xmarks

X marks the spot. A command-line solver for first and second degree equations in x.

Type an equation the way you would write it on paper, get the real solutions.

>>> 5*x - 3 = 2*x + 6
Solved:  x = 3

>>> x**2 - 5*x + 6 = 0
Solved:  x1 = 3, x2 = 2

>>> 2(x - 3) = 4
Solved:  x = 5

No eval(), no algebra libraries: a hand-written recursive descent parser turns the equation into a polynomial and solves it.

---

Quick start

git clone https://github.com/ParallelNode/xmarks.git
cd xmarks
python linear_eq.py

Requires Python 3.8+. Type an equation and press Enter. Type exit to quit.

---

What you can write

You can use	Example
+ - * / ^ ** and parentheses	(x - 1)*(x - 2) = 0
Implicit multiplication	2x + 4 = 0, 2(x - 3) = 4
Division by a number	x/2 = 3
Integer powers, 0 to 100	x**2 - 4*x + 4 = 0
Unary minus	-(3x + 2) = 4, -x^2 = -4

Possible results: one value, two values, No solution, Infinite solutions, No real solutions.

---

Solve many equations from a file

Type file at the prompt, then the path of a text file with one equation per line. Blank lines and lines starting with # are ignored.

equations.txt

# my equations
2x + 4 = 0
x/2 = 3
x**2 + x + 1 = 0

>>> file
filepath>>> equations.txt
2x + 4 = 0  ->  x = -2
x/2 = 3  ->  x = 6
x**2 + x + 1 = 0  ->  No real solutions

A wrong line shows an error and the rest still run.

---

How it works

text  →  tokenizer  →  recursive descent parser  →  polynomial  →  solver
"3x+2=8"   [3, x, +, 2]      expr → term → unary → power → factor     {1: 3, 0: -6}     x = 2

Every polynomial is a dictionary {degree: coefficient}. Everything on the right of the = is moved to the left, then the equation is solved directly (1st degree) or with the discriminant (2nd degree).

---

Errors

Code	Cause	Example
Error0	no =	x + 1
Error1	degree above 2, or division by x	x**3 + x = 0
Error2	invalid character	3x + $ = 4
Error3	more than one =	x + 1 == 0
Error4	variable other than x	y + 1 = 0

---

Limits

• Only the unknown x
• Only real solutions
• Up to degree 2
• Equations are typed at the prompt or read from a file (not passed as command-line arguments)

---

Optional banner

On startup the program can show a colored braille-art banner made by banner_gen.py. It needs:

pip install pillow numpy

and an image named images.jpg next to the scripts (not included). Without them the program works the same and prints a short warning.

banner_gen.py also works on its own:

python banner_gen.py picture.jpg -w 100 --mode combo --color