HTML Exercises

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%%html

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<style>

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@import 'https://fonts.googleapis.com/css?family=Ewert&effect=3d';

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</style>

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<p id='change_font' class='font-effect-3d' onclick='setFont()'>

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Click to change the font</p>

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<input type='color' id='set_color' value='#36ff36' 

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       style='padding-left:20px'>

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<p id='change_color' class='font-effect-3d' 

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   onclick='setColor()'>

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Click to change the color</p>

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<script>

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function setFont()

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    {doc=document.getElementById('change_font');

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     doc.style='font-family:Ewert; font-size:200%';}

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function setColor()

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    {var c=document.getElementById('set_color').value;

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     doc=document.getElementById('change_color')

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     doc.style='font-size:250%'; doc.style.color=c;}

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

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Messages

Parametric Plotting R

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print(r.eval("""

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svg(filename='Rplots.svg',width=6,height=5,

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    pointsize=12,onefile=TRUE,family='times',bg='white',

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

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T<-seq(from=0,to=2*pi,by=.01*pi)

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col<-function(i) {rgb(.005*i,0,1-.005*i)}

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curve<-function(t) {list(sin(2*t),sin(5*t))}

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X<-sapply(T,curve)[1,]; Y<-sapply(T,curve)[2,] 

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for(i in 1:200){

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    plot(X[i],Y[i],pch=13,cex=.9,

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         xlim=c(-1.2,1.2),ylim=c(-1.2,1.2),

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         col=col(i),xlab='x',ylab='y')

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    par(new=TRUE)}

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grid(); dev.off()

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"""))

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

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Messages

Selected Features

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import pandas,pylab; from sklearn import linear_model as lm

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from sklearn import datasets,feature_selection

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from sklearn.ensemble import GradientBoostingClassifier as GBC

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from sklearn.ensemble import AdaBoostClassifier as ABC

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def pd_style():

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    return [dict(selector='th',

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                 props=[('font-size','14pt'),

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                        ('min-width','80px')]),

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            dict(selector='td',

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                 props=[('font-size','10pt'),

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                        ('min-width','80px'),

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                        ('text-align','center')]),

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            dict(selector='tr:hover th:hover',

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                 props=[('color','darkblue'),

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                        ('max-width','80px'),

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                        ('text-shadow','3px 3px 3px #aaa')]),

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            dict(selector='tr:hover td:hover',

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                 props=[('font-size','14pt'),

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                        ('max-width','80px'),

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                        ('text-shadow','3px 3px 3px #aaa')])]

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wine=datasets.load_wine(); X,y=wine.data,wine.target

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selected_features=pandas.DataFrame(columns=range(13))

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selected_features.loc['Gradient Boosting']=\

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GBC().fit(X,y).feature_importances_

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selected_features.loc['Ada Boost']=\

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ABC().fit(X,y).feature_importances_

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kbest=feature_selection\

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.SelectKBest(score_func=feature_selection.chi2,k=3)

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selected_features.loc['Select KBest']=kbest.fit(X,y).pvalues_

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lmlr=lm.LogisticRegression(

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    solver='liblinear',multi_class='ovr')

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rfe=feature_selection.RFE(lmlr,n_features_to_select=3)

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selected_features.loc['RFE']=1/rfe.fit(X,y).ranking_

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display(selected_features.T.style.set_table_styles(pd_style()))

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f,ax=pylab.subplots(1,figsize=(6,4))

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selected_features.T.plot(ax=ax)

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pylab.grid(); pylab.show()

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

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Messages

Interactive 3D Animations

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from sage.plot.plot3d.shapes import Sphere

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var('x,y,z'); c='#3030ff'; n=12

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s1=Sphere(8,color=c,opacity=.05).translate(0,0,0)

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s2=Sphere(3,color=c).translate(0,0,0)

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sn=[s1+s2+Sphere(1,color=(.2*i,0,.3*i))\

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   .translate(0,7*cos(pi*i/n),4*sin(pi*i/n)) 

