omath 0.1.1

Math and string utilities built from first principles - no dependencies

omath

A Python library built from first principles for educational purposes.

Philosophy

This library intentionally avoids:

• External dependencies
• Standard library helpers (str.lower(), str.split(), re, collections, itertools)
• Built-in shortcuts

Everything is implemented using only:

• Loops and conditionals
• Lists and dicts
• Strings
• ord() and chr()

Why? To understand how things work at the lowest level. Every function in this library could be a teaching moment.

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Installation

From PyPI

pip install omath

From GitHub

pip install git+https://github.com/OmMishra16/omath.git

From Source

git clone https://github.com/OmMishra16/omath.git
cd omath
pip install -e .

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Quick Start

import omath

# Arithmetic
result = omath.multiply(7, 8)  # 56 (uses repeated addition internally)

# Geometry
area = omath.circle_area(5)  # 78.53975

# Strings
lower = omath.to_lowercase("HELLO")  # "hello" (uses ord/chr, not str.lower)

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API Reference

Arithmetic Module

All arithmetic operations are implemented from first principles:

• multiply() uses repeated addition
• divide() uses repeated subtraction
• power() uses repeated multiplication

add(a, b)

Returns the sum of two numbers.

>>> omath.add(10, 5)
15
>>> omath.add(-3, 7)
4

subtract(a, b)

Returns the difference of two numbers.

>>> omath.subtract(10, 3)
7
>>> omath.subtract(5, 8)
-3

multiply(a, b)

Returns the product of two numbers using repeated addition.

>>> omath.multiply(7, 8)
56
>>> omath.multiply(-4, 5)
-20
>>> omath.multiply(0, 100)
0

How it works internally:

multiply(3, 4) = 3 + 3 + 3 + 3 = 12

divide(a, b)

Returns the integer quotient of a / b using repeated subtraction.

>>> omath.divide(20, 4)
5
>>> omath.divide(17, 5)
3
>>> omath.divide(100, 7)
14
>>> omath.divide(10, 0)
None  # Division by zero returns None

How it works internally:

divide(17, 5):
  17 - 5 = 12 (count: 1)
  12 - 5 = 7  (count: 2)
  7 - 5 = 2   (count: 3)
  2 < 5, stop
  Result: 3

modulo(a, b)

Returns the remainder of a / b.

>>> omath.modulo(17, 5)
2
>>> omath.modulo(100, 7)
2
>>> omath.modulo(10, 0)
None  # Modulo by zero returns None

power(base, exponent)

Returns base raised to exponent (non-negative integers only).

>>> omath.power(2, 10)
1024
>>> omath.power(5, 3)
125
>>> omath.power(7, 0)
1
>>> omath.power(2, -1)
None  # Negative exponents not supported

How it works internally:

power(2, 4) = multiply(multiply(multiply(1, 2), 2), 2), 2)
            = 1 * 2 * 2 * 2 * 2 = 16

absolute(n)

Returns the absolute value of n.

>>> omath.absolute(-42)
42
>>> omath.absolute(42)
42
>>> omath.absolute(0)
0

PI

A constant approximation of pi (3.14159).

>>> omath.PI
3.14159

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Geometry Module

Functions for calculating areas, perimeters, and volumes.

circle_area(radius)

Returns the area of a circle (PI * r^2).

>>> omath.circle_area(5)
78.53975
>>> omath.circle_area(1)
3.14159
>>> omath.circle_area(10)
314.159

circle_circumference(radius)

Returns the circumference of a circle (2 * PI * r).

>>> omath.circle_circumference(5)
31.4159
>>> omath.circle_circumference(1)
6.28318

rectangle_area(width, height)

Returns the area of a rectangle.

>>> omath.rectangle_area(4, 5)
20
>>> omath.rectangle_area(10, 10)
100

rectangle_perimeter(width, height)

Returns the perimeter of a rectangle (2 * (width + height)).

>>> omath.rectangle_perimeter(4, 5)
18
>>> omath.rectangle_perimeter(10, 10)
40

triangle_area(base, height)

Returns the area of a triangle (base * height / 2).

