Filling between Two Curves

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print(r.eval("""

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library(stats) # f1=2^x, f2=4*x-x^2, x1=0, x2=4

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f<-function(x) {2^x-(4*x-x^2)}

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print(integrate(f,lower=0,upper=4))

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svg(filename='Rplots.svg',width=7,height=7,pointsize=12,

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    onefile=T,family='times',bg='white',

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    antialias=c('default','none','gray','subpixel'))

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n<-100; x<-seq(0,4,len=n)

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xy1<-data.frame(x=x,y=2^x)

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xy2<-data.frame(x=x,y=4*x-x^2)

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min_xy<-pmin(xy1,xy2); max_xy<-pmax(xy1,xy2)

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plot(x,xy2$y,type='o',cex=.5,col='#3636ff',

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     xlab='',ylab=''); par(new=T) 

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plot(x,xy1$y,type='o',cex=.5,col='#ff3636',

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     xlim=c(0,4),ylim=c(0,4),xlab='x',ylab='y',

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     fg='gray',col.axis='gray',col.lab='gray')

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polygon(c(xy1$x,rev(xy1$x)),c(max_xy$y,rev(min_xy$y)),

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        col=rgb(.9,0,.9,.3))

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grid(col='gray'); dev.off()

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"""))

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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Messages

HTML Objects & Functions

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%%html

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<style>

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@import 'https://fonts.googleapis.com/css?family=Ewert';

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</style>

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<button style='background-color:silver; color:#3636ff; 

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               font-family:Ewert; font-size:120%;'

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type='button'onclick='fun()'>

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Click to Display a Random Number in the Interval [0;1]

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</button><p id='demo' 

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style='color:#3636ff; font-family:Ewert; font-size:200%;'>

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</p><script>

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var idx='demo';

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function fun() {

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    return document.getElementById(idx).innerHTML=Math.random()};

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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Messages

Interactive Complex Plotting 2

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@interact

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def _(n=[4,7,10,13]):

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    var('z'); cf=2*exp((log(z^n)+1)/(z^n-1)); d=1.3

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    complex_plot(cf,(-d,d),(-d,d)).show(figsize=(5,5))

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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Messages

JSON Files

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import warnings; warnings.filterwarnings('ignore')

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import pandas,numpy; g=Graphics() 

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fp='https://raw.githubusercontent.com/'+\

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   'OlgaBelitskaya/data/main/external_json/'

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sd=pandas.read_json(fp+'cuae-wd7h.json')

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for i in range(sd.shape[0]):

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    coord=numpy.array(sd['the_geom'][i][u'coordinates'])

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    c1=colormaps.jet(8*i)[:3]; c2=['black','gray']

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    mean=numpy.mean([numpy.mean(coord[j][0],axis=0) 

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                     for j in range(coord.shape[0])],axis=0)

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    g+=sum([polygon2d(coord[j][0],rgbcolor=c1,alpha=.75) 

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            for j in range(coord.shape[0])])

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    p=points((-73.95,40.7),size=0,rgbcolor=c1,

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             legend_label='D '+str(i+1),legend_color=c1)

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    p.set_legend_options(bbox_to_anchor=(1.25,1.05))

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    g+=p+text(str(i+1),mean,color=c2[i%2],

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              fontsize=12,fontweight='bold') 

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g.show(title='NYC School Districts',figsize=7,gridlines=True)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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Messages

Interactive Parameters

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@interact

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def _(a=[7,9,11],b=[10,14,18],m=[48,36,24,16]):

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    x(t)=cos(t)+cos(a*t)/2+sin((a+b)*t)/3

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    y(t)=sin(t)+sin(a*t)/2+cos((a+b)*t)/3

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    def col(c): return colormaps.hsv(5*c)[:3]

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    p=sum([parametric_plot((x,y),

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                           (t,(i-1)*pi/24,i*pi/24),

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                            color=col(i)) 

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          for i in [1..m]])

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    p.show(aspect_ratio=1,figsize=6,gridlines=True)

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---

Messages

"Glass" Geometry

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def v(k): 

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    v=[[[k,k,k],[k,k,k-1],[k-1,k,k],[k,k-1,k]],

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      [[k-1,k-1,k],[k-1,k-1,k-1],[k-1,k,k],[k,k-1,k]],

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      [[k,k,-k],[k,k,-k+1],[k-1,k,-k],[k,k-1,-k]],

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      [[k-1,k-1,-k],[k-1,k-1,-k+1],[k-1,k,-k],[k,k-1,-k]]]

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    return v

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def col(i,cm): return colormaps[cm](55*i)[:3]

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p=sum([Polyhedron(vertices=v(1)[i]).render_solid(opacity=.5,

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       color=col(i,'hsv')) for i in [0..3]])

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c1=cube((.5,.5,0),.5,opacity=.5,color=col(4,'hsv'))

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c2=cube((.5,.5,0),2,opacity=.1,color=col(2,'hsv'))

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(p+c1+c2).show(frame=False)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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Messages

Interactive Linear Programming Problem

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@interact

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def _(a=[2,3,4],b=[3,4,5],c=[1,2,3]):

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    A=([a,1],[1,a+1]); B=(b,b+1); C=(c,c+4)

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    s='Interactive Linear Programming Problem'

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    P=InteractiveLPProblem(

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        A,B,C,['x','y'],problem_type='max',

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        constraint_type='<=',variable_type='>=')

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    pretty_print(s,fontsize=15)

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    pretty_print((P.standard_form(),

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                  P.optimal_solution()),fontsize=15)

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    P.plot().show(figsize=5,legend_font_size=12)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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Messages