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    for i in [0..2*n]]

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animate(sn,frame=False)

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

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Messages

Interactive 3D Lines

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sx='x=-%.1f*cos(%.1f*t)-%.1f*cos(%.1f*t)+%.1f*sin(%.1f*t)'

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sy='y=-%.1f*cos(%.1f*t)+%.1f*sin(%.1f*t)-%.1f*sin(%.1f*t)'

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sz='z=%.1f*cos(%.1f*t)'; p1,p2='$\\mathscr{\\small{','}}$'

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def L(i): return (-a*cos(d*i)-b*cos(e*i)+c*sin(f*i),

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                  -c*cos(f*i)+a*sin(d*i)-b*sin(e*i),

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                  a*cos(g*i))

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@interact

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def _(a=[10,15,20],b=[2,4,6],c=[15,10,5]):

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    d=.1; e=.4; f=.2; g=.3; var('t')

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    pretty_print(html(p1+sx%(a,d,b,e,c,f)+p2))

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    pretty_print(html(p1+sy%(c,f,a,d,b,e)+p2))

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    pretty_print(html(p1+sz%(a,g)+p2))

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    def L(i): return (-a*cos(d*i)-b*cos(e*i)+c*sin(f*i),

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                      -c*cos(f*i)+a*sin(d*i)-b*sin(e*i),

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                      a*cos(g*i))

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    p=sum([line3d([L(i),L(i+1)],radius=.5,

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                  color=colormaps.winter(4*i)[:3]) 

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           for i in [0..64]])

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    p.show(frame=False)

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

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Messages

Interactive Curve Plotting

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@interact

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def _(n=[1..11]):

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    var('x')

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    f=[exp(-x^2)*sin(pi*x^n),

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       exp(-x^2),-exp(-x^2)]

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    p=sum([plot(f[i],(-2,2),color=hue(.3*i)) 

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         for i in [0..2]])

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    p.show(figsize=(5,4),gridlines=True)

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

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Messages

Interactive Exploration of Complex Functions

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@interact

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def _(N=[2*10^3,5*10^3,10^4]): 

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    L=[CC(0,0)]

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    c=[colormaps.cool((N^(-1)).n()*i)[:3] 

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       for i in [1..N]]

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    z=lambda n:exp(I*pi*n*ln(n/4)*2^.5).n() 

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    for n in [1..N]: L.append(L[n-1]+CC(z(n))) 

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    p=sum([line([L[i],L[i+1]],color=c[i]) 

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           for i in [200..N-1]])

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    p.show(figsize=(5,5))

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

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Messages

Cells Linked by ID

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%%html

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<style>

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

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</style>

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<input type='number' id='inputtemp' value='86' width=200

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       style='font-family:Miss Fajardose; font-size:200%; 

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              background-color:silver; color:#3636ff; 

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              text-align:center; width:200px; border:double #ff3636;'>

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</input>

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<p style='background-color:white; color:#3636ff; text-align:left; 

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          font-family:Miss Fajardose; font-size:300%;'

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   id='texttemp'>

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Evaluate the next code cell for converting 

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a Fahrenheit temperature to Celsius</p>

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

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          text-align:center; width:200px; border:double #36ff36;

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          font-family:Miss Fajardose; font-size:200%;'

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   id='outtemp'>Click `Run SageMath` below</p>

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

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Messages

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%%javascript

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function f2c() {

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    var f=document.getElementById('inputtemp').value;

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    return Math.round((5/9)*(f-32)) };

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document.getElementById('outtemp').innerHTML=f2c();

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

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Messages

Linear Models

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print(r.eval("""

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svg(filename='Rplots.svg',widt=5,height=5,pointsize=12,

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    onefile=TRUE,family='times',bg='ghostwhite',

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

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model<-lm(weight~height,data=women)

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plot(women$height,women$weight,col='violet',pch=10)

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abline(model,col='purple'); grid(); dev.off()

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"""))

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

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Messages