I had idea in Mind, idea about storing numbers in computer memory in form of numerator and denominator / pl: 'licznik i mianownik' /, in an attempt to simplify precise calculations.
I wrote some code to factor numbers, to find prime factors of a number / pl: 'rozkład liczby na czynniki pierwsze' /.
But this code does more than just determining if number is prime, and if not - finding prime factors of this number. It stores paths and partial calculations, it gives not only one solution, but all of possible solutions, that perhaps can be used and reused in creative ways.
Then I had another idea - what if numbers were stored in such form, in form of factorization tree. Perhaps adding trees, or other operations on factorization trees would allow for some swift, abstract calculations.
Then I remembered Geometry with Linear Algbera, and neutral elements of operations on structures such as Groups, Rings and Fields / pl: 'Grupy, Pierścienie i Ciała' /.
What kind of FactorizationTree would be a neutral element of FactorizationTrees' Addition?
How about Multiplying FactorizationTrees?
I'll admit that most of this is just musings and considerings, I admit that I let my imagination run wild this time.
This blog has a place for ideas exploration, after all.
I might need to research following topics:
- Abstract Algebra,
- Group Theory,
- Ring Theory,
- Field Theory,
- Inverse element / pl: 'element odwrotny' /,
- Binary operation / pl: 'działanie binarne' /,
- Homomorphism / pl: 'homomorfizm' /,
- Isomorphism / pl: 'izomorfizm' /.
/ TO BE CONTINUED, HOPEFULLY. /
