Djelitelji broja $100\,000$

verzija: SageMath 9.4

pozitivni djelitelji broja $100\,000$

In [1]:
divisors(100000)
Out[1]:
[1,
 2,
 4,
 5,
 8,
 10,
 16,
 20,
 25,
 32,
 40,
 50,
 80,
 100,
 125,
 160,
 200,
 250,
 400,
 500,
 625,
 800,
 1000,
 1250,
 2000,
 2500,
 3125,
 4000,
 5000,
 6250,
 10000,
 12500,
 20000,
 25000,
 50000,
 100000]

Ukupno je 36 takvih brojeva

In [2]:
len(divisors(100000))
Out[2]:
36

Graf parcijalno uređenog skupa svih djelitelja broj $100\,000$ uz relaciju "dijeli"

In [3]:
G=DiGraph([divisors(100000),lambda x,y:mod(y,x)==0])
In [4]:
G.plot(layout="circular",graph_border=True,vertex_size=5,vertex_labels=False,figsize=[6,6])
Out[4]:

Hasseov dijagram

In [5]:
pus=Poset((divisors(100000),lambda x,y:mod(y,x)==0)) 
pus.show(vertex_color='yellow',vertex_size=1250,figsize=[10,8],aspect_ratio=0.6)

Graf relacije u zelenoj boji

In [6]:
G.plot(layout="circular",graph_border=True,vertex_size=5,vertex_labels=False,edge_color="green",figsize=[6,6])
Out[6]:

Graf relacije u šarenim bojama

In [7]:
from sage.plot.colors import Colormaps
maps=Colormaps()
In [8]:
bridovi=G.edges()
ne=G.num_edges()
boje=[maps.copper(float(i/400))[:-1] for i in range(ne)]
boje_bridova={}
for br in range(ne):
    boje_bridova[boje[br]]=[]
for i in range(G.num_edges()):
    boje_bridova[boje[i]].append(bridovi[i])
G.plot(layout="circular",graph_border=True,vertex_size=5,vertex_labels=False,edge_colors=boje_bridova,figsize=[6,6])
Out[8]:
In [9]:
sorted(colormaps)
Out[9]:
['Accent',
 'Blues',
 'BrBG',
 'BuGn',
 'BuPu',
 'CMRmap',
 'Dark2',
 'GnBu',
 'Greens',
 'Greys',
 'OrRd',
 'Oranges',
 'PRGn',
 'Paired',
 'Pastel1',
 'Pastel2',
 'PiYG',
 'PuBu',
 'PuBuGn',
 'PuOr',
 'PuRd',
 'Purples',
 'RdBu',
 'RdGy',
 'RdPu',
 'RdYlBu',
 'RdYlGn',
 'Reds',
 'Set1',
 'Set2',
 'Set3',
 'Spectral',
 'Wistia',
 'YlGn',
 'YlGnBu',
 'YlOrBr',
 'YlOrRd',
 'afmhot',
 'autumn',
 'binary',
 'bone',
 'brg',
 'bwr',
 'cool',
 'coolwarm',
 'copper',
 'cubehelix',
 'flag',
 'gist_earth',
 'gist_gray',
 'gist_heat',
 'gist_ncar',
 'gist_rainbow',
 'gist_stern',
 'gist_yarg',
 'gnuplot',
 'gnuplot2',
 'gray',
 'hot',
 'hsv',
 'jet',
 'nipy_spectral',
 'ocean',
 'pink',
 'prism',
 'rainbow',
 'seismic',
 'spring',
 'summer',
 'tab10',
 'tab20',
 'tab20b',
 'tab20c',
 'terrain',
 'winter']

Pripadni neusmjereni graf u šarenim bojama

In [10]:
G2=G.copy()
G2.remove_loops()
G1=G2.to_undirected()
bridovi1=G1.edges()
ne1=G1.num_edges()
boje1=[maps.copper(float(i/400))[:-1] for i in range(ne1)]
boje_bridova1={}
for br in range(ne1):
    boje_bridova1[boje1[br]]=[]
for i in range(G1.num_edges()):
    boje_bridova1[boje[i]].append(bridovi1[i])
G1.plot(layout="circular",graph_border=True,vertex_size=5,vertex_labels=False,edge_colors=boje_bridova1,figsize=[6,6])
Out[10]:

Neusmjereni jednobojni grafovi

In [11]:
G3=G.copy()
G3.remove_loops()
G3=G3.to_undirected()
slika1=G3.plot(layout="circular",vertex_size=0,vertex_labels=False,edge_color='black')
slika2=G3.plot(layout="circular",vertex_size=0,vertex_labels=False,edge_color='green')
graphics_array([slika1,slika2]).show(figsize=[9,8])
In [ ]: