Python半素因式分解方程求解器问题

Question

我是一名农民/新手数论研究员。几年前，我碰巧发现了素数分布中出现的一种模式，该模式将素数的数量与 300 个类似斐波那契数列的运算联系起来。好吧，作为一个一直使用笔和纸的人，当我将我的方法转换为计算机代码时，我不知所措（所以我聘请了一名程序员用 Perl 实现我的代码）。该代码有效，但不是我现在需要的过程；我想询问程序员社区，他们认为使此（Python）代码工作的最佳方法是什么。另外，作为一名研究人员，我并不太关心人们将此代码用于自己的用途 - 我只是想看看你用它做什么！

Perl 程序生成的结果发表在 AT&T Online Encyclopedia of Integer Sequences 中。 https://oeis.org/search?q=helkenberg&language=english& ;go=Search

下面的程序是我最近的努力，但我一生都无法弄清楚如何让代码的某些部分工作。

例如（来自下面的较大程序），

print"""THIS CODE WILL NOT COMPILE (example p*q = 29*73)
print [(int(p) + 90*x_0) * int(q)+ 90*x_0)]/90 #example 23
print [(int(p) + 90*x_1) * (int(q)+90*x_1)]/90 #example 215

z(0) = [(int(p) + 90*x_0) * int(q)+ 90*x_0)]/90
z(1) = [(int(p) + 90*x_1) * (int(q)+90*x_1)]/90
#This defines a new process, a Fibonacci-like sequence:

a = z(1) - z(0) #example (192=215-23)
g = 180 #think the unit circle, clock cycles

m_0 = a + g #example 192+180 = 372

z(2) = m_0 + z(1) #example 587 = 372 + 215

m_1 = m_0 + g #example 552 = 372 + 180

z(3) = z(2)+ m_1 #example 1139 = 587 + 552

m_2 = m_1 + g #example 732 = 552 + 180

z(4) = z(3) + m_2 #example 1871 = 1139 + 732

我正在自学如何编码，但我一生都无法弄清楚如何实现它！

最后，我需要使用这些值（z 项）来求解以下形式的方程：

0 = r - [(((90*n))+29)*y) + z_n]
0 = r - [(((90*n))+73)*y) + z_n]

其中 z 项用于 29 和 73（作为示例）

这是我到目前为止所得到的。

print    "1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139"

variable = raw_input('copy and paste the above number')

#This valuable function reduces an arbitrarily large number to the SUM OF ITS DIGITS
new_variable = sum(map(int, str(variable)))
print new_variable

next_step = sum(map(int, str(new_variable)))
print next_step

new_step = sum(map(int, str(next_step)))

print "The digital root of our test number is", new_step, "A fine answer."

if int(new_step) > 9:
print "We cannot have a two digit digital root!Enter the sum of those two numbers here!"

newest_data = raw_input ('>enter the digital root here')

#newest_data = raw_input ()

if new_step == 3:
print "This number is divisible by 3."
if new_step == 6:
print "This number is divisible by 3."
if new_step == 9:
print "This number is divisible by 3 and 9."

if newest_data == 3:
print "This number is divisible by 3."
if newest_data == 6:
print "This number is divisible by 3."
if newest_data == 9:
print "This number is divisible by 3 and 9."

print "What is the last digit of our number?"
last_digit = raw_input("Last digit here")

print last_digit

if int(last_digit) == 0:
print "This number is divisible by 2 and 5."
if int(last_digit) == 2:
print "This number is divisible by 2."
if int(last_digit) == 4:
print "This number is divisible by 2."
if int(last_digit) == 6:
print "This number is divisible by 2."
if int(last_digit) == 8:
print "This number is divisible by 2."