>>> omath.triangle_area(10, 5)
25
>>> omath.triangle_area(8, 6)
24

square_area(side)

Returns the area of a square (side^2).

>>> omath.square_area(5)
25
>>> omath.square_area(12)
144

cube_volume(side)

Returns the volume of a cube (side^3).

>>> omath.cube_volume(3)
27
>>> omath.cube_volume(5)
125

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Strings Module

All string operations are implemented using ord() and chr() — no built-in string methods like str.lower() or str.split().

to_lowercase(s)

Converts a string to lowercase using ASCII math.

>>> omath.to_lowercase("HELLO WORLD")
'hello world'
>>> omath.to_lowercase("PyThOn")
'python'
>>> omath.to_lowercase("123 ABC")
'123 abc'

How it works internally:

'A' = chr(65), 'a' = chr(97)
Difference = 32
So: chr(ord('A') + 32) = 'a'

to_uppercase(s)

Converts a string to uppercase using ASCII math.

>>> omath.to_uppercase("hello world")
'HELLO WORLD'
>>> omath.to_uppercase("PyThOn")
'PYTHON'

split_by_char(s, delimiter)

Splits a string by a delimiter character.

>>> omath.split_by_char("a,b,c,d", ",")
['a', 'b', 'c', 'd']
>>> omath.split_by_char("hello world", " ")
['hello', 'world']
>>> omath.split_by_char("one-two-three", "-")
['one', 'two', 'three']

strip_whitespace(s)

Removes leading and trailing whitespace (spaces, tabs, newlines).

>>> omath.strip_whitespace("  hello  ")
'hello'
>>> omath.strip_whitespace("\t\n  text  \n\t")
'text'
>>> omath.strip_whitespace("no_whitespace")
'no_whitespace'

contains(haystack, needle)

Checks if needle exists in haystack.

>>> omath.contains("hello world", "world")
True
>>> omath.contains("hello world", "xyz")
False
>>> omath.contains("abcdef", "cde")
True
>>> omath.contains("short", "very long string")
False

reverse_string(s)

Reverses a string.

>>> omath.reverse_string("hello")
'olleh'
>>> omath.reverse_string("Python")
'nohtyP'
>>> omath.reverse_string("12345")
'54321'

is_palindrome(s)

Checks if a string is a palindrome (ignores case and non-letter characters).

>>> omath.is_palindrome("racecar")
True
>>> omath.is_palindrome("A man a plan a canal Panama")
True
>>> omath.is_palindrome("hello")
False
>>> omath.is_palindrome("Was it a car or a cat I saw")
True

char_count(s)

Counts occurrences of each character in a string.

>>> omath.char_count("hello")
{'h': 1, 'e': 1, 'l': 2, 'o': 1}
>>> omath.char_count("aaa")
{'a': 3}
>>> omath.char_count("abab")
{'a': 2, 'b': 2}

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Submodule Access

You can also import submodules directly:

# Import specific module
from omath import arithmetic
from omath import geometry
from omath import strings

# Use functions
arithmetic.multiply(5, 5)
geometry.circle_area(10)
strings.reverse_string("test")

Or import specific functions:

from omath import add, multiply, power
from omath import circle_area, rectangle_area
from omath import to_lowercase, is_palindrome

result = multiply(add(2, 3), power(2, 3))  # (2+3) * 2^3 = 40

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Educational Value

This library is designed to help you understand:

1. How multiplication works — It's just repeated addition
2. How division works — It's just repeated subtraction
3. How string methods work — ASCII codes and character manipulation
4. How Python packages work — Module structure, __init__.py, imports

Example: Understanding to_lowercase()

Instead of using str.lower(), we use ASCII math:

def to_lowercase(s):
    result = ''
    for char in s:
        code = ord(char)
        # A-Z are 65-90, a-z are 97-122
        # Difference is 32
        if 65 <= code <= 90:
            result = result + chr(code + 32)
        else:
            result = result + char
    return result

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Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

1. Fork the repository
2. Create your feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add some amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

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License

This project is licensed under the MIT License - see the LICENSE file for details.

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Author

Om Mishra - GitHub