Share
Share with:
Link:
Copy link
Code: Select all
extproc weave.cmd
goto :eof
!topic about
A program to produce the digit-tables as shown on DozenOnline, one for the digits
one for the intuitive division test.
!src
!inc program; Here is the proggie.
!end
!topic - Numbers
Relative to a base, numbers have a co-composite and a co-prime part. This is the
regular bit and the period bit,
coprime classes
u coprime = 1 (ie regular)
a coprime divides alpha or A2
w coprime divides omega or A1
y coprime divides A1A2 = R2
e other coprimes
cocomposite class
n cocomposite = 1
r# cocomposite divides b^#
s# cocomposite divides b^{1#},
general class
p prime number
c composite number NSFA
q number contains a square factor
x number is a proper power
No letter is used twice, so it's possible to grep for inclusion or exclusion of a
particular letter.
!topic - Digits of Base $base
The style is to calculate the class-string for each number to the base, and then print
the two tables separately.
Digits Divisibility
un unit, purple purple
ur1 divisor red red
ur2 ring 2 pink shade of red.
ur3 ring 3 ,, ,,
wn div A1
an div A2
yn div R2
en coprime
wr cp | A1
ar cp | A2
yr cp | R2
er totitive
For the coprimes, there is some sort of shading by grey, as follows. We either do this
the hard way, or use f1103 to do the hard work. This would entail constructing a vector
for the base, and then dotting it against successive rows of f1103. It also means that
we would have to distribute f1103 to users.
en, i=1 dark grey
en, i=2 mid grey
en, i>2 light grey
Since the intent is to evodently find the long periods vide the other ones that the GQR
finds, we could change i=2 into i | 2x
select
when i = 1 then dark-grey
when 2x // i = 0 then mid-grey
otherwise light-grey
!topic - Meþod of attack.
Since we have to get the ring of the regular, and the coprime, the easiest way
is to do successive GCD until 1 is the gcd
eg b = 120 n = 7168 gcd = 8 ring = 0
b = 8 n = 896 gcd = 8 ring = 1
b = 8 n = 112 gcd = 8 ring = 2
b = 8 n = 14 gcd = 2 ring = 3
b = 2 n = 7 gcd = 1 ring = 4
r4
Having found this, we then do
select
when 7 equals 1 then type = u
when 7 divides 120-1 then type = w
when 7 divides 120+1 then type = a
when 7 divides 120*120-1 then type = y
otherwise type = o
r4w 1/7168 = 0:00 02 01 08 68 68 68 68 68 has 4 leads and a period of 1.
The co-composite is 7168/7 = 1024,
This happens without having to do any factorisations.
!topic - General Class
This tells us about the number.
p Number is prime
c Number is composite NSFA
q Number contains a square factor
x Number is a proper power.
Code: Select all
Yates Carmichael Size
1 R 1 R 1 R
2 11 2 11 2 11
3 111 4 101 6 R1
4 101 3 111 4 101
5 11111 6 R1 3 111
6 R1 8 10001 10 R0R1
7 1111111 5 11111 12 RR01
8 10001 10 R0R1 8 10001
9 1001001 12 RR01 5 11111
10 R0R1 7 1111111 14 R0R0R1
11 11111111111 14 R0R0R1 18 RRR001
12 RR01 16 100000001 9 1001001
Looking forward to it!icarus @ Nov 8 2017, 04:24 AM wrote: The cutting and pasting of HTML from the automation means that I can put up a summary in about 5 minutes. The thing that takes the most time is writing the tags for the "Digit Map", etc.! But it is time to turn in. Will hit many more tomorrow. The algorithm isn't perfect, but I don't want to delay things by "fixing" it.
But Tapatalk has completely obliterated all the beautiful digit maps and tables icarus developed here. Truly unconscionable.icarus wrote: