https://github.com/petru-braha/algebraic-structures

Visualisation of the concepts learned in algebra
https://github.com/petru-braha/algebraic-structures

Last synced: about 2 months ago
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Visualisation of the concepts learned in algebra

• Host: GitHub
• URL: https://github.com/petru-braha/algebraic-structures
• Owner: petru-braha
• Created: 2024-06-19T12:46:46.000Z (8 months ago)
• Default Branch: master
• Last Pushed: 2024-07-22T07:58:15.000Z (7 months ago)
• Last Synced: 2024-07-22T09:28:10.723Z (7 months ago)
• Language: C++
• Homepage:
• Size: 48.7 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: readMe.md

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README

        
# Algebra

## TO DO / actual strategy:

- i have doubts about the implementation of the numbers. i will now focus only on sets

- after implementing sets, i will focus on building the second version of my numbers

### Purpose:

- finite sets: check subsets and properties

- infinite structures: check properties, find formula

- finite structures: the most important (Zn, Fn)

- types of structures: semi-groups, monoids, groups, rings, division rings, integral domain, fields, vector spaces

- computations: multiplying values / is the result in the structure

- commutativity

- check if it is closed

- check if it is a subgroup / field

### Implementation:

- it is not that important to be stingy about the memory (taking into account this article: https://www.quora.com/What-is-the-practical-use-for-large-numbers-with-an-extremely-high-amount-of-digits-millions)

- extend the number to a maximum capacity of 3GB, where a single digit takes up 1B.

- limit the maximum number of bytes taking into account, how many RAM GB is free.

- good practice! reduce before any operation the fractions

- a primitive float will be represented just with 2 decimals, arbitrary decision

### future development: 

- expression classes, polynomials: vector < [complex_number constant, new type x, int integer] > 

- vector spaces

### what i would do different if i will start a similar project again (version 2):

- i will implement the numbers as an array of digits and not list! in this current vision i ran into 2 problems

	- O(n) - access time of a bit instead of linear. this evolves into O(n^2) - addition between two numbers (not great)

	- the original plan was to build a large number depending on the available space. i wished to maximize the information of a number in small quantities.

	- let's consider the following number: 10

		- can be represented in 4 bytes, as a int

		- can be represented in 2 bytes, as a array of char

		- natural numbers class: total cost of my implementation : 16(first digit node) + 16(second digit node) + 8(the variable "bytes" - unsigned long long int) + 8(vfptr - the virtual table) = 48 bytes == 12 * sizeof((int)10).

	

	- *UPDATE*: i found a better choice!: array of unsigned long long int values (check "version 2.md").