Sharedsage_worksheets / ternary.sageOpen in CoCalc
Author: Ken Levasseur
Description: Worksheets related to Applied Discrete Structures
1
def b_div_by_3(n):
2
if n%3==2:
3
return (n//3)+1
4
else:
5
return n//3
6
7
def b_mod_3(n):
8
if n%3==2:
9
return -1
10
else:
11
return n%3
12
13
def tern(n):
14
if n==0:
15
return [0]
16
elif abs(n)==1:
17
return [n]
18
else:
19
return [b_mod_3(n)]+tern(b_div_by_3(n))
20
21
def tern_powers(n):
22
t=tern(n)
23
l=len(t)
24
return [[3^(k) for k in range(len(t))],t]
25
26
from sage.plot.polygon import Polygon
27
28
def visual_tern(n):
29
dat=tern_powers(n)
30
exp=1/2
31
w=2*abs(n)^exp
32
pic=Graphics()
33
nb=0
34
pb=0
35
nbase=[]
36
pbase=[]
37
for k in reversed(range(len(dat[0]))):
38
if dat[1][k]>0:
39
pbase=pbase+[dat[0][k]]
40
s=dat[0][k]^exp.n()
41
pic+=polygon([(w-s,pb),(w+s,pb),(w+s,pb+s),(w-s,pb+s)])
42
pic+=text(str(dat[0][k]),(w,pb+s/2),color='yellow')
43
pb+=s
44
elif dat[1][k]<0:
45
nbase=nbase+[dat[0][k]]
46
s=dat[0][k]^exp.n()
47
pic+=polygon([(-w+s,nb),(-w-s,nb),(-w-s,nb+s),(-w+s,nb+s)])
48
pic+=text(str(dat[0][k]),(-w,nb+s/2),color='yellow')
49
nb+=s
50
if n>0:
51
s=n^exp
52
pic+=polygon([(-w+s,nb),(-w-s,nb),(-w-s,nb+s),(-w+s,nb+s)],color='black')
53
pic+=text(str(n),(-w,nb+s/2),color='red')
54
else:
55
s=(-n)^exp
56
pic+=polygon([(w+s,pb),(w-s,pb),(w-s,pb+s),(w+s,pb+s)],color='black')
57
pic+=text(str(n),(w,pb+s/2),color='red')
58
pic+=line([(-2*w,0),(2*w,0)],color='black')
59
pic+=polygon([(0,0),(w/4,-w/4),(-w/4,-w/4)],color='red')
60
pic+=text(str(n)+" = sum("+str(pbase)+")-sum("+str(nbase)+")",(0,-(abs(n)^exp)))
61
pic.show(axes=False)