digital_root = int(new_step)
new_digit = int(last_digit)

if digital_root == 1 and new_digit == 1:
print "your primitive is 91"

elif digital_root == 1 and new_digit == 3:
print "your primitive is 73"

elif digital_root == 1 and new_digit == 7:
print "your primitive is 37"

elif digital_root == 1 and new_digit == 9:
print "your primitive is 19"

elif digital_root == 2 and new_digit == 1:
print "your primitive is 11"

elif digital_root == 2 and new_digit == 3:
print "your primitive is 73"

elif digital_root == 2 and new_digit == 7:
print "your primitive is 47"

elif digital_root == 2 and new_digit == 9:
print "your primitive is 29"

elif digital_root == 4 and new_digit == 1:
print "your primitive is 31"

elif digital_root == 4 and new_digit == 3:
print "your primitive is 13"

elif digital_root == 4 and new_digit == 7:
print "your primitive is 67"

elif digital_root == 4 and new_digit == 9:
print "your primitive is 49"

elif digital_root == 5 and new_digit == 1:
print "your primitive is 41"

elif digital_root == 5 and new_digit == 3:
print "your primitive is 23"

elif digital_root == 5 and new_digit == 7:
print "your primitive is 77"

elif digital_root == 5 and new_digit == 9:
print "your primitive is 59"

elif digital_root == 7 and new_digit == 1:
print "your primitive is 61"

elif digital_root == 7 and new_digit == 3:
print "your primitive is 43"

elif digital_root == 7 and new_digit == 7:
print "your primitive is 7"

elif digital_root == 7 and new_digit == 9:
print "your primitive is 79"

elif digital_root == 8 and new_digit == 1:
print "your primitive is 71"

elif digital_root == 8 and new_digit == 3:
print "your primitive is 53"

elif digital_root == 8 and new_digit == 7:
print "your primitive is 17"

elif digital_root == 8 and new_digit == 9:
print "your primitive is 89"


primitive = raw_input("enter primitive here")
new_value = int(variable) - int(primitive)
stored_data = new_value/90

print "this is our new number, the position of our test number in a dr,ld index.", stored_data

print "This number above is our test number (r)."

tuple = [73,91,19,37,11,23,29,77,47,59,83,41,13,61,31,43,49,7, 67,79,17,89,53,71]

print tuple
print " the example is based on 29*73"
p = raw_input("p from tuple (to be defined)") # example 29
q = raw_input("q associated with p") #example 73

#def make_incrementor (n): return lambda x: x + n
#cannot figure this one out
#notice x_0 and then x_1:
print"""THIS CODE WILL NOT COMPILE (example p*q = 29*73)
print [(int(p) + 90*x_0) * int(q)+ 90*x_0)]/90 #example 23
print [(int(p) + 90*x_1) * (int(q)+90*x_1)]/90 #example 215

z(0) = [(int(p) + 90*x_0) * int(q)+ 90*x_0)]/90
z(1) = [(int(p) + 90*x_1) * (int(q)+90*x_1)]/90

#This defines a new process, a Fibonacci-like sequence:

a = z(1) - z(0) #example (192=215-23)
g = 180 #think the unit circle, clock cycles

m_0 = a + g #example 192+180 = 372

z(2) = m_0 + z(1) #example 587 = 372 + 215

m_1 = m_0 + g #example 552 = 372 + 180

z(3) = z(2)+ m_1 #example 1139 = 587 + 552

m_2 = m_1 + g #example 732 = 552 + 180

z(4) = z(3) + m_2 #example 1871 = 1139 + 732

"""

print "seed values for sequence z = [23, 215]"
print "set of z terms [23, 215, 587, 1139, 1871,.....] "


print "notice the last-digit pattern for the z term means that every term of z will end  in a [3, 5, 7, 9, 1], in that order, but also IN A POWER SERIES. Also notice that our test number (r) ends with the last digit 8. So prior to computing w, we know that none of the solutions represented by z (where z = r) are possible."

print """
there are 24 equations (posed as alternatives):

r = stored_data test number, RSA-100 clock position
print "RSA-100 = 19 +     (90*16917833643583704005951315312584860330200756832904229873976761050890255147321698862822226118800068)"
Startng at 19 degrees, RSA100 is 169..... 1/4 rotations from the 0 position on the clock face.

#special case: where r-z = 0, factor found.

