This question has kind of motivated me to try and write something worthwhile. I am making some progress but am not quite there. Still I think I have enough to give an idea where I'm heading

I have posted the output to where im at currently, as getting namespaces and actually trying to figure out how the data types are going to go is well, some fun

More than just solving the OP logic problem, the intention is perhaps more to write something that can be used as support for educational purposes. It is understandable that much of this has already been implemented in many math modules already. However, I maybe just entertaining my own sentiments, but there is something refreshing about getting down to the atomic structure of numbers. And just simply seeing the arithmetic in action. And any excuse to use Perl, for which I think this purpose is suited, is a good excuse.

Hopefully I'll get the logic side of the OP shortly. Fifty quid on it. I did however figure out that I may not have supposed to have been getting negative denominators when row reducing. I guess thats what happens when you take the inverse of a negative fraction by turning it upside down. :p

This looks like a problem that could be dealt with using prime factorisation. But, to get a prime factorisation you need to check the possible combinations of a sum.

tentatively, problem restated: Given a number A, and a List B consisting of one or more numbers, which numbers from B:

• are divisors of A
• can be summed to any divisor of A
• are divisors of any other number in B
• can be summed to any divisor of any other number from B

• are divisors of A
• can be summed to any divisor of A
• are divisors of any other number in B that is a divisor of A
• can be summed with any other number in B to A or any B That is a Divisor of A.

When all numbers in B satisfy (some or all?) of these conditions, supply the multiplicities of the numbers required for firstly the summations up to the divisors of both A and B, and secondly any reaminders of numbers that are not divisors but are used in the summation composition.

note: restatement subject to re-interpretation using more appropriate terminology where required. That is, I may mean factor where I have stated divisor. I may mean composite summation. Also to be clarified - where remainders that are not divisors are used in the summation.

Before moving on to a List of multiple numbers, understanding how the failing case works is probably key. With A being 3 and a B being a List or Set from 2.

• A: Prim Nat '|||' (3)
• B: List(2)

where B contains only 1 item, B could be construed as a List or a Set. Right now, I am (attempting to be) keeping it simple as an argument list.

Plan of action, is to match A with B. A is a number, B is a List. done. Ok, Let us use b to mean the number in the List.

Plan of action, is to match A with b. Failure is a result of either

• b not being a divisor of A
• any multiple of b not being a divisor of A

getting there, I can now 'split' rather, substitute and count the substitutions, so to say, and test for a remainder, which is half the problem.

output as it stands

TOP
my @vn;
my $m;
for my $n ( 2, 3, 5, 7, 15, 43 ){

    $m = num_to_nat($n);
    push @vn, get_mark_from_nat($m) ;
};

print join "\t", @vn;
print "\n",
# print  map { join( ' ', $_, '(' . wildmark_to_num($_) . ')' ) } @vn;
#print "\n";

my @hexvn;
#                                  ______
@hexvn = map [ $_, sprintf( "%0x", length($_) ), 'my todo hex()', tran
+sform_to_hex($_), "\n" ], @vn;

print  map { my $arr = $_ ; join "\t", map{ join ' ', $_ } @$arr } @he
+xvn;
print "\n";

OUTPUT
||      |||     |||||   ||||||| ||||||||||||||| ||||||||||||||||||||||
+|||||||||||||||||||||

testing prim nat: ||
split_pat: (?^u:(\|\|))
splitted: 1 x || h remainder:
prim nat was ||
prim nat now


testing prim nat: |||
split_pat: (?^u:(\|\|))
splitted: 1 x || h remainder: |
prim nat was |||
prim nat now |


testing prim nat: |||||
split_pat: (?^u:(\|\|))
splitted: 2 x || h remainder: |
prim nat was |||||
prim nat now |


testing prim nat: |||||||
split_pat: (?^u:(\|\|))
splitted: 3 x || h remainder: |
prim nat was |||||||
prim nat now |


testing prim nat: |||||||||||||||
split_pat: (?^u:(\|\|))
splitted: 7 x || h remainder: |
prim nat was |||||||||||||||
prim nat now |


testing prim nat: |||||||||||||||||||||||||||||||||||||||||||
split_pat: (?^u:(\|\|))
splitted: 21 x || h remainder: |
prim nat was |||||||||||||||||||||||||||||||||||||||||||
prim nat now |

||      2       my todo hex()   1 x ||  remainder:
|||     3       my todo hex()   1 x ||  remainder: |
|||||   5       my todo hex()   2 x ||  remainder: |
||||||| 7       my todo hex()   3 x ||  remainder: |
||||||||||||||| f       my todo hex()   7 x ||  remainder: |
|||||||||||||||||||||||||||||||||||||||||||     2b      my todo hex() 
+  21 x || remainder: |

Press any key to continue . . .
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progress report Re: check possible combination of sum using given array. out by 5168!