📑  SageMath Online Mini Campus. Code Set 10

The set of interactive pages with the following structure:

Example of Computations $⟹$ Your Experiments $⟹$ Python Modules $⟹$ Other Languages

Example of Computations

Click the $\mathbb{activate}$ button below to display an interactive example.

@interact
def _(n=[3,4,5,6]):
    g=Graph({},loops=True,multiedges=True,sparse=True)
    def add(g,x,y):
        g.add_edges([(x,y,'a'),(x,y,'a'),(x,y,'b'),
                     (x,y,'b'),(x,y,'c'),(x,y,'c'),
                     (x,y,'d'),(x,y,'d'),(x,y,'e'),
                     (x,y,'e'),(x,y,'f'),(x,y,'f')])
    [add(g,i,i+1) for i in [1..n-1]] 
    [add(g,i,i+5) for i in [1..n-1]]; add(g,n,1)
    g.graphplot(vertex_size=0,vertex_labels=False,
                color_by_label=True).show(figsize=(5,5))

Your Experiments

Type your own SageMath code lines below and click the $\mathbb{evaluate}$ button.

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g=graphs.HoffmanSingletonGraph()

t=Graph()

t.add_edges(g.min_spanning_tree(

    starting_vertex=0))

[t.set_edge_label(u,v,u) for u,v,l in t.edges()]

t.show(layout='tree',tree_root=0,

       color_by_label=True,

       vertex_size=0,figsize=(7,7))

This code cell was evaluated automatically.

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@interact

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def _(N=[5,4,..,1]):

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    f1(x,y,z,t)=x^2+y^2-.5*z*t^2

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    f2(x,y,z,t)=x^2+y^2+.5*z*t^2

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    p1=sum([implicit_plot3d(

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        f1(x,y,z,i),(x,-i,i),(y,-i,i),(z,-2,2),

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        color=hue(sin(.24*i)),opacity=.7,

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        plot_points=5,frame=False) for i in [1..N]])

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    p2=sum([implicit_plot3d(

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        f2(x,y,z,i),(x,-i,i),(y,-i,i),(z,-1,0),

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        color=hue(sin(.24*i)),opacity=.3,

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        plot_points=5,frame=False) for i in [1..N]])

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    p3=plot3d(lambda x,y:0,(-N,N),(-N,N),

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              color='steelblue',opacity=.5)

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    (p1+p2+p3).show()

activate again

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

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Messages

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@interact

def _(n=[4,5,..,8]):

    f(u,v)=exp(-(u^n+v^n)/n)

    s1(u,t)=(u,-.1*t,.1*t)

    s2(v,t)=(v,-.1*t,.1*t)

    pvf=sum([plot_vector_field(

        f(u,v).gradient(),s1(u,i),s2(v,i),

        color=hue(i/3)) for i in [1..3]])

    pvf.show(figsize=(5,5),frame=False)

Python Modules

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import pylab,numpy

from mpl_toolkits.mplot3d import Axes3D

t=1.1; cq=numpy.arange(0,1,.13)

cq=numpy.concatenate((cq,numpy.repeat(cq,2)))

xq=[1,-1,1,-1,1,-1,1,-1]

yq=[1,1,-1,-1,1,1,-1,-1]

zq=[1,1,1,1,-1,-1,-1,-1]

f=pylab.figure(figsize=(7,7))

ax=f.add_subplot(111,projection='3d')

q=ax.quiver(8*[0],8*[0],8*[0],xq,yq,zq,

            colors=pylab.cm.hsv(cq),lw=10,alpha=.5) 

ax.set_xlabel(r'$\mathscr{X}$',fontsize=15)

ax.set_ylabel(r'$\mathscr{Y}$',fontsize=15) 

ax.set_zlabel(r'$\mathscr{Z}$',fontsize=15)

ax.set_xlim(-t,t); ax.set_ylim(-t,t)

ax.set_zlim(-t,t); pylab.show()

Other Languages (R, HTML, ...)

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%%r

kmeans_clust<-kmeans(mtcars$wt,5); kmeans_clust

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%%html

<style>

.pressed {display:inline-block; padding:15px 15px; 

          outline:none; font-size:20px; 

          cursor:pointer; text-align:center; 

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

          border:none; border-radius:10px; 

          box-shadow:0 5px slategray;}

.pressed:hover {background-color:#ff3636}

.pressed:active {background-color:#36ff36; 

                 box-shadow:0 5px #aaa; 

                 transform:translateY(5px);}

</style>                        

<button class='pressed'>$\mathbb{Pressed \; Effect}$

</button>