0 = r - [(((90*n))+19)*y) + z_n]
0 = [(((r-z_n)/y)-19)]/x - 90]

0 = r - [(((90*n)+91)*y) + z_n]
0 = [(((r-z_n)/y)-91)]/n - 90]

0 = r - [(((90*n)+37)*y) + z_n]
0 = [(((n-z_n)/y)-37)]/n - 90]

0 = r - [(((90*n)+73)*y) + z_n]
0 = [(((r-z_n)/y)-73)]/n - 90]

0 = r - [(((90*n)+11)*y) + z_n]
0 = [(((r-z_n)/y)-11)]/n - 90]

0 = r - [(((90*n)+59)*y) + z_n]
0 = [(((r-z_n)/y)-59)]/n - 90]

0 = r - [(((90*n)+29)*y) + z_n]
0 = [(((r-z_n)/y)-29)]/x - 90]

0 = r - [(((90*n)+41)*y) + z_n]
0 = [(((r-z_n)/y)-41)]/n - 90]

0 = r - [(((90*n)+47)*y) + z_n]
0 = [(((r-z_n)/y)-47)]/n - 90]

0 = r - [(((90*n)+77)*y) + z_n]
0 = [(((r-z_n)/y)-77)]/n - 90]

0 = r - [(((90*n)+83)*y) + z_n]
0 = [(((r-z_n)/y)-83)]/n - 90]

0 = r - [(((90*n)+23)*y) + z_n]
0 = [(((r-z_n)/y)-83)]/n - 90]

0 = r - [(((90*n)+13)*y) + z_n]
0 = [(((r-z_n)/y)-13)]/n - 90]

0 = r - [(((90*n)+43)*y) + z_n]
0 = [(((r-z_n)/y)-43)]/n - 90]

0 = r - [(((90*n)+31)*y) + z_n]
0 = [(((r-z_n)/y)-31)]/n - 90]

0 = r - [(((90*n)+79)*y) + z_n]
0 = [(((r-z_n)/y)-79)]/n - 90]

0 = r - [(((90*n)+49)*y) + z_n]
0 = [(((r-z_n)/y)-49)]/n - 90]

0 = r - [(((90*n)+61)*y) + z_n]
0 = [(((r-z_n)/y)-61)]/n - 90]

0 = r - [(((90*n)+67)*y) + z_n
0 = [(((r-z_n)/y)-67)]/n - 90]

0 = r - [(((90*n)+7)*y) + z_n]
0 = [(((r-z_n)/y)-7)]/n - 90]

0 = r - [(((90*n)+17)*y) + z_n]
0 = [(((r-z_n)/y)-17)]/n - 90]

0 = r - [(((90*n)+53)*y) + z_n]
0 = [(((r-z_n)/y)-53)]/n - 90]

0 = r - [(((90*n)+71)*y) + z_n]
0 = [(((r-z_n)/y)-71)]/n - 90]

0 = r - [(((90*n)+89)*y) + z_n]
0 = [(((r-z_n)/y)-89)]/n - 90]
"""



#Here is the OLD PROGRAM in Perl

#!/usr/bin/perl

use strict;
use warnings;

use Math::BigInt;
use POSIX;
use Getopt::Long;

my $rsa              = '';
my $p                = '';
my $q                = '';
my $digit_root_chart = '';

GetOptions(
'rsa|r=s'   => \$rsa,
'p=s'       => \$p,
'q=s'       => \$q,
'digit|d=i' => \$digit_root_chart,
) or die "Problem with command";

# /*
#  * General algorithm goes here.
#  *
#  */

my $length_of_semiprime = length($rsa);
my $digit_root          = &digit_root($rsa);

print "digit root: $digit_root\n";

$rsa = Math::BigInt->new($rsa);
print "rsa: $rsa\n";
my $new_rsa = $rsa->copy();
$new_rsa -=
  $digit_root_chart;  # need to figure out a way to tablize the digit root table
$new_rsa /= 90;
print "new_rsa: $new_rsa\n";

$p = Math::BigInt->new($p);
$q = Math::BigInt->new($q);
my $y = &first_two_calcs( $p, $q );
print "p = $p, q = $q\n";
&check_for_factor( $p, $q, $y );

$p += 90;
$q += 90;
my $z = &first_two_calcs( $p, $q );
print "p = $p, q = $q\n";
&check_for_factor( $p, $q, $z );

$p += 90;
$q += 90;
print "p = $p, q = $q\n";
my @r = &second_calcs( $y, $z );
$y = $r[0];
$z = $r[1];
&check_for_factor( $p, $q, $z );

while (1) {
   $p += 90;
   $q += 90;

my @t = &third_calc( $y, $z );
$y = $t[0];
$z = $t[1];

if ( $z <= $new_rsa ) {
    &check_for_factor( $p, $q, $z )
      if ( ( length($p) || length($q) ) >=
        ( ( $length_of_semiprime / 2 ) - 1 ) );
}
else {
    last;
}
}

# This sub() is used for the first two calculations
sub first_two_calcs {
my ( $p, $q ) = @_;
my $z = $p * $q;
my $x = $z / 9;

# if its a whole number we move along
if ( ( $z % 9 ) == 0 ) {
    print "($p * $q) / 9 = $x\n";
}
else {
    print "num doesn't div evenly: ($p * $q) / 9 = $x\n";
    $x = int( $x / 10 );
    print "new num: (($p * $q) / 9) / 10 = $x\n";
}
return $x;
}

# /*
#  * This sub() checks to see if it is a factor.
#  *
#  */
sub check_for_factor {
my ( $p, $q, $z ) = @_;

print "Check_for_factor(p = $p, q = $q, z = $z)\n";

for ( $p, $q ) {
    my $temp = $new_rsa - $z;
    my $y    = ( $temp / $_ );

    if ( ( $temp % $_ ) == 0 ) {
        print "\n******* factor found: $_ for $rsa *******\n";
        exit(0);
    }
    elsif ( ( int( $y / 10 ) ) == $new_rsa ) {
        print "\n******* factor found: $_ for $rsa *******\n";
        exit(0);
    }
    else {
        print "factor NOT found: ($new_rsa - $z) / $_ = $y\n";
    }
}
}

# This sub() is used for the rest of the calculations
sub second_calcs {
my ( $y, $z ) = @_;
my $j = $z - $y;
my $k = $j + 180;
my $l = $z + $k;

print "$z - $y = |$j|\n";
print "$j + 180 = $k\n";
print "$k + $z = $l\n";

return ( $k, $l );
}

sub third_calc {
my ( $y, $z ) = @_;

my $k = $y + 180;
my $l = $z + $k;

return ( $k, $l );
}

# /*
#  * This sub() calcs the digit root:
#  * example: $rsa = 12345
#  * 1 + 2 + 3 + 4 + 5 = 15 and 1 + 5 = 6 (digit root)
#  */
sub digit_root {
my $rsa = shift;

$rsa = Math::BigInt->new($rsa);

return ( 1 + ( ( $rsa - 1 ) % 9 ) );
}

Answer 1

我认为您的代码的主要问题（您标记为“此代码将无法编译”的部分）是您在应该使用的地方使用 [方括号]使用括号。在Python中，与数学不同，方括号表示一种非常具体的数据类型，称为列表。您应该用常规括号替换方括号。

print ((int(p) + 90*x_0) * int(q)+ 90*x_0))/90 #example 23 
print ((int(p) + 90*x_1) * (int(q)+90*x_1))/90 #example 215  
z(0) = ((int(p) + 90*x_0) * int(q)+ 90*x_0))/90 
z(1) = ((int(p) + 90*x_1) * (int(q)+90*x_1))/90 

另外，z(n) 会给你带来问题。我不太确定 z(0) 应该以编程方式是什么。然而，除非 z 是一个函数，否则您可能希望 z 是一个 n 元素的列表。在这种情况下，您可以使用 z[1], z[2], ... z[n] 访问这些元素。

这可能并不是一切都错了，但这是一个开始。我建议阅读 python.org 上的 python 教程，并查看 python 代码示例来提高您的能力理解。