l.show(aspect_ratio=[1,1,1])This code cell was evaluated automatically.
xxxxxxxxxxdef _(N=[200,175,..,50]): L=[CC(0,0)]; z=lambda n:exp(I*pi*n*2^.2).n() c=[colormaps.hsv((200^(-1)).n()*i)[:3] for i in [1..200]] for n in [1..N]: L.append(L[n-1]+CC(z(n))) p=sum([line([L[i],L[i+1]],color=c[i]) for i in [1..N-1]]) p.show(figsize=(5,5),axes=False)xxxxxxxxxxX=[x for x in srange(-2,2,.2)]Y=[exp(-x^2)*sin(pi*x^3) for x in X] Y1,Y2=[exp(-x^2) for x in X],[-exp(-x^2) for x in X]m,M='◎','☕'c=[colormaps.cool(80*i)[:3] for i in [0,1,2]]t=sum([text(m,(x,y),fontsize=10,rgbcolor=c[i],gridlines=True) for i in [0..2] for (x,y) in list(zip(X,[Y1,Y2,Y][i]))])animate([t+text(M,(x,y),fontsize=30,rgbcolor=c[2]) for (x,y) in list(zip(X,Y))])xxxxxxxxxximport numpy,pylab,urllib,warningsfrom scipy.io import wavfilefrom IPython.display import display,Audiowarnings.filterwarnings('ignore')url='https://storage.googleapis.com/audioset/miaow_16k.wav'input_file=urllib.request.urlopen(url)output_file=open('miaow_16k.wav','wb')output_file.write(input_file.read())output_file.close(); input_file.close()_,wav=wavfile.read('miaow_16k.wav');wav=wav.astype('float')/numpy.iinfo(numpy.int16).maxdisplay(Audio(wav,rate=int(16000)))f,ax=pylab.subplots(1,figsize=(6,5))ax.plot(wav,c='#3636ff',lw=.05,alpha=.9)ax.set_ylabel('amplitude'); pylab.show()xxxxxxxxxx%%rsvg(filename='Rplots.svg',width=7,height=4, pointsize=12,onefile=T,family='times',bg='white', antialias=c('default','none','gray','subpixel'))col.lst<-c('skyblue','red2','coral','orchid3', 'bisque','tan','green3','blue4')plot(1:8,rep(1,8),axes=FALSE,pch=15,cex=8, col=col.lst,xlab=NA,ylab=NA,xlim=c(1,8))axis(1,at=1:8,labels=sprintf('%s',col.lst), col='white',cex.axis=.9,padj=-18)dev.off()<script src='https://d3js.org/d3.v4.min.js'></script> was added in the page head.
xxxxxxxxxx%%html<style>#svg1 {background-color:slategray;} text {fill:#fff; font-size:135%;} .point {stroke:#fff; stroke-width:1;} .grid line,.grid path {stroke:#fff; stroke-opacity:.9; shape-rendering:crispEdges;} </style><svg id='svg1'/><script>var n=255,m=35,margin={top:m,right:m,bottom:m,left:m}, width=500-margin.left-margin.right,height=500-margin.top-margin.bottom;var tt1='translate('+margin.left+','+margin.top+')', tt2='translate(0,'+height+')';var xScale=d3.scaleLinear().domain([-1,1]).range([0,width]); var yScale=d3.scaleLinear().domain([-1,1]).range([height,0]);function make_x_gridlines() {return d3.axisBottom(xScale).ticks(11)};function make_y_gridlines() {return d3.axisLeft(yScale).ticks(11)};var pointColor=d3.scaleSequential().domain([0,n]) .interpolator(d3.interpolateCool); var data=d3.range(0,n).map(function(i){return {'x':Math.sin(.05*i), 'y':Math.sin(.125*i)}})var svg=d3.select('#svg1').attr('width',width+margin.left+margin.right) .attr('height',height+margin.top+margin.bottom) .append('g').attr('transform',tt1);svg.append('g').attr('class','x axis') .call(d3.axisBottom(xScale).tickSize(.5)) .attr('transform',tt2); svg.append('g').attr('class','y axis') .call(d3.axisLeft(yScale).tickSize(.5)); svg.append('g').attr('class','grid').attr('transform',tt2) .call(make_x_gridlines().tickSize(-height).tickFormat(''));svg.append('g').attr('class','grid') .call(make_y_gridlines().tickSize(-width).tickFormat(''));svg.selectAll('.point').data(data).enter() .append('circle').attr('class','point').attr('r',4) .attr('fill',function(d,i){return pointColor(i)}) .attr('cx',function(d) {return xScale(d.x)}) .attr('cy',function(d) {return yScale(d.y)});