Discrete Mathematics Computer Algebra System

Main idea

Discrete Computer Algebra System (DM_CAS) - is ETU DM&TI course project, aimed at creating a computer algebra system that is capable of performing the simplest operations on: natural, integer, rational numbers, as well as polynomials. For Natural, Integer, Rational and Polynomial data types own classes have been created, UI written using the ncourses library.
P.S. The program has been tested only on Ubuntu and Debian distributions, so use Linux :)

---

Build from source

1. Building

Install dependencies

sudo apt install build-essential cmake libncurses-dev libgtest-dev

Execute following command in project root directory to build project:

bash ./build.sh

2. Run all tests

cd build && ctest

2. Execute

To exectute builded binary, you need to write following in terminal:

./build/DM_CAS

---

Help

So, you execute the program, now you have a lot of questions. Lets take it in order:

Interface:

• In line with "->" you can write operations, which you want to calculate. In line with "=" you can see calculated result (or "!=" if error occured);
• Also you can save variables with command like: <VAR_NAME> = <VALUE>. You can access the variable by adding the '$' sign before name of variable;
• F3 - to enable/disable autoscroll;
• F4 - by default, all numbers interpreted as Natural, to switch calculation mode you need to press F4 key. So program have only four calculation modes: Natural, Integer, Rational, Polynomial. To use another data type without switch between modes, you need to add suffix: n - for Natural, i - for Integer, r - for Rational, p - for Polynomial;
• F5 and F6 - to scroll help message;
• To scroll in main area you need to use Page Up and Page Down buttons;
• Also you can scroll by results and expressions by pressing Up arrow and Down arrow keys on keyboard.
• To exit from program you need to press Ctrl + C hotkey.
• Examples of writing types:
  • Natural: 1, 0, 2342, 43n;
  • Integer: -1098, 0, 213125, 12i;
  • Rational: -12/13, -15/-13, 23/-5, 5.6, 0.10, 0/5, 23, -5, 90/34r;
  • Polynomial: 1, 5, {5/3^3;1^0} (for polynomial like: (5/3)x^3 + 1), {56^2;1}p.

Available commands

So, you can use operations from this table with given arguments in format like this: [<NAME>_<ARG_TYPES>_<RET_TYPE>] <ARGS>. Alternative names with human-readable names are presented below:

---

Operations

Operation	Compatible types	Example
Increment	Natural, Integer	a ++
Decrement	Natural, Integer	a --
Derivative	Polynomial	{a^k;b^n} '
Addition	All types	a + b
Substraction	All types	a - b
Multiplication	All types (also you can multiply polynomial on rational number)	a * b
Shift	Natural, Integer, Polynomial (mul by x^k)	a << k (k - Natural)
Div	All types	a / b
Mod	Natural, Integer, Polynomial	a % b
Factorial	Natural	a !

---

Functions with one argument

Functions	Compatible types	Example
is_zero	All types	[is_zero] a
abs	Integer, Rational	[abs] a
is_pos	Integer, Rational	[is_pos] a
neg - multiply on -1	Integer, Rational	[neg] a
Nat - try cast to Natural	Integer, Rational	[Nat] a
Int - try cast to Integer	Natural, Rational	[Int] a
Rat - cast to Rational	Natural, Integer	[Rat] a
Pol - cast to Polynomial	Natural, Integer, Rational	[Pol] a
is_int - check for an Integer	Rational, Polynomial	[in_int] a
msc - most significant coefficient	Polynomial	[msc] a
deg - degree of Polynomial	Polynomial	[deg] a
fac	Polynomial	[fac] a
inverse	Rational	[inverse] a
simple_roots	Polynomial	[simple_roots] a

---

Functions with two arguments

Functions	Compatible types	Example
cmp	Natural, Integer, Rational	[cmp] a b
gcd	Natural, Integer, Polynomial	[gcd] a b
lcm	Natural, Integer	[lcm